Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Journal of Chemical Physics

Second-quantized molecular time scale generalized Langevin equation theory: Fermion equivalent chain

H. Keith McDowell

Published May 15, 1987• 10 citations
Publisher

Abstract

A second-quantized version of molecular time scale generalized Langevin equation theory is developed in an equivalent chain format for quantum fermion systems. The approach allows for nonlinear Hamiltonians and strong coupling to the bath. A bath average is defined which permits reduced dynamics prescriptions to be developed for the case of one-electron Hamiltonians. The bath average is shown to be defined such that perturbations of a primary zone damp away at long time.

DOI
10.1063/1.452504

Related papers

Second-quantized molecular time scale generalized Langevin equation theory: Boson equivalent chain

H. Keith McDowell

A second-quantized version of molecular time scale generalized Langevin equation theory is developed in an equivalent chain format for quantum boson systems. The approach allows for nonlinear Hamiltonians and strong coupling to the bath. A bath average is defined which permits reduced dynamics prescriptions to be developed. The bath average is shown to be consistent with the notion that perturbations of a primary zone should damp away at long time.

The Journal of Chemical Physics•Feb 1, 1987•15 citations

A theory of electron baths: One-electron system dynamics

H. Keith McDowell

The second-quantized, many-electron, atomic, and molecular Hamiltonian is partitioned both by the identity or labeling of the spin orbitals and by the dynamics of the spin orbitals into a system coupled to a bath. The electron bath is treated by a molecular time scale generalized Langevin equation approach designed to include one-electron dynamics in the system dynamics. The bath is formulated as an equivalent chain of spin orbitals through the introduction of equivalent-chain annihilation and creation operators. Both the dynamics and the quantum grand canonical statistical properties of the electron bath are examined. Two versions for the statistical properties of the bath are pursued. Using a weak bath assumption, a bath statistical average is defined which allows one to achieve a reduced dynamics description of the electron system which is coupled to the electron bath. In a strong bath assumption effective Hamiltonians are obtained which reproduce the dynamics of the bath and which lead to the same results as found in the weak bath assumption. The effective (but exact) Hamiltonian is found to be a one-electron Hamiltonian. A reduced dynamics equation of motion for the system population matrix is derived and found to agree with a previous version. This equation of motion is useful for studying electron transfer in the system when coupled to an electron bath.

The Journal of Chemical Physics•Feb 1, 1992•2 citations

Second-quantized molecular time scale generalized Langevin equation theory and the quantum oscillator

H. Keith McDowell

The short-time Gaussian approximation to the molecular time scale generalized Langevin equation (MTGLE) friction kernel is introduced and used to compute the time dependence of a fluctuation time correlation function. The fluctuations are shown to have two time scales, namely, the dissipation time scale and a quantum time scale given by exp[−2πkTt/ℏ]. Absorption and emission spectral functions for a quantum oscillator coupled to a bath are derived with no approximations made. The second-quantized MTGLE approach is applied to the problem of a quantum oscillator coupled linearly to a bath of quantum oscillators. The method is shown to be consistent with previous work and to provide a systematic methodology to examine more general many-body boson problems.

The Journal of Chemical Physics•Oct 15, 1987•10 citations

Second-Order Langevin Equation in Quantized Hamilton Dynamics

Eric M. Heatwole, Oleg V. Prezhdo

We derive a semi-classical Langevin equation that, in conjuction with a quantum fluctuation–dissipation theorem, can be used to run canonical dynamics and to determine thermal averages in the second-order quantized Hamilton dynamics (QHD-2). In contrast to our earlier work [J. Chem. Phys. 122 (2005) 234109], the bath is no longer treated classically, and the friction is represented at the second-order. As a result, the quantum fluctuation variables are kept close to their optimal values, similarly to the recently developed phase-space canonical averaging for QHD-2 [J. Chem. Phys. 126 (2007) 204108]. The theory is exact for the quantum harmonic oscillator and the free particle, and gives good agreement with the quantum answer for a variety of quartic potentials.

Journal of the Physical Society of Japan•Mar 26, 2008•15 citations

Second-order quantized Hamilton dynamics coupled to classical heat bath

Eric M. Heatwole, Oleg V. Prezhdo

Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.

The Journal of Chemical Physics•Jun 15, 2005•19 citations

Repeated quantum interactions Quantum Langevin equation and the low density limit

Ameur Dhahri

We consider a repeated quantum interaction model describing a small system $\Hh_S$ in interaction with each one of the identical copies of the chain $\bigotimes_{\N^*}\C^{n+1}$, modeling a heat bath, one after another during the same short time intervals $[0,h]$. We suppose that the repeated quantum interaction Hamiltonian is split in two parts: a free part and an interaction part with time scale of order $h$. After giving the GNS representation, we establish the relation between the time scale $h$ and the classical low density limit. We introduce a chemical potential $μ$ related to the time $h$ as follows: $h^2=e^{βμ}$. We further prove that the solution of the associated discrete evolution equation converges strongly, when $h$ tends to 0, to the unitary solution of a quantum Langevin equation directed by Poisson processes.

arXiv:0803.3059•Mar 20, 2008•0 citations
A second-quantized version of molecular time scale generalized Langevin equation theory is developed in an equivalent chain format for quantum fermion systems. The approach allows for nonlinear Hamiltonians and strong coupling to the bath. A bath average is defined which permits reduced dynamics prescriptions to be developed for the case of one-electron Hamiltonians. The bath average is shown to be defined such that perturbations of a primary zone damp away at long time.
The second-quantized, many-electron, atomic, and molecular Hamiltonian is partitioned both by the identity or labeling of the spin orbitals and by the dynamics of the spin orbitals into a system coupled to a bath. The electron bath is treated by a molecular time scale generalized Langevin equation approach designed to include one-electron dynamics in the system dynamics. The bath is formulated as an equivalent chain of spin orbitals through the introduction of equivalent-chain annihilation and creation operators. Both the dynamics and the quantum grand canonical statistical properties of the electron bath are examined. Two versions for the statistical properties of the bath are pursued. Using a weak bath assumption, a bath statistical average is defined which allows one to achieve a reduced dynamics description of the electron system which is coupled to the electron bath. In a strong bath assumption effective Hamiltonians are obtained which reproduce the dynamics of the bath and which lead to the same results as found in the weak bath assumption. The effective (but exact) Hamiltonian is found to be a one-electron Hamiltonian. A reduced dynamics equation of motion for the system population matrix is derived and found to agree with a previous version. This equation of motion is useful for studying electron transfer in the system when coupled to an electron bath.
The short-time Gaussian approximation to the molecular time scale generalized Langevin equation (MTGLE) friction kernel is introduced and used to compute the time dependence of a fluctuation time correlation function. The fluctuations are shown to have two time scales, namely, the dissipation time scale and a quantum time scale given by exp[−2πkTt/ℏ]. Absorption and emission spectral functions for a quantum oscillator coupled to a bath are derived with no approximations made. The second-quantized MTGLE approach is applied to the problem of a quantum oscillator coupled linearly to a bath of quantum oscillators. The method is shown to be consistent with previous work and to provide a systematic methodology to examine more general many-body boson problems.
We derive a semi-classical Langevin equation that, in conjuction with a quantum fluctuation–dissipation theorem, can be used to run canonical dynamics and to determine thermal averages in the second-order quantized Hamilton dynamics (QHD-2). In contrast to our earlier work [J. Chem. Phys. 122 (2005) 234109], the bath is no longer treated classically, and the friction is represented at the second-order. As a result, the quantum fluctuation variables are kept close to their optimal values, similarly to the recently developed phase-space canonical averaging for QHD-2 [J. Chem. Phys. 126 (2007) 204108]. The theory is exact for the quantum harmonic oscillator and the free particle, and gives good agreement with the quantum answer for a variety of quartic potentials.
Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.
We consider a repeated quantum interaction model describing a small system $\Hh_S$ in interaction with each one of the identical copies of the chain $\bigotimes_{\N^*}\C^{n+1}$, modeling a heat bath, one after another during the same short time intervals [0,h][0,h][0,h]. We suppose that the repeated quantum interaction Hamiltonian is split in two parts: a free part and an interaction part with time scale of order hhh. After giving the GNS representation, we establish the relation between the time scale hhh and the classical low density limit. We introduce a chemical potential μμμ related to the time hhh as follows: h2=eβμh^2=e^{βμ}h2=eβμ. We further prove that the solution of the associated discrete evolution equation converges strongly, when hhh tends to 0, to the unitary solution of a quantum Langevin equation directed by Poisson processes.