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Gelin MF, Chen L, Domcke W. Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals. Chem Rev 2022; 122:17339-17396. [PMID: 36278801 DOI: 10.1021/acs.chemrev.2c00329] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.
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Affiliation(s)
- Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching,Germany
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2
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Wang G, Liu YX, Zhu Y, Cappellaro P. Nanoscale Vector AC Magnetometry with a Single Nitrogen-Vacancy Center in Diamond. NANO LETTERS 2021; 21:5143-5150. [PMID: 34086471 DOI: 10.1021/acs.nanolett.1c01165] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Detection of AC magnetic fields at the nanoscale is critical in applications ranging from fundamental physics to materials science. Isolated quantum spin defects, such as the nitrogen-vacancy center in diamond, can achieve the desired spatial resolution with high sensitivity. Still, vector AC magnetometry currently relies on using different orientations of an ensemble of sensors, with degraded spatial resolution, and a protocol based on a single NV is lacking. Here we propose and experimentally demonstrate a protocol that exploits a single NV to reconstruct the vectorial components of an AC magnetic field by tuning a continuous driving to distinct resonance conditions. We map the spatial distribution of an AC field generated by a copper wire on the surface of the diamond. The proposed protocol combines high sensitivity, broad dynamic range, and sensitivity to both coherent and stochastic signals, with broad applications in condensed matter physics, such as probing spin fluctuations.
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Affiliation(s)
- Guoqing Wang
- Research Laboratory of Electronics and Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Yi-Xiang Liu
- Research Laboratory of Electronics and Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Yuan Zhu
- Research Laboratory of Electronics and Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Paola Cappellaro
- Research Laboratory of Electronics and Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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3
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Dann R, Kosloff R, Salamon P. Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1255. [PMID: 33287023 PMCID: PMC7712823 DOI: 10.3390/e22111255] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/06/2020] [Revised: 10/29/2020] [Accepted: 11/01/2020] [Indexed: 02/01/2023]
Abstract
Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production.
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Affiliation(s)
- Roie Dann
- The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel;
| | - Ronnie Kosloff
- The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel;
| | - Peter Salamon
- Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-7720, USA;
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4
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Engelhardt G, Platero G, Cao J. Discontinuities in Driven Spin-Boson Systems due to Coherent Destruction of Tunneling: Breakdown of the Floquet-Gibbs Distribution. PHYSICAL REVIEW LETTERS 2019; 123:120602. [PMID: 31633942 DOI: 10.1103/physrevlett.123.120602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Indexed: 06/10/2023]
Abstract
If an open quantum system is periodically driven with high frequency and the driving commutes with the system-bath coupling operator, it is known that the system approaches a Floquet-Gibbs state, a generalization of Gibbs states to periodically driven systems. Here, we investigate the stationary state of an ac-driven system when the driving and dissipation are noncommutative. Then, the resulting stationary state does not obey the Floquet-Gibbs distribution, and the system dynamics is determined by inelastic scattering processes of the driving field. Based on the Floquet-Redfield formalism, we show that the probability distribution can exhibit population inversion and discontinuities, i.e., jumps, for parameters at which coherent destruction of tunneling takes place. These discontinuities can be observed as intensity jumps in the emission into the bath.
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Affiliation(s)
- Georg Engelhardt
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
| | - Gloria Platero
- Instituto de Ciencia de Materiales de Madrid, CSIC, 28049 Madrid, Spain
| | - Jianshu Cao
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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5
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Abstract
A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented. The theory of open quantum systems is employed to define system bath partitions. The Markovian master equation defines an isothermal partition between the system and bath. Two methods to derive the quantum master equation are described: the weak coupling limit and the repeated collision model. The role of the eigenoperators of the free system dynamics is highlighted, in particular, for driven systems. The thermodynamical relations are pointed out. Models that lead to loss of coherence, i.e., dephasing are described. The implication of the laws of thermodynamics to simulating transport and spectroscopy is described. The indications for self-averaging in large quantum systems and thus its importance in modeling are described. Basic modeling by the surrogate Hamiltonian is described, as well as thermal boundary conditions using the repeated collision model and their use in the stochastic surrogate Hamiltonian. The problem of modeling with explicitly time dependent driving is analyzed. Finally, the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.
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Affiliation(s)
- Ronnie Kosloff
- The Institute of Chemistry and The Fritz Haber Centre for Theoretical Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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6
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Introduction to Quantum Thermodynamics: History and Prospects. FUNDAMENTAL THEORIES OF PHYSICS 2018. [DOI: 10.1007/978-3-319-99046-0_1] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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7
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Wang J, Lai Y, Ye Z, He J, Ma Y, Liao Q. Four-level refrigerator driven by photons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:050102. [PMID: 26066099 DOI: 10.1103/physreve.91.050102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2015] [Indexed: 06/04/2023]
Abstract
We propose a quantum absorption refrigerator driven by photons. The model uses a four-level system as its working substance and couples simultaneously to hot, cold, and solar heat reservoirs. Explicit expressions for the cooling power Q̇(c) and coefficient of performance (COP) η(COP) are derived, with the purpose of revealing and optimizing the performance of the device. Our model runs most efficiently under the tight coupling condition, and it is consistent with the third law of thermodynamics in the limit T→0.
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Affiliation(s)
- Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Yiming Lai
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Zhuolin Ye
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Jizhou He
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Yongli Ma
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Qinghong Liao
- Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China
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8
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Abstract
Quantum thermodynamics supplies a consistent description of quantum heat engines and refrigerators up to a single few-level system coupled to the environment. Once the environment is split into three (a hot, cold, and work reservoir), a heat engine can operate. The device converts the positive gain into power, with the gain obtained from population inversion between the components of the device. Reversing the operation transforms the device into a quantum refrigerator. The quantum tricycle, a device connected by three external leads to three heat reservoirs, is used as a template for engines and refrigerators. The equation of motion for the heat currents and power can be derived from first principles. Only a global description of the coupling of the device to the reservoirs is consistent with the first and second laws of thermodynamics. Optimization of the devices leads to a balanced set of parameters in which the couplings to the three reservoirs are of the same order and the external driving field is in resonance. When analyzing refrigerators, one needs to devote special attention to a dynamical version of the third law of thermodynamics. Bounds on the rate of cooling when Tc→0 are obtained by optimizing the cooling current. All refrigerators as Tc→0 show universal behavior. The dynamical version of the third law imposes restrictions on the scaling as Tc→0 of the relaxation rate γc and heat capacity cV of the cold bath.
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Affiliation(s)
- Ronnie Kosloff
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel;
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9
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Yuan Y, Wang R, He J, Ma Y, Wang J. Coefficient of performance under maximum χ criterion in a two-level atomic system as a refrigerator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052151. [PMID: 25493783 DOI: 10.1103/physreve.90.052151] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2014] [Indexed: 06/04/2023]
Abstract
A two-level atomic system as a working substance is used to set up a refrigerator consisting of two quantum adiabatic and two isochoric processes (two constant-frequency processes ω_{a} and ω_{b} with ω_{a}<ω_{b}), during which the two-level system is in contact with two heat reservoirs at temperatures T_{h} and T_{c}(<T_{h}). Considering finite-time operation of two isochoric processes, we derive analytical expressions for cooling rate R and coefficient of performance (COP) ɛ. The COP at maximum χ(=ɛR) figure of merit is numerically determined, and it is proved to be in nice agreement with the so-called Curzon and Ahlborn COP ɛ_{CA}=sqrt[1+ɛ_{C}]-1, where ɛ_{C}=T_{c}/(T_{h}-T_{c}) is the Carnot COP. In the high-temperature limit, the COP at maximum χ figure of merit, ɛ^{*}, can be expressed analytically by ɛ^{*}=ɛ_{+}≡(sqrt[9+8ɛ_{C}]-3)/2, which was derived previously as the upper bound of optimal COP for the low-dissipation or minimally nonlinear irreversible refrigerators. Within the context of irreversible thermodynamics, we prove that the value of ɛ_{+} is also the upper bound of COP at maximum χ figure of merit when we regard our model as a linear irreversible refrigerator.
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Affiliation(s)
- Yuan Yuan
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Rui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Jizhou He
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Yongli Ma
- State Key Laboratory of Surface Physics and Department of Physics, Shanghai 200433, China
| | - Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China and State Key Laboratory of Surface Physics and Department of Physics, Shanghai 200433, China
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10
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Liu F. Calculating work in adiabatic two-level quantum Markovian master equations: a characteristic function method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032121. [PMID: 25314409 DOI: 10.1103/physreve.90.032121] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2014] [Indexed: 06/04/2023]
Abstract
We present a characteristic function method to calculate the probability density functions of the inclusive work in adiabatic two-level quantum Markovian master equations. These systems are steered by some slowly varying parameters and the dissipations may depend on time. Our theory is based on the interpretation of the quantum jump for the master equations. In addition to the calculation, we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions, which is exactly the same as in the case of isolated systems. A periodically driven two-level model is used to demonstrate the method.
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Affiliation(s)
- Fei Liu
- School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
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11
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Peñate-Rodríguez HC, Dorta-Urra A, Bargueño P, Rojas-Lorenzo G, Miret-Artés S. A Langevin Canonical Approach to the Dynamics of Chiral Systems: Thermal Averages and Heat Capacity. Chirality 2014; 26:319-25. [DOI: 10.1002/chir.22326] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2013] [Accepted: 03/03/2014] [Indexed: 01/06/2023]
Affiliation(s)
- Helen C. Peñate-Rodríguez
- Instituto Superior de Tecnologías y Ciencias Aplicadas; La Habana Cuba
- Instituto de Física Fundamental (CSIC); Madrid Spain
| | - Anais Dorta-Urra
- Unidad asociada UAM-CSIC, Instituto de Física Fundamental (CSIC); Madrid Spain
| | - Pedro Bargueño
- Departamento de Física; Universidad de los Andes; Bogotá Distrito Capital Colombia
| | - German Rojas-Lorenzo
- Instituto Superior de Tecnologías y Ciencias Aplicadas; La Habana Cuba
- Instituto de Física Fundamental (CSIC); Madrid Spain
| | - Salvador Miret-Artés
- Departamento de Física; Universidad de los Andes; Bogotá Distrito Capital Colombia
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12
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Liu F. Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042122. [PMID: 24827208 DOI: 10.1103/physreve.89.042122] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2014] [Indexed: 06/03/2023]
Abstract
We present two kinds of Bochkov-Kuzovlev work equalities in a two-level system that is described by a quantum Markovian master equation. One is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint. We show that these two equalities are indeed equivalent. Importantly, this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function. We use a numerical model to verify these results.
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Affiliation(s)
- Fei Liu
- School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
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13
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Yan F, Gustavsson S, Bylander J, Jin X, Yoshihara F, Cory DG, Nakamura Y, Orlando TP, Oliver WD. Rotating-frame relaxation as a noise spectrum analyser of a superconducting qubit undergoing driven evolution. Nat Commun 2013; 4:2337. [DOI: 10.1038/ncomms3337] [Citation(s) in RCA: 80] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2013] [Accepted: 07/23/2013] [Indexed: 11/09/2022] Open
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14
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15
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Alicki R, Fannes M. Entanglement boost for extractable work from ensembles of quantum batteries. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042123. [PMID: 23679388 DOI: 10.1103/physreve.87.042123] [Citation(s) in RCA: 107] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Indexed: 05/28/2023]
Abstract
Motivated by the recent interest in thermodynamics of micro- and mesoscopic quantum systems we study the maximal amount of work that can be reversibly extracted from a quantum system used to temporarily store energy. Guided by the notion of passivity of a quantum state we show that entangling unitary controls extract in general more work than independent ones. In the limit of a large number of copies one can reach the thermodynamical bound given by the variational principle for the free energy.
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Affiliation(s)
- Robert Alicki
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Poland.
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16
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Szczygielski K, Gelbwaser-Klimovsky D, Alicki R. Markovian master equation and thermodynamics of a two-level system in a strong laser field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012120. [PMID: 23410296 DOI: 10.1103/physreve.87.012120] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2012] [Indexed: 06/01/2023]
Abstract
The recently developed technique combining the weak-coupling limit with the Floquet formalism is applied to a model of a two-level atom driven by a strong laser field and weakly coupled to heat baths. First, the case of a single electromagnetic bath at zero temperature is discussed and the formula for resonance fluorescence is derived. The expression describes the well-known Mollow triplet, but its details differ from the standard ones based on additional simplifying assumptions. The second example describes the case of two thermal reservoirs: an electromagnetic one at finite temperature and the second dephasing one, which can be realized as a phononic or buffer gas reservoir. It is shown using the developed thermodynamical approach that the latter system can work in two regimes depending on the detuning sign: a heat pump transporting heat from the dephasing reservoir to an electromagnetic bath or heating both, always at the expense of work supplied by the laser field.
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17
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Wang J, He J. Efficiency at maximum power output of an irreversible Carnot-like cycle with internally dissipative friction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:051112. [PMID: 23214743 DOI: 10.1103/physreve.86.051112] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2012] [Revised: 10/11/2012] [Indexed: 06/01/2023]
Abstract
We investigate the efficiency at the maximum power output (EMP) of an irreversible Carnot engine performing finite-time cycles between two reservoirs at constant temperatures T(h) and T(c) (<T(h)), taking into account the internally dissipative friction in two "adiabatic" processes. The EMP is retrieved to be situated between η(C)/2 and η(C)/(2-η(C)), with η(C) = 1-T(c)/T(h) being the Carnot efficiency, whether the internally dissipative friction is considered or not. When dissipations of two "isothermal" and two "adiabatic" processes are symmetric, respectively, and the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation, the Curzon-Ahlborn (CA) efficiency η(CA) = 1-sqrt[T(c)/T(h)] is derived.
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Affiliation(s)
- Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China.
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18
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Wang R, Wang J, He J, Ma Y. Performance of a multilevel quantum heat engine of an ideal N-particle Fermi system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:021133. [PMID: 23005748 DOI: 10.1103/physreve.86.021133] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2012] [Revised: 07/14/2012] [Indexed: 06/01/2023]
Abstract
We generalize the quantum heat engine (QHE) model which was first proposed by Bender et al. [J. Phys. A 33, 4427 (2000)] to the case in which an ideal Fermi gas with an arbitrary number N of particles in a box trap is used as the working substance. Besides two quantum adiabatic processes, the engine model contains two isoenergetic processes, during which the particles are coupled to energy baths at a high constant energy E(h) and a low constant energy E(c), respectively. Directly employing the finite-time thermodynamics, we find that the power output is enhanced by increasing particle number N (or decreasing minimum trap size L(A)) for given L(A) (or N), without reduction in the efficiency. By use of global optimization, the efficiency at possible maximum power output (EPMP) is found to be universal and independent of any parameter contained in the engine model. For an engine model with any particle-number N, the efficiency at maximum power output (EMP) can be determined under the condition that it should be closest to the EPMP. Moreover, we extend the heat engine to a more general multilevel engine model with an arbitrary 1D power-law potential. Comparison between our engine model and the Carnot cycle shows that, under the same conditions, the efficiency η = 1 - E(c)/E(h) of the engine cycle is bounded from above the Carnot value η(c) =1 - T(c)/T(h).
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Affiliation(s)
- Rui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China
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19
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Wang J, He J, Wu Z. Efficiency at maximum power output of quantum heat engines under finite-time operation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031145. [PMID: 22587076 DOI: 10.1103/physreve.85.031145] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2011] [Revised: 03/12/2012] [Indexed: 05/31/2023]
Abstract
We study the efficiency at maximum power, η(m), of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures T(h) and T(c), respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), η(m) becomes identical to the Carnot efficiency η(C)=1-T(c)/T(h). For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency η(m) at maximum power output is bounded from above by η(C)/(2-η(C)) and from below by η(C)/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency η(CA)=1-√(T(c)/T(h)) is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
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Affiliation(s)
- Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China.
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20
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Baiz CR, Kubarych KJ, Geva E. Molecular theory and simulation of coherence transfer in metal carbonyls and its signature on multidimensional infrared spectra. J Phys Chem B 2011; 115:5322-39. [PMID: 21375310 DOI: 10.1021/jp109357d] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
We present a general and comprehensive theoretical and computational framework for modeling ultrafast multidimensional infrared spectra of a vibrational excitonic system in liquid solution. Within this framework, we describe the dynamics of the system in terms of a quantum master equation that can account for population relaxation, dephasing, coherence-to-coherence transfer, and coherence-to-population transfer. A unique feature of our approach is that, in principle, it does not rely on any adjustable fitting parameters. More specifically, the anharmonic vibrational Hamiltonian is derived from ab initio electronic structure theory, and the system-bath coupling is expressed explicitly in terms of liquid degrees of freedom whose dynamics can be obtained via molecular dynamics simulations. The applicability of the new approach is demonstrated by employing it to model the recently observed signatures of coherence transfer in the two-dimensional spectra of dimanganese decacarbonyl in liquid cyclohexane. The results agree well with experiment and shed new light on the nature of the molecular interactions and dynamics underlying the spectra and the interplay between dark and bright states, their level of degeneracy, and the nature of their interactions with the solvent.
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Affiliation(s)
- Carlos R Baiz
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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21
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Gelin MF, Egorova D, Domcke W. Manipulating electronic couplings and nonadiabatic nuclear dynamics with strong laser pulses. J Chem Phys 2009; 131:124505. [DOI: 10.1063/1.3236577] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Shi Q, Geva E. A self-consistent treatment of electron transfer in the limit of strong friction via the mixed quantum classical Liouville method. J Chem Phys 2009; 131:034511. [DOI: 10.1063/1.3176509] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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23
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Dobrovitski VV, Feiguin AE, Hanson R, Awschalom DD. Decay of Rabi oscillations by dipolar-coupled dynamical spin environments. PHYSICAL REVIEW LETTERS 2009; 102:237601. [PMID: 19658973 DOI: 10.1103/physrevlett.102.237601] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2009] [Indexed: 05/28/2023]
Abstract
We study the Rabi oscillations decay of a spin decohered by a spin bath whose internal dynamics is caused by dipolar coupling between the bath spins. The form and rate of decay as a function of the intrabath coupling is obtained analytically, and confirmed numerically. The complex form of decay smoothly varies from power law to exponential, and the rate changes nonmonotonically with the intrabath coupling, decreasing for both slow and fast baths. The form and rate of Rabi oscillations decay can be used to experimentally determine the intrabath coupling strength for a broad class of solid-state systems.
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Affiliation(s)
- V V Dobrovitski
- Ames Laboratory U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
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Egorova D, Gelin MF, Thoss M, Wang H, Domcke W. Effects of intense femtosecond pumping on ultrafast electronic-vibrational dynamics in molecular systems with relaxation. J Chem Phys 2008; 129:214303. [DOI: 10.1063/1.3026509] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
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25
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Nest M, Kosloff R. Quantum dynamical treatment of inelastic scattering of atoms at a surface at finite temperature: the random phase thermal wave function approach. J Chem Phys 2007; 127:134711. [PMID: 17919047 DOI: 10.1063/1.2786088] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
We present quantum dynamical calculations for the inelastic scattering of atoms at a nonrigid surface at finite temperature. The surface degrees of freedom are discretized and treated in a multiconfigurational wave function picture. The thermal averaging is carried out with the random phase thermal wave function approach. We show that it is sufficient to restrict the random phases to the intermediate basis of single particle functions, discuss the convergence of the method with the number of configurations and realizations, and analyze the flow of energy between different parts of the system for a range of temperatures between 4 and 500 K.
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Affiliation(s)
- M Nest
- Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Str. 25, 14476 Potsdam, Germany.
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26
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Kleinekathöfer U. Non-Markovian theories based on a decomposition of the spectral density. J Chem Phys 2006; 121:2505-14. [PMID: 15281847 DOI: 10.1063/1.1770619] [Citation(s) in RCA: 108] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
For the description of dynamical effects in quantum mechanical systems on ultrashort time scales, memory effects play an important role. Meier and Tannor [J. Chem. Phys. 111, 3365 (1999)] developed an approach which is based on a time-nonlocal scheme employing a numerical decomposition of the spectral density. Here we propose two different approaches which are based on a partial time-ordering prescription, i.e., a time-local formalism and also on a numerical decomposition of the spectral density. In special cases such as the Debye spectral density the present scheme can be employed even without the numerical decomposition of the spectral density. One of the proposed schemes is valid for time-independent Hamiltonians and can be given in a compact quantum master equation. In the case of time-dependent Hamiltonians one has to introduce auxiliary operators which have to be propagated in time along with the density matrix. For the example of a damped harmonic oscillator these non-Markovian theories are compared among each other, to the Markovian limit neglecting memory effects and time dependencies, and to exact path integral calculations. Good agreement between the exact calculations and the non-Markovian results is obtained. Some of the non-Markovian theories mentioned above treat the time dependence in the system Hamiltonians nonperturbatively. Therefore these methods can be used for the simulation of experiments with arbitrary large laser fields.
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Gopalakrishnan K, Bodenhausen G. Lifetimes of the singlet-states under coherent off-resonance irradiation in NMR spectroscopy. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2006; 182:254-9. [PMID: 16875857 DOI: 10.1016/j.jmr.2006.07.001] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2006] [Revised: 07/03/2006] [Accepted: 07/06/2006] [Indexed: 05/11/2023]
Abstract
Singlet-states |S=(|alphabeta> - |betaalpha>)/sq.rt.2 can be excited in pairs of coupled spins I and S, first by preparing either a non-vanishing zero-quantum coherence I(+)S(-) or a state of longitudinal two-spin order I(z)S(z) and then by applying a coherent radio-frequency (RF) irradiation with a carrier frequency omega(rf) = (Omega(I) + Omega(S))/2 that lies half-way between the chemical shifts of the two spins involved. The life-times T(S) can be much longer than the spin-lattice relaxation time T(1) of longitudinal magnetization, but singlet-states are ultimately relaxed, not only by dipolar interactions between the active spins or with the external spins, but also as a result of a non-vanishing offset Deltaomega = omega(rf) - (Omega(I) + Omega(S))/2 or an insufficient amplitude of the RF irradiation that fails to fulfill the condition omega(1) >> DeltaOmega = (Omega(I) - Omega(S)). In this work, the effect of off-resonance irradiation is explored and an approximate formula for the effective relaxation rate of the singlet population is provided on the basis of perturbation theory. The qualitative features of the dependence of the relaxation rate of the singlet population on the offset Deltaomega and on the difference DeltaOmega of the chemical shifts of the two spins are illustrated by comparison with numerical simulations.
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Affiliation(s)
- Karthik Gopalakrishnan
- Laboratoire de Résonance Magnétique Biomoléculaire, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, BCH, CH-1015 Lausanne, Switzerland
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28
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Zhang ML, Ka BJ, Geva E. Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation. J Chem Phys 2006; 125:44106. [PMID: 16942133 DOI: 10.1063/1.2218342] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics, and the inhomogeneous term accounts for initial system-bath correlations. In this paper, we propose a new approach for calculating the memory kernel and inhomogeneous term for arbitrary initial state and system-bath coupling. The memory kernel and inhomogeneous term are obtained by numerically solving a single inhomogeneous Volterra equation of the second kind for each. The new approach can accommodate a very wide range of projection operators, and requires projection-free two-time correlation functions as input. An application to the case of a two-state system with diagonal coupling to an arbitrary bath is described in detail. Finally, the utility and self-consistency of the formalism are demonstrated by an explicit calculation on a spin-boson model.
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Affiliation(s)
- Ming-Liang Zhang
- Department of Chemistry and FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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29
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Wu F, Chen L, Wu S, Sun F, Wu C. Performance of an irreversible quantum Carnot engine with spin 1∕2. J Chem Phys 2006; 124:214702. [PMID: 16774426 DOI: 10.1063/1.2200693] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The purpose of this paper is to investigate the effect of quantum properties of the working medium on the performance of an irreversible Carnot cycle with spin 12. The optimal relationship between the dimensionless power output P* versus the efficiency eta for the irreversible quantum Carnot engine with heat leakage and other irreversible losses is derived. Especially, the performances of the engine at low temperature limit and at high temperature limit are discussed.
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Affiliation(s)
- Feng Wu
- Postgraduate School, Naval University of Engineering, Wuhan 430033, People's Republic of China
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30
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Plakhotnik T. Optical Bloch equations and enhanced decay of Rabi oscillations in strong driving fields. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.08.027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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31
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Welack S, Schreiber M, Kleinekathöfer U. The influence of ultrafast laser pulses on electron transfer in molecular wires studied by a non-Markovian density-matrix approach. J Chem Phys 2006; 124:044712. [PMID: 16460205 DOI: 10.1063/1.2162537] [Citation(s) in RCA: 120] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
New features of molecular wires can be observed when they are irradiated by laser fields. These effects can be achieved by periodically oscillating fields but also by short laser pulses. The theoretical foundation used for these investigations is a density-matrix formalism where the full system is partitioned into a relevant part and a thermal fermionic bath. The derivation of a quantum master equation, either based on a time-convolutionless or time-convolution projection-operator approach, incorporates the interaction with time-dependent laser fields nonperturbatively and is valid at low temperatures for weak system-bath coupling. From the population dynamics the electrical current through the molecular wire is determined. This theory including further extensions is used for the determination of electron transport through molecular wires. As examples, we show computations of coherent destruction of tunneling in asymmetric periodically driven quantum systems, alternating currents and the suppression of the directed current by using a short laser pulse.
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Affiliation(s)
- Sven Welack
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany.
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32
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Shi Q, Geva E. A semiclassical generalized quantum master equation for an arbitrary system-bath coupling. J Chem Phys 2004; 120:10647-58. [PMID: 15268091 DOI: 10.1063/1.1738109] [Citation(s) in RCA: 83] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The Nakajima-Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC-GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard-Jones atoms.
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Affiliation(s)
- Qiang Shi
- Department of Chemistry and the FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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35
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Xu R, Yan Y, Ohtsuki Y, Fujimura Y, Rabitz H. Optimal control of quantum non-Markovian dissipation: Reduced Liouville-space theory. J Chem Phys 2004; 120:6600-8. [PMID: 15267552 DOI: 10.1063/1.1665486] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
An optimal control theory for open quantum systems is constructed containing non-Markovian dissipation manipulated by an external control field. The control theory is developed based on a novel quantum dissipation formulation that treats both the initial canonical ensemble and the subsequent reduced control dynamics. An associated scheme of backward propagation is presented, allowing the efficient evaluation of general optimal control problems. As an illustration, the control theory is applied to the vibration of the hydrogen fluoride molecule embedded in a non-Markovian dissipative medium. The importance of control-dissipation correlation is evident in the results.
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Affiliation(s)
- Ruixue Xu
- Open Laboratory of Bond-Selective Chemistry, University of Science and Technology of China, Hefei, China.
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36
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Shi Q, Geva E. A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling. J Chem Phys 2003. [DOI: 10.1063/1.1624830] [Citation(s) in RCA: 91] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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38
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Koch CP, Klüner T, Kosloff R. A complete quantum description of an ultrafast pump-probe charge transfer event in condensed phase. J Chem Phys 2002. [DOI: 10.1063/1.1450124] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
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39
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Geva E. Optimization of laser-driven intramolecular hydrogen transfer in the presence of dephasing. J Chem Phys 2002. [DOI: 10.1063/1.1431276] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Palao JP, Kosloff R, Gordon JM. Quantum thermodynamic cooling cycle. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:056130. [PMID: 11736037 DOI: 10.1103/physreve.64.056130] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2001] [Indexed: 05/23/2023]
Abstract
The quantum-mechanical and thermodynamic properties of a three-level molecular cooling cycle are derived. An inadequacy of earlier models is rectified in accounting for the spontaneous emission and absorption associated with the coupling to the coherent driving field via an environmental reservoir. This additional coupling need not be dissipative, and can provide a thermal driving force-the quantum analog of classical absorption chillers. The dependence of the maximum attainable cooling rate on temperature, at ultralow temperatures, is determined and shown to respect the recently established fundamental bound based on the second and third laws of thermodynamics.
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Affiliation(s)
- J P Palao
- Department of Physical Chemistry and the Fritz Haber Research Center for Molecular Dynamics, Hebrew University, Jerusalem 91904, Israel
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41
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42
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Plakhotnik T. Spectral line shapes of single molecules beyond the sudden jump model. J Chem Phys 2001. [DOI: 10.1063/1.1345721] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Geva E, Rosenman E, Tannor D. On the second-order corrections to the quantum canonical equilibrium density matrix. J Chem Phys 2000. [DOI: 10.1063/1.481928] [Citation(s) in RCA: 60] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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44
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Direct simulation of non-linear interparticle collisional relaxation of ensembles of two-level systems. Chem Phys 2000. [DOI: 10.1016/s0301-0104(00)00095-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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45
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Longo S, Bruno D, Capitelli M, Minelli P. A Monte Carlo model for the non-equilibrium coherent kinetics of ensembles of two level systems. Chem Phys Lett 2000. [DOI: 10.1016/s0009-2614(99)01236-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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46
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Ashkenazi G, Kosloff R, Ratner MA. Photoexcited Electron Transfer: Short-Time Dynamics and Turnover Control by Dephasing, Relaxation, and Mixing. J Am Chem Soc 1999. [DOI: 10.1021/ja981998p] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Guy Ashkenazi
- Contribution from the Department of Physical Chemistry and Fritz Haber Institute for Molecular Dynamics, Hebrew University, Jerusalem, Israel, and Department of Chemistry, Northwestern University, Evanston, Illinois 60208
| | - Ronnie Kosloff
- Contribution from the Department of Physical Chemistry and Fritz Haber Institute for Molecular Dynamics, Hebrew University, Jerusalem, Israel, and Department of Chemistry, Northwestern University, Evanston, Illinois 60208
| | - Mark A. Ratner
- Contribution from the Department of Physical Chemistry and Fritz Haber Institute for Molecular Dynamics, Hebrew University, Jerusalem, Israel, and Department of Chemistry, Northwestern University, Evanston, Illinois 60208
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47
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48
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49
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Davis WB, Wasielewski MR, Kosloff R, Ratner MA. Semigroup Representations, Site Couplings, and Relaxation in Quantum Systems. J Phys Chem A 1998. [DOI: 10.1021/jp9813544] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- William B. Davis
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, Chemistry Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, and Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 90904, Israel
| | - Michael R. Wasielewski
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, Chemistry Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, and Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 90904, Israel
| | - Ronnie Kosloff
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, Chemistry Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, and Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 90904, Israel
| | - Mark A. Ratner
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, Chemistry Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, and Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 90904, Israel
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50
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