The Theory of Open Quantum Systems

Breuer, Heinz‐Peter; Petruccione, Francesco

doi:10.1093/acprof:oso/9780199213900.001.0001

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“…The cumulant approach, [16][17][18][19][20][21][22] recently discussed and successfully applied to spin-boson and linear vibronic coupling Hamiltonian model, [23][24][25][26] allows to take into account the change of the reaction rate with time, describing the population P (t) of the state of interest with an equation of the form…”

Section: Introductionmentioning

confidence: 99%

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Borrelli

Peluso

2015

J. Chem. Theory Comput.

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This is the author's final version of the contribution published as:Borrelli, Raffaele; Peluso, Andrea. Quantum dynamics of radiationless electronic transitions including normal modes displacements and duschinsky rotations: A second-order cumulant approach. JOURNAL OF CHEMICAL THEORY AND COMPUTATION. 11 (2) AbstractAn analytical expression for the population dynamics of electronic radiationless transitions has been derived from the second order expansion of the quantum evolution operator in the Liouville space and the cumulant theory. The expression includes the effect of both normal mode displacements and Duschinsky rotations and allows to take into account both equilibrium and non-equilibrium initial conditions. The methodology has been applied to model the electron-transfer process between the accessory bacteriochlorophyll and the bacteriopheophytine in bacterial reactions centers, providing a rate in good agreement with experimental findings.

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Section: Introductionmentioning

confidence: 99%

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Borrelli

Peluso

2015

J. Chem. Theory Comput.

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“…We can derive the QME, the equation of motion of the system S, by applying the Born-Markov approximation [1] to Eq. (2).…”

Section: Quantum Master Equationmentioning

confidence: 99%

“…1) near the reservoir b, andŶ b,λ is a self-adjoint operator of the reservoir b. We next decomposê X b,λ into eigenoperators ofĤ S [1]:…”

Section: Quantum Master Equationmentioning

confidence: 99%

“…In quantum systems, one of the theoretical frameworks widely used for open systems is the quantum master equation (QME) [1], an equation of motion for the density matrix of the system. In fact, the QME is used in various fields of physics: e.g., quantum optics [1,2], nuclear magnetic resonance [3], electron transfer in chemical physics and biophysics [4,5], heat transport [6,7,8,9,10,11,12,13,14], electronic transport in mesoscopic conductors [15,16,17,18,19], spin transport [20], and nonequilibrium thermodynamics and statistical physics [21,22,23,24,25]. Therefore, the QME is a reliable approach to investigating NESS in various systems (c.f.…”

Section: Introductionmentioning

confidence: 99%

“…A method of treating larger systems in the framework of the QME is the stochastic unraveling of QME (also known as quantum jump, quantum trajectory, and Monte Carlo wave function method) [1,2,34,35,36,37,38,39,41,42,40,5,10,11]. In this method, since one treats a wave function instead of a density matrix, one can investigate systems larger than those in the direct methods.…”

Section: Introductionmentioning

confidence: 99%

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A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

Yuge

Sugita

2015

J. Phys. Soc. Jpn.

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We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part R. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to R to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.

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State Preservation of Open Quantum Systems

Cong

2014

Control of Quantum Systems

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Decoherence is a serious obstacle to the preservation of quantum superposition and entanglement over long periods of time (Giulini et al., 1996). Decoherence means non-unitary evolutions (Ai, Li, and Long, 2006;Niwa, Matsumoto, and Imai, 2002;Facchi et al., 2005) and results in the loss of information and/or probability leakage toward the environment. This issue has attracted much attention and a number of interesting schemes have been proposed to preserve coherence. Among these schemes are quantum error-. Error-avoiding codes encode information into the degenerate subspace of the error operators so that the information will not be affected by the error operators, while error-correcting codes restore the loss of information due to decoherence or quantum dissipation by monitoring the system and conditionally carrying on suitable feedback control. Their applications are limited by the requirement of using redundant qubit resources. Bang-bang control uses high-frequency pulses to average out the decoherence effect. However, it has the essential requirement that the bath retains some memory of its interaction with the system, so it is not useful for a system subject to Markovian decoherence. Lidar and Schneider (2005) therefore proposed a new method called tracking-control to solve the problem of stabilizing the coherence of a single qubit subject to Markovian decoherence. Recently, Zhang et al. (2010) proposed a feedback control strategy based on quantum weak measurements to protect the coherence of a qubit system in which the stochastic noise was considered. However, their work was restricted to a single-qubit system and they only Control of Quantum Systems: Theory and Methods, First Edition. Shuang Cong.

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The Theory of Open Quantum Systems

Abstract: Classical probability theory and stochastic processes 3 8.4.3 Spectral detection and the dressed atom References IV NON-MARKOVIAN QUANTUM PROCESSES 9 Projection operator techniques. 441 9.1 The Nakajima-Zwanzig projection operator technique 9.1.

Cited by 4,694 publications

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Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

State Preservation of Open Quantum Systems

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