Condensed phase vibrational relaxation: calibration of approximate relaxation theories with analytical and numerically exact results

Coalson, Rob D.; Evans, Deborah G.

doi:10.1016/j.chemphys.2003.08.028

Cited by 18 publications

(28 citation statements)

References 42 publications

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“…where the populations of bath are defined by p n = e −En/kT 20 m=1 e −Em/kT (20) and |Ψ n (t) are the solutions to the Schrödinger equation for all initial states |Ψ n (0) = |ψ(0) ⊗ |n . The initial system state was chosen as a superposition state |ψ(0) = (|0 + |1 )/ √ 2.…”

Section: Exact Numerical Approachmentioning

confidence: 99%

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Kraus decomposition for chaotic environments

Çetinbaş¹,

Wilkie²

2008

Physics Letters A

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We consider a system interacting with a chaotic thermodynamic bath. We derive an explicit and exact Kraus operator sum representation (OSR) for the open system reduced density. The OSR preserves the Hermiticity, complete positivity and norm. We show that it is useful as a numerical tool by testing it against exact results for a qubit interacting with an isolated flawed quantum computer. We also discuss some interesting qualitative aspects of the OSR.

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Section: Exact Numerical Approachmentioning

confidence: 99%

“…At high temperatures random matrix theories [16], or classical trajectory simulations such as the Wigner method [17], can be used. Redfield theory [18,19] and its generalizations [20,21] can also be employed. But at the very low temperatures relevant to quantum computing technologies the options are more limited.…”

Section: Introductionmentioning

confidence: 99%

Kraus decomposition for chaotic environments

Çetinbaş¹,

Wilkie²

2008

Physics Letters A

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“…18,19 These derivations explicitly show that both forms of generalized Redfield theory account for non-Markovian behavior and have similar applicability requirements. [19][20][21] Specifically, since Redfield theory is tantamount to second-order perturbation theory in the system-bath coupling, truncation at low order is only accurate for η < 1, where η = max[ 2λ…”

Section: Appendix A: Derivation Of Redfield Equationsmentioning

confidence: 99%

Extending the applicability of Redfield theories into highly non-Markovian regimes

Montoya−Castillo

Berkelbach

Reichman

2015

The Journal of Chemical Physics

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We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high-frequency bath degrees of freedom only, while the low-frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. We further generalize the method to multi-site models and compare with exact results for a model of the Fenna-Matthews-Olson complex. The results from the method are found to dramatically improve Redfield dynamics in highly non-Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low-frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.

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“…The methodology has been employed for generating accurate benchmark results and has found numerous applications in chemical and condensed matter physics (for example, see Refs. [31][32][33][34][35][36][37][38][39][40][41][42][43]; it has also been extended to fermionic environments. [44][45][46] The i-QuAPI methodology employs a path integral 47,48 representation of the system's reduced density matrix in terms of localized system states.…”

Section: Introductionmentioning

confidence: 99%

On iterative path integral calculations for a system interacting with a shifted dissipative bath

Walters

Banerjee

Makri

2015

The Journal of Chemical Physics

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Real-time path integral calculations for the propagation of a system in contact with a harmonic dissipative environment often employ the iterative quasi-adiabatic propagator path integral (i-QuAPI) methodology. We compare two simple ways of applying this methodology to a bath initially in equilibrium with the localized state of the system (e.g., the donor in the case of charge transfer). The first way involves modifying the phase of the system via a time-local phase given in terms of integrals of the spectral density or in terms of the coefficients entering the QuAPI-discretized influence functional. In the iterative decomposition of the path integral, this approach requires consistent memory truncation to avoid extremely slow convergence. The second, alternative approach involves shifting the coordinate of the system, to bring the donor state in equilibrium with the bath, and requires no further modification of the i-QuAPI algorithm.

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Condensed phase vibrational relaxation: calibration of approximate relaxation theories with analytical and numerically exact results

Cited by 18 publications

References 42 publications

Kraus decomposition for chaotic environments

Kraus decomposition for chaotic environments

Extending the applicability of Redfield theories into highly non-Markovian regimes

On iterative path integral calculations for a system interacting with a shifted dissipative bath

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