1
|
Chen ZH, Wang Y, Xu RX, Yan Y. Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory vs core-system hierarchy construction. J Chem Phys 2023; 158:074102. [PMID: 36813728 DOI: 10.1063/5.0134700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the λ(t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which, in turn, confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for "visualizing" the correlated solvation dynamics.
Collapse
Affiliation(s)
- Zi-Hao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| |
Collapse
|
2
|
Abstract
The idea of an open quantum system was introduced in the 1950s as a response to the problems encountered in areas such as nuclear magnetic resonance and the decay of unstable atoms. Nowadays, dynamical models of open quantum systems have become essential components in many applications of quantum mechanics. This paper provides an overview of the fundamental concepts of open quantum systems. All underlying definitions, algebraic methods and crucial theorems are presented. In particular, dynamical semigroups with corresponding time-independent generators are characterized. Furthermore, evolution models that induce memory effects are discussed. Finally, measures of non-Markovianity are recapped and interpreted from a perspective of physical relevance.
Collapse
|
3
|
Tanimura Y. Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM). J Chem Phys 2021; 153:020901. [PMID: 32668942 DOI: 10.1063/5.0011599] [Citation(s) in RCA: 163] [Impact Index Per Article: 54.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.
Collapse
Affiliation(s)
- Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| |
Collapse
|
4
|
Du PL, Wang Y, Xu RX, Zhang HD, Yan Y. System–bath entanglement theorem with Gaussian environments. J Chem Phys 2020; 152:034102. [DOI: 10.1063/1.5134745] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Peng-Li Du
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei, Anhui 230026, China
| |
Collapse
|
5
|
Mulvihill E, Schubert A, Sun X, Dunietz BD, Geva E. A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation. J Chem Phys 2019; 150:034101. [DOI: 10.1063/1.5055756] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Barry D. Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| |
Collapse
|
6
|
Rauf Abdullah N, Tang CS, Manolescu A, Gudmundsson V. Competition of static magnetic and dynamic photon forces in electronic transport through a quantum dot. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:375301. [PMID: 27420809 DOI: 10.1088/0953-8984/28/37/375301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We investigate theoretically the balance of the static magnetic and the dynamical photon forces in the electron transport through a quantum dot in a photon cavity with a single photon mode. The quantum dot system is connected to external leads and the total system is exposed to a static perpendicular magnetic field. We explore the transport characteristics through the system by tuning the ratio, [Formula: see text], between the photon energy, [Formula: see text], and the cyclotron energy, [Formula: see text]. Enhancement in the electron transport with increasing electron-photon coupling is observed when [Formula: see text]. In this case the photon field dominates and stretches the electron charge distribution in the quantum dot, extending it towards the contact area for the leads. Suppression in the electron transport is found when [Formula: see text], as the external magnetic field causes circular confinement of the charge density around the dot.
Collapse
Affiliation(s)
- Nzar Rauf Abdullah
- Physics Department, Faculty of Science and Science Education, School of Science, University of Sulaimani, Kurdistan Region, Iraq. Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
| | | | | | | |
Collapse
|
7
|
Abdullah NR, Tang CS, Manolescu A, Gudmundsson V. Coherent transient transport of interacting electrons through a quantum waveguide switch. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:015301. [PMID: 25425564 DOI: 10.1088/0953-8984/27/1/015301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigate coherent electron-switching transport in a double quantum waveguide system in a perpendicular static or vanishing magnetic field. The finite symmetric double waveguide is connected to two semi-infinite leads from both ends. The double waveguide can be defined as two parallel finite quantum wires or waveguides coupled via a window to facilitate coherent electron inter-wire transport. By tuning the length of the coupling window, we observe oscillations in the net charge current and a maximum electron conductance for the energy levels of the two waveguides in resonance. The importance of the mutual Coulomb interaction between the electrons and the influence of two-electron states is clarified by comparing results with and without the interaction. Even though the Coulomb interaction can lift two-electron states out of the group of active transport states the length of the coupling window can be tuned to locate two very distinct transport modes in the system in the late transient regime before the onset of a steady state. A static external magnetic field and quantum-dots formed by side gates (side quantum dots) can be used to enhance the inter-waveguide transport which can serve to implement a quantum logic device. The fact that the device can be operated in the transient regime can be used to enhance its speed.
Collapse
Affiliation(s)
- Nzar Rauf Abdullah
- Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
| | | | | | | |
Collapse
|
8
|
Zhang ZD, Wang J. Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics. J Chem Phys 2014; 140:245101. [DOI: 10.1063/1.4884125] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Z. D. Zhang
- Department of Physics and Astronomy, SUNY Stony Brook, New York 11794, USA
| | - J. Wang
- Department of Physics and Astronomy, SUNY Stony Brook, New York 11794, USA
- Department of Chemistry, SUNY Stony Brook, New York 11794, USA
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
| |
Collapse
|
9
|
Abdullah NR, Tang CS, Manolescu A, Gudmundsson V. Electron transport through a quantum dot assisted by cavity photons. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:465302. [PMID: 24132041 DOI: 10.1088/0953-8984/25/46/465302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We investigate transient transport of electrons through a single quantum dot controlled by a plunger gate. The dot is embedded in a finite wire with length Lx assumed to lie along the x-direction with a parabolic confinement in the y-direction. The quantum wire, originally with hard-wall confinement at its ends, ±Lx/2, is weakly coupled at t = 0 to left and right leads acting as external electron reservoirs. The central system, the dot and the finite wire, is strongly coupled to a single cavity photon mode. A non-Markovian density-matrix formalism is employed to take into account the full electron-photon interaction in the transient regime. In the absence of a photon cavity, a resonant current peak can be found by tuning the plunger-gate voltage to lift a many-body state of the system into the source-drain bias window. In the presence of an x-polarized photon field, additional side peaks can be found due to photon-assisted transport. By appropriately tuning the plunger-gate voltage, the electrons in the left lead are allowed to undergo coherent inelastic scattering to a two-photon state above the bias window if initially one photon was present in the cavity. However, this photon-assisted feature is suppressed in the case of a y-polarized photon field due to the anisotropy of our system caused by its geometry.
Collapse
Affiliation(s)
- Nzar Rauf Abdullah
- Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
| | | | | | | |
Collapse
|
10
|
RODRÍGUEZ-ACHACH MANUEL, PÉREZ GABRIEL, CERDEIRA HILDAA. QUANTUM AND THERMAL CORRECTIONS TO A CLASSICALLY CHAOTIC DISSIPATIVE SYSTEM. STOCH DYNAM 2011. [DOI: 10.1142/s0219493704001000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The effects of quantum and thermal corrections on the dynamics of a damped nonlinearly kicked harmonic oscillator are studied. This is done via the quantum Langevin equation formalism working on a truncated moment expansion of the density matrix of the system. We find that the type of bifurcations present in the system change upon quantization and that chaotic behavior appears for values of the nonlinear parameter that are far below the chaotic threshold for the classical model. Upon increase of temperature or Planck's constant, bifurcation points and chaotic thresholds are shifted towards lower values of the nonlinear parameter. There is also an anomalous reverse behavior for low values of the cutoff frequency.
Collapse
Affiliation(s)
- MANUEL RODRÍGUEZ-ACHACH
- Departamento de Física Aplicada, Cinvestav del IPN, Unidad Mérida, A. P. 73 "Cordemex", 97310 Mérida, Yucatán, México
| | - GABRIEL PÉREZ
- Departamento de Física Aplicada, Cinvestav del IPN, Unidad Mérida, A. P. 73 "Cordemex", 97310 Mérida, Yucatán, México
| | | |
Collapse
|
11
|
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.
Collapse
Affiliation(s)
- Carlos R Baiz
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | | | | |
Collapse
|
12
|
Moskalenko AS, Rok DA, Umanskii SY. Response signal in a femtosecond pump-probe experiment in a condensed medium with account of the memory induced by the relaxation medium. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2011. [DOI: 10.1134/s1990793110111016] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
13
|
Moskalenko AS, Rok DA, Umanskii SY. The dynamics of coherent wave packets in a medium with memory. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2010. [DOI: 10.1134/s1990793110050015] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
14
|
Hughes KH, Christ CD, Burghardt I. Effective-mode representation of non-Markovian dynamics: a hierarchical approximation of the spectral density. I. Application to single surface dynamics. J Chem Phys 2009; 131:024109. [PMID: 19603972 DOI: 10.1063/1.3159671] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
An approach to non-Markovian system-environment dynamics is described which is based on the construction of a hierarchy of coupled effective environmental modes that is terminated by coupling the final member of the hierarchy to a Markovian bath. For an arbitrary environment, which is linearly coupled to the subsystem, the discretized spectral density is replaced by a series of approximate spectral densities involving an increasing number of effective modes. This series of approximants, which are constructed analytically in this paper, guarantees the accurate representation of the overall system-plus-bath dynamics up to increasing times. The hierarchical structure is manifested in the approximate spectral densities in the form of the imaginary part of a continued fraction similar to Mori theory. The results are described for cases where the hierarchy is truncated at the first-, second-, and third-order level. It is demonstrated that the results generated from a reduced density matrix equation of motion and large dimensional system-plus-bath wavepacket calculations are in excellent agreement. For the reduced density matrix calculations, the system and hierarchy of effective modes are treated explicitly and the effects of the bath on the final member of the hierarchy are described by the Caldeira-Leggett equation and its generalization to zero temperature.
Collapse
Affiliation(s)
- Keith H Hughes
- School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW, United Kingdom.
| | | | | |
Collapse
|
15
|
Shi Q, Geva E. A derivation of the mixed quantum-classical Liouville equation from the influence functional formalism. J Chem Phys 2006; 121:3393-404. [PMID: 15303902 DOI: 10.1063/1.1771641] [Citation(s) in RCA: 102] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show that the mixed quantum-classical Liouville equation is equivalent to linearizing the forward-backward action in the influence functional. Derivations are provided in terms of either the diabatic or adiabatic basis sets. An application of the mixed quantum-classical Liouville equation for calculating the memory kernel of the generalized quantum master equation is also presented. The accuracy and computational feasibility of such an approach is demonstrated in the case of a two-level system nonlinearly coupled to an anharmonic bath.
Collapse
Affiliation(s)
- Qiang Shi
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| | | |
Collapse
|
16
|
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.
Collapse
|
17
|
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.
Collapse
Affiliation(s)
- Ming-Liang Zhang
- Department of Chemistry and FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| | | | | |
Collapse
|
18
|
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.
Collapse
Affiliation(s)
- Sven Welack
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany.
| | | | | |
Collapse
|
19
|
Biexcitons-bose condensation and optical response. ACTA ACUST UNITED AC 2006. [DOI: 10.1007/bfb0041582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
|
20
|
Pomyalov A, Tannor DJ. The non-Markovian quantum master equation in the collective-mode representation: Application to barrier crossing in the intermediate friction regime. J Chem Phys 2005; 123:204111. [PMID: 16351244 DOI: 10.1063/1.2121649] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantum-mechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a non-Markovian quantum master equation (NM-QME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NM-QME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the non-Markovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensed-phase rate constants.
Collapse
Affiliation(s)
- Anna Pomyalov
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, 76100 Israel
| | | |
Collapse
|
21
|
Hänggi P, Ingold GL. Fundamental aspects of quantum Brownian motion. CHAOS (WOODBURY, N.Y.) 2005; 15:26105. [PMID: 16035907 DOI: 10.1063/1.1853631] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
With this work we elaborate on the physics of quantum noise in thermal equilibrium and in stationary nonequilibrium. Starting out from the celebrated quantum fluctuation-dissipation theorem we discuss some important consequences that must hold for open, dissipative quantum systems in thermal equilibrium. The issue of quantum dissipation is exemplified with the fundamental problem of a damped harmonic quantum oscillator. The role of quantum fluctuations is discussed in the context of both, the nonlinear generalized quantum Langevin equation and the path integral approach. We discuss the consequences of the time-reversal symmetry for an open dissipative quantum dynamics and, furthermore, point to a series of subtleties and possible pitfalls. The path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.
Collapse
Affiliation(s)
- Peter Hänggi
- Institut für Physik, Universität Augsburg, 86135 Augsburg, Germany
| | | |
Collapse
|
22
|
Abstract
Quantum dissipation involves both energy relaxation and decoherence, leading toward quantum thermal equilibrium. There are several theoretical prescriptions of quantum dissipation but none of them is simple enough to be treated exactly in real applications. As a result, formulations in different prescriptions are practically used with different approximation schemes. This review examines both theoretical and application aspects on various perturbative formulations, especially those that are exact up to second-order but nonequivalent in high-order system-bath coupling contributions. Discrimination is made in favor of an unconventional formulation that in a sense combines the merits of both the conventional time-local and memory-kernel prescriptions, where the latter is least favorite in terms of the applicability range of parameters for system-bath coupling, non-Markovian, and temperature. Also highlighted is the importance of correlated driving and dissipation effects, not only on the dynamics under strong external field driving, but also in the calculation of field-free correlation and response functions.
Collapse
Affiliation(s)
- YiJing Yan
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong.
| | | |
Collapse
|
23
|
Mo Y, Xu RX, Cui P, Yan Y. Correlation and response functions with non-Markovian dissipation: A reduced Liouville-space theory. J Chem Phys 2005; 122:84115. [PMID: 15836028 DOI: 10.1063/1.1853353] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime.
Collapse
Affiliation(s)
- Yan Mo
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China
| | | | | | | |
Collapse
|
24
|
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.
Collapse
Affiliation(s)
- Qiang Shi
- Department of Chemistry and the FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| | | |
Collapse
|
25
|
|
26
|
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
|
27
|
|
28
|
Kirkwood JC, Scheurer C, Chernyak V, Mukamel S. Simulations of energy funneling and time- and frequency-gated fluorescence in dendrimers. J Chem Phys 2001. [DOI: 10.1063/1.1334612] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
29
|
Burghardt I. Reduced dynamics with initial correlations: Multiconfigurational approach. J Chem Phys 2001. [DOI: 10.1063/1.1329648] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
30
|
Meier C, Tannor DJ. Non-Markovian evolution of the density operator in the presence of strong laser fields. J Chem Phys 1999. [DOI: 10.1063/1.479669] [Citation(s) in RCA: 301] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
|
31
|
Desposito MA, Hernandez ES. Fully coupled model versus rotating-wave approximation in the asymptotic time evolution of spin systems. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/28/4/007] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
32
|
|
33
|
Scheurer C, Saalfrank P. Hydrogen transfer in vibrationally relaxing benzoic acid dimers: Time‐dependent density matrix dynamics and infrared spectra. J Chem Phys 1996. [DOI: 10.1063/1.471110] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
34
|
Scheurer C, Saalfrank P. Density matrix model for hydrogen transfer in the benzoic acid dimer. Chem Phys Lett 1995. [DOI: 10.1016/0009-2614(95)01009-x] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
35
|
Rahman M. Reduction of overdamped stochastic processes in the coherent state representation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:2486-2496. [PMID: 9963692 DOI: 10.1103/physreve.52.2486] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
36
|
Despósito MA, Hernández ES. Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:7510-7518. [PMID: 9908102 DOI: 10.1103/physreva.46.7510] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
37
|
Despósito MA, Gatica SM, Hernández ES. Asymptotic regime of quantal stochastic and dissipative motion. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:3234-3242. [PMID: 9908491 DOI: 10.1103/physreva.46.3234] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
38
|
Haus JW, Kehr KW. Generalized effective-medium approximation for particle transport: Random-trap model. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:4341-4354. [PMID: 10000083 DOI: 10.1103/physrevb.44.4341] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
39
|
Lumsden CJ. Hierarchical behavior in fit dynamical systems. Bull Math Biol 1985; 47:591-612. [PMID: 4084693 DOI: 10.1007/bf02460128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
|
40
|
Cox I, Hagston W, Roberts M. Non-equilibrium statistical mechanics of open systems. Mol Phys 1981. [DOI: 10.1080/00268978100102271] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
41
|
|
42
|
On the Hamiltonian content of biodynamics. Bull Math Biol 1980. [DOI: 10.1007/bf02460790] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
43
|
Theory of Atomic Processes in Strong Resonant Electromagnetic Fields. ADVANCES IN ATOMIC AND MOLECULAR PHYSICS 1980. [DOI: 10.1016/s0065-2199(08)60008-1] [Citation(s) in RCA: 30] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
|
44
|
King FW, Schatz GC. Stochastic theory of vibrational energy transfer in collinear atom-diatom collisions: the role of non-markovian effects. Mol Phys 1979. [DOI: 10.1080/00268977900101641] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
45
|
H�nggi P. On derivations and solutions of master equations and asymptotic representations. ACTA ACUST UNITED AC 1978. [DOI: 10.1007/bf01323672] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
46
|
|
47
|
|
48
|
On the equivalence of generalized Langevin equation and generalized master equation. ACTA ACUST UNITED AC 1977. [DOI: 10.1007/bf01313375] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
49
|
Kitahara K, Metiu H, Ross J, Silbey R. Dynamical theory of migration of an adsorbed atom on solid surfaces. J Chem Phys 1976. [DOI: 10.1063/1.433437] [Citation(s) in RCA: 45] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
50
|
Suzuki M. Scaling Theory of Non-Equilibrium Systems near the Instability Point. II: Anomalous Fluctuation Theorems in the Extensive Region. ACTA ACUST UNITED AC 1976. [DOI: 10.1143/ptp.56.477] [Citation(s) in RCA: 80] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
|