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Non-Markovian Quantum Dynamics in a Squeezed Reservoir. ENTROPY 2022; 24:e24030352. [PMID: 35327864 PMCID: PMC8946918 DOI: 10.3390/e24030352] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 02/22/2022] [Indexed: 02/07/2023]
Abstract
We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system–environment coupling strength and, thus, the strength of the dissipation.
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2
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Hartmann R, Strunz WT. Open Quantum System Response from the Hierarchy of Pure States. J Phys Chem A 2021; 125:7066-7079. [PMID: 34353022 DOI: 10.1021/acs.jpca.1c03339] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The spectral properties of a quantum system are essential when probing theoretical predictions against experimental data. For an open quantum system strongly interacting with its environment, spectral features are challenging to calculate. Here we demonstrate that the stochastic Hierarchy of Pure States (HOPS) approach is well suited to calculate the response of an open quantum system to a, possibly strong, coherent probe driving. For weak driving, where Kubo's linear response theory is applicable, it turns out that the HOPS method is highly efficient since fluctuations inherent to the stochastic dynamics cancel for the response function and, thus, allow us to obtain the susceptibility easily. Our results are in agreement with experimental data for a strongly damped spin system showing that the transition from oscillatory to overdamped motion is also reflected by the transmission spectrum. As a further application we demonstrate that the susceptibility, quantifying the amplitude of the response, as a function of temperature exhibits a maximum which is the hallmark of stochastic resonance. Beyond the linear regime, the exact open system dynamics shows the asymptotic Floquet state. We use the topic of probe driving and response to present the HOPS approach in a novel and self-contained way. This includes the importance sampling scheme which yields the nonlinear HOPS as well as the stochastic treatment of a thermal initial environmental state within the zero temperature formalism. Special attention is given to the exponential representation of the algebraic Ohmic bath correlation function and the truncation condition for the hierarchy.
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Affiliation(s)
- Richard Hartmann
- Institut für Theoretische Physik, Technische Universität Dresden, Dresden, D-01062, Germany
| | - Walter T Strunz
- Institut für Theoretische Physik, Technische Universität Dresden, Dresden, D-01062, Germany
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3
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Wehner J, Engel V. Stochastically correlated versus uncorrelated quantum-state diffusion dynamics in different electronic states: third-order polarizations and two-dimensional vibronic spectra. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.08.042] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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4
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Ren J, Shuai Z, Kin-Lic Chan G. Time-Dependent Density Matrix Renormalization Group Algorithms for Nearly Exact Absorption and Fluorescence Spectra of Molecular Aggregates at Both Zero and Finite Temperature. J Chem Theory Comput 2018; 14:5027-5039. [DOI: 10.1021/acs.jctc.8b00628] [Citation(s) in RCA: 61] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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Coccia E, Troiani F, Corni S. Probing quantum coherence in ultrafast molecular processes: Anab initioapproach to open quantum systems. J Chem Phys 2018; 148:204112. [DOI: 10.1063/1.5022976] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Emanuele Coccia
- Department of Chemical Sciences, University of Padova, via Marzolo 1, Padova, Italy
- CNR Institute of Nanoscience, via Campi 213/A, Modena, Italy
| | - Filippo Troiani
- CNR Institute of Nanoscience, via Campi 213/A, Modena, Italy
| | - Stefano Corni
- Department of Chemical Sciences, University of Padova, via Marzolo 1, Padova, Italy
- CNR Institute of Nanoscience, via Campi 213/A, Modena, Italy
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6
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Hughes S, Richter M, Knorr A. Quantized pseudomodes for plasmonic cavity QED. OPTICS LETTERS 2018; 43:1834-1837. [PMID: 29652376 DOI: 10.1364/ol.43.001834] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Accepted: 03/13/2018] [Indexed: 06/08/2023]
Abstract
We present a quantized pseudomode theory for solving system-level cavity quantum electrodynamics with quantum emitters coupled to plasmonic resonators. Exploiting the Green function response of a silver nanoparticle and an exact solution for the input-output coupling, we study the non-Markovian coupling regimes of multi-mode vacuum Rabi oscillations and coherently pumped multi-photon resonances from the higher lying ladder states of collective plasmon modes. The nonlinear pumping regime also facilitates pronounced population inversion of a single two-level atom through multiphoton resonances dominated by dark plasmons.
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Zhang PP, Bentley CDB, Eisfeld A. Flexible scheme to truncate the hierarchy of pure states. J Chem Phys 2018; 148:134103. [DOI: 10.1063/1.5022225] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- P.-P. Zhang
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - C. D. B. Bentley
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - A. Eisfeld
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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Tamascelli D, Smirne A, Huelga SF, Plenio MB. Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2018; 120:030402. [PMID: 29400486 DOI: 10.1103/physrevlett.120.030402] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2017] [Indexed: 06/07/2023]
Abstract
We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments-one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.
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Affiliation(s)
- D Tamascelli
- Università degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, I-20133 Milano, Italy
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany
| | - A Smirne
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany
| | - S F Huelga
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany
| | - M B Plenio
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany
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9
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Ke Y, Zhao Y. Perturbation expansions of stochastic wavefunctions for open quantum systems. J Chem Phys 2017; 147:184103. [DOI: 10.1063/1.4996737] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yaling Ke
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
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Ritschel G, Strunz WT, Eisfeld A. Closures of the functional expansion hierarchy in the non-Markovian quantum state diffusion approach. J Chem Phys 2017; 147:064113. [DOI: 10.1063/1.4986251] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
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11
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Ke Y, Zhao Y. Hierarchy of stochastic Schrödinger equation towards the calculation of absorption and circular dichroism spectra. J Chem Phys 2017; 146:174105. [DOI: 10.1063/1.4982230] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Roden JJJ, Bennett DIG, Whaley KB. Long-range energy transport in photosystem II. J Chem Phys 2017; 144:245101. [PMID: 27369543 DOI: 10.1063/1.4953243] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
We simulate the long-range inter-complex electronic energy transfer in photosystem II-from the antenna complex, via a core complex, to the reaction center-using a non-Markovian (ZOFE) quantum master equation description that allows the electronic coherence involved in the energy transfer to be explicitly included at all length scales. This allows us to identify all locations where coherence is manifested and to further identify the pathways of the energy transfer in the full network of coupled chromophores using a description based on excitation probability currents. We investigate how the energy transfer depends on the initial excitation-localized, coherent initial excitation versus delocalized, incoherent initial excitation-and find that the overall energy transfer is remarkably robust with respect to such strong variations of the initial condition. To explore the importance of vibrationally enhanced transfer and to address the question of optimization in the system parameters, we systematically vary the strength of the coupling between the electronic and the vibrational degrees of freedom. We find that the natural parameters lie in a (broad) region that enables optimal transfer efficiency and that the overall long-range energy transfer on a ns time scale appears to be very robust with respect to variations in the vibronic coupling of up to an order of magnitude. Nevertheless, vibrationally enhanced transfer appears to be crucial to obtain a high transfer efficiency, with the latter falling sharply for couplings outside the optimal range. Comparison of our full quantum simulations to results obtained with a "classical" rate equation based on a modified-Redfield/generalized-Förster description previously used to simulate energy transfer dynamics in the entire photosystem II complex shows good agreement for the overall time scales of excitation energy transport.
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Affiliation(s)
- Jan J J Roden
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Doran I G Bennett
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - K Birgitta Whaley
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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13
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Lim J, Ing DJ, Rosskopf J, Jeske J, Cole JH, Huelga SF, Plenio MB. Signatures of spatially correlated noise and non-secular effects in two-dimensional electronic spectroscopy. J Chem Phys 2017; 146:024109. [DOI: 10.1063/1.4973975] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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14
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Ferialdi L. Exact Closed Master Equation for Gaussian Non-Markovian Dynamics. PHYSICAL REVIEW LETTERS 2016; 116:120402. [PMID: 27058061 DOI: 10.1103/physrevlett.116.120402] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Indexed: 06/05/2023]
Abstract
Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This very general result allows us to investigate a vast variety of physical systems. We show that the master equation for non-Markovian quantum Brownian motion is a particular case of our general result. Furthermore, we derive the master equation unraveled by a non-Markovian, dissipative stochastic Schrödinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.
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Affiliation(s)
- L Ferialdi
- Mathematisches Institut, Ludwig-Maximilians Universität, Theresienstraße 39, 80333 Munich, Germany
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15
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Song K, Bai S, Shi Q. A time domain two-particle approximation to calculate the absorption and circular dichroism line shapes of molecular aggregates. J Chem Phys 2015; 143:064109. [DOI: 10.1063/1.4928584] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kai Song
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Shuming Bai
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
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16
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Moix JM, Ma J, Cao J. Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation. J Chem Phys 2015; 142:094108. [PMID: 25747062 DOI: 10.1063/1.4908601] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.
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Affiliation(s)
- Jeremy M Moix
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Jian Ma
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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17
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Ritschel G, Suess D, Möbius S, Strunz WT, Eisfeld A. Non-Markovian Quantum State Diffusion for temperature-dependent linear spectra of light harvesting aggregates. J Chem Phys 2015; 142:034115. [DOI: 10.1063/1.4905327] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Diósi L, Ferialdi L. General non-markovian structure of Gaussian master and stochastic Schrödinger equations. PHYSICAL REVIEW LETTERS 2014; 113:200403. [PMID: 25432028 DOI: 10.1103/physrevlett.113.200403] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2014] [Indexed: 06/04/2023]
Abstract
General open quantum systems display memory features, their master equations are non-Markovian. We show that the subclass of Gaussian non-Markovian open system dynamics is tractable in a depth similar to the Markovian class. The structure of master equations exhibits a transparent generalization of the Lindblad structure. We find and parametrize the class of stochastic Schrödinger equations that unravel a given master equation, such a class was previously known for Markovian systems only. We show that particular non-Markovian unravelings known in the literature are special cases of our class.
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Affiliation(s)
- L Diósi
- Wigner Research Center for Physics, H-1525 Budapest 114, P.O. Box 49, Hungary
| | - L Ferialdi
- Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstrasse 39, 80333 Munich, Germany
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Suess D, Eisfeld A, Strunz WT. Hierarchy of stochastic pure states for open quantum system dynamics. PHYSICAL REVIEW LETTERS 2014; 113:150403. [PMID: 25375694 DOI: 10.1103/physrevlett.113.150403] [Citation(s) in RCA: 84] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2014] [Indexed: 06/04/2023]
Abstract
We derive a hierarchy of stochastic evolution equations for pure states (quantum trajectories) for open quantum system dynamics with non-Markovian structured environments. This hierarchy of pure states (HOPS) is generally applicable and provides the exact reduced density operator as an ensemble average over normalized states. The corresponding nonlinear equations are presented. We demonstrate that HOPS provides an efficient theoretical tool and apply it to the spin-boson model, the calculation of absorption spectra of molecular aggregates, and energy transfer in a photosynthetic pigment-protein complex.
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Affiliation(s)
- D Suess
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany
| | - A Eisfeld
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - W T Strunz
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany
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Simulation of quantum dynamics based on the quantum stochastic differential equation. ScientificWorldJournal 2013; 2013:424137. [PMID: 23781156 PMCID: PMC3679721 DOI: 10.1155/2013/424137] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2013] [Accepted: 04/28/2013] [Indexed: 11/22/2022] Open
Abstract
The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.
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Jing Y, Chen L, Bai S, Shi Q. Equilibrium excited state and emission spectra of molecular aggregates from the hierarchical equations of motion approach. J Chem Phys 2013; 138:045101. [DOI: 10.1063/1.4775843] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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22
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Roden J, Strunz WT, Whaley KB, Eisfeld A. Accounting for intra-molecular vibrational modes in open quantum system description of molecular systems. J Chem Phys 2012. [DOI: 10.1063/1.4765329] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Gelin MF, Sharp LZ, Egorova D, Domcke W. Bath-induced correlations and relaxation of vibronic dimers. J Chem Phys 2012; 136:034507. [DOI: 10.1063/1.3676063] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gelin MF, Egorova D, Domcke W. Exact quantum master equation for a molecular aggregate coupled to a harmonic bath. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041139. [PMID: 22181119 DOI: 10.1103/physreve.84.041139] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2011] [Revised: 09/04/2011] [Indexed: 05/31/2023]
Abstract
We consider a molecular aggregate consisting of N identical monomers. Each monomer comprises two electronic levels and a single harmonic mode. The monomers interact with each other via dipole-dipole forces. The monomer vibrational modes are bilinearly coupled to a bath of harmonic oscillators. This is a prototypical model for the description of coherent exciton transport, from quantum dots to photosynthetic antennae. We derive an exact quantum master equation for such systems. Computationally, the master equation may be useful for the testing of various approximations employed in theories of quantum transport. Physically, it offers a plausible explanation of the origins of long-lived coherent optical responses of molecular aggregates in dissipative environments.
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Affiliation(s)
- Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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