Non-stochastic matrix Schrödinger equation for open systems

Joubert-Doriol, Loïc; Ryabinkin, Ilya G.; Izmaylov, Artur F.

doi:10.1063/1.4903829

Cited by 7 publications

(11 citation statements)

References 29 publications

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“…McLachlan TDVP conserves the energy for the closed system. 74 However, even in NOSSE, the subsystem population is still not conserved for a general open system. To remedy this deficiency, we combined minimization of the NOSSE error due to a finite parametrization with the Lagrange multipliers method to constrain the subsystem population tr{mm † }, the corresponding Lagrangian functional is…”

Section: Dynamics Of Open Systemsmentioning

confidence: 99%

“…where m −1 = (m † m) −1 m † is a pseudo inverse. 74 Calculation of the pseudo inverse can be avoided by reconstructing the density matrix as ρ = kl,ss |ϕ ks ρ kl,ss ϕ ls | where ρ kl,ss = n M n,ks M * n,ls , and using Eq. ( 55) and Eq.…”

Section: Dynamics Of Open Systemsmentioning

confidence: 99%

“…It has been shown that Eq. (51) combined with the McLachlan TDVP conserves the energy for the closed system 74. However, even in NOSSE, the subsystem population is still not conserved for a general open system.…”

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confidence: 99%

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Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians

Joubert-Doriol

Izmaylov

2018

J. Phys. Chem. A

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We review techniques for simulating fully quantum nonadiabatic dynamics using the frozen-width moving Gaussian basis functions to represent the nuclear wave function. A choice of these basis functions is primarily motivated by the idea of the on-the-fly dynamics that will involve electronic structure calculations done locally in the vicinity of each Gaussian center and thus avoiding the "curse of dimensionality" appearing in large systems. For quantum dynamics involving multiple electronic states there are several aspects that need to be addressed. First, the choice of the electronic-state representation is one of most defining in terms of formulation of resulting equations of motion. We will discuss pros and cons of the standard adiabatic and diabatic representations as well as the relatively new moving crude adiabatic (MCA) representation. Second, if the number of electronic states can be fixed throughout the dynamics, the situation is different for the number of Gaussians needed for an accurate expansion of the total wave function. The latter increases its complexity along the course of the dynamics and a protocol extending the number of Gaussians is needed. We will consider two common approaches for the extension: (1) spawning and (2) cloning. Third, equations of motion for individual Gaussians can be chosen in different ways, implications for the energy conservation related to these ways will be discussed. Finally, to extend the success of moving basis approaches to quantum dynamics of open systems we will consider the Nonstochastic Open System Schrödinger Equation (NOSSE).

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Section: Dynamics Of Open Systemsmentioning

confidence: 99%

Section: Dynamics Of Open Systemsmentioning

confidence: 99%

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Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians

Joubert-Doriol

Izmaylov

2018

J. Phys. Chem. A

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“…25 NOSSE does not have issues with energy conservation within the TDVP framework because it is formulated with respect to a square root of the density. The square root dynamics is unitary for an isolated system and allows for the full reconstruction of the system density matrix evolution by evaluating the square at each time.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is to resolve the non-conservation problems using a hybrid approach: To address the energy non-conservation problem in isolated systems we apply the TDVP not to the QME equation but to its recently developed equivalent, non-stochastic open system Schrödinger equation (NOSSE) 25 . NOSSE does not have issues with energy conservation within the TDVP framework because it is formulated with respect to a square root of the density.…”

Section: Introductionmentioning

confidence: 99%

Problem-free time-dependent variational principle for open quantum systems

Joubert-Doriol

Izmaylov

2015

The Journal of Chemical Physics

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Methods of quantum nuclear wave-function dynamics have become very efficient in simulating large isolated systems using the time-dependent variational principle (TDVP). However, a straightforward extension of the TDVP to the density matrix framework gives rise to methods that do not conserve the energy in the isolated system limit and the total system population for open systems where only energy exchange with environment is allowed. These problems arise when the system density is in a mixed state and is simulated using an incomplete basis. Thus, the basis set incompleteness, which is inevitable in practical calculations, creates artificial channels for energy and population dissipation. To overcome this unphysical behavior, we have introduced a constrained Lagrangian formulation of TDVP applied to a non-stochastic open system Schrödinger equation [L. Joubert-Doriol, I. G. Ryabinkin, and A. F. Izmaylov, J. Chem. Phys. 141, 234112 (2014)]. While our formulation can be applied to any variational ansatz for the system density matrix, derivation of working equations and numerical assessment is done within the variational multiconfiguration Gaussian approach for a two-dimensional linear vibronic coupling model system interacting with a harmonic bath.

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Open system dynamics using Gaussian-based multiconfigurational time-dependent Hartree wavefunctions: Application to environment-modulated tunneling

Picconi

Burghardt

2019

The Journal of Chemical Physics

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A variational approach for the quantum dynamics of statistical mixtures is developed, which is based upon the representation of the natural states of the mixture in terms of hybrid Gaussian-based Multiconfiguration Time-Dependent Hartree (G-MCTDH) wavefunctions. The method, termed ρG-MCTDH, is combined with a treatment of dissipation and decoherence based on the nonstochastic open-system Schrödinger equations. The performance and the convergence properties of the approach are illustrated for a two-dimensional tunneling system, where the primary tunneling coordinate, represented by flexible single-particle functions, is resonantly coupled to a second harmonic mode, represented by Gaussian wave packets. The harmonic coordinate is coupled to the environment and two different processes are studied: (i) vibrational relaxation at zero temperature described by a master equation in the Lindblad form and (ii) thermalization induced by the Caldeira-Leggett master equation. In the second case, the evolution from a quantum tunneling regime to a quasistationary classical-limit distribution, driven by the heat bath, is visualized using a flux analysis.

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Non-stochastic matrix Schrödinger equation for open systems

Cited by 7 publications

References 29 publications

Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians

Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians

Problem-free time-dependent variational principle for open quantum systems

Open system dynamics using Gaussian-based multiconfigurational time-dependent Hartree wavefunctions: Application to environment-modulated tunneling

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