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

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Quantum-mechanical and quasiclassical dynamics of coupled quasiparticle-boson systems

R. Steib, J. L. Schoendorff, H. J. Korsch, P. Reineker

Published Jun 1, 1998• 9 citations
Publisher

Abstract

Statistical and dynamical properties of a quasiparticle coupled to polarization vibrations in a dimer model are investigated using a full quantum-mechanical approach. The propagation of the system is described in terms of spin-boson coherent states and compared to various quasiclassical descriptions of the system. The spectrum of the energy eigenvalues and the level spacing distributions of the system are calculated and turn out to be almost regular, especially in the strong coupling limit. It is demonstrated that the usual quasiclassical approach to this problem is not quite satisfactory. This is because the quantum fluctuations in the spin variable give rise to entangled states and correlations which hence should be included in a quasiclassical description. We show that a limited but satisfactory quasiclassical approximation may be given using a suitable integrable reference Hamiltonian.

DOI
10.1103/physreve.57.6534

Related papers

Mixed quantum-classical versus full quantum dynamics: Coupled quasiparticle-oscillator system

Holger Schanz, Bernd Esser

The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu- tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn- amical Born-Oppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.

arXiv:chao-dyn/9609018•Physical Review A•May 1, 1997•30 citations

A semiclassical self-consistent-field approach to dissipative dynamics: The spin–boson problem

Gerhard Stock

A semiclassical time-dependent self-consistent-field approach for the description of dissipative quantum phenomena is proposed. The total density operator is approximated by a semiclassical ansatz, which couples the system degrees of freedom to the bath degrees of freedom in a self-consistent manner, and is thus in the spirit of a classical-path description. The capability of the approach is demonstrated by comparing semiclassical calculations for a spin–boson model with an Ohmic bath to exact path-integral calculations. It is shown that the semiclassical model nicely reproduces the complex dissipative behavior of the spin–boson model for a large range of model parameters. The validity and accuracy of the semiclassical approach is discussed in some detail. It is shown that the method is essentially based on the assumption of complete randomization of nuclear phases. In particular, the assumption of phase randomization allows one to perform the trace over the bath variables through quasiclassical sampling of the nuclear initial conditions without invoking any further approximation.

The Journal of Chemical Physics•Jul 22, 1995•113 citations

Spin–spin model for two-level system/bath problems: A numerical study

Andrei A. Golosov, Stefan I. Tsonchev, Philip Pechukas +1 more

We study a new model for treating quantum dissipative systems, in which the bath is modeled as a collection of spins coupled to the system of interest. We develop a quasiclassical method to study this model, approximating the quantum Heisenberg equations by the classical ones, supplemented with stochastic initial conditions carefully chosen so that the results obtained from the classical equations are as close as possible to the quantum results. Using this method we compare the dynamics of such a spin–spin system with that of a spin–boson system, in which the bath is modeled as a collection of harmonic oscillators. We verify numerically that when the system-bath coupling is spread over many bath spins (the Brownian motion limit), the spin–spin model can be mapped on the spin–boson model (although with a temperature dependent spectral density). We also demonstrate that the two dissipative models are qualitatively very different in a non-Brownian motion regime.

The Journal of Chemical Physics•Dec 8, 1999•22 citations

New applications and insights from strongly coupled open quantum systems

C Hogg (13538632)

An understanding of strongly coupled open quantum systems is crucial for the realisation of many of today’s emerging quantum technologies. However, actually simulating a quantum system that strongly interacts, or couples, with its environment is no easy task. This thesis tackles a number of topics in the field of strongly coupled open quantum systems. Given the computational challenges of solving the full open system dynamics, we first discuss how and why a quasiclassical stochastic approach can be used to simulate the dynamics of a quantum harmonic oscillator that is strongly coupled to its environment. We build upon the established analytical agreement by implementing the quasiclassical stochastic case numerically in the SpiDy.jl Julia package. Motivated by the applications to magnetic modelling, we then solve the full open quantum systems model for a single spin coupled arbitrarily strongly to multiple heat baths. In doing so, we find that the presence of multiple baths can actually increase the system-environment entanglement in the steady state. We also compare this to a fully classical approach and find that, for isotropic environmental coupling, the environment-induced effects in the equilibrium state only appear quantum mechanically. Finally, we couple these two topics together by considering the quasiclassical stochastic simulation of a single quantum spin, helping to understand the regimes of validity beyond the linear harmonic oscillator. This is with the larger aim to eventually be able to encode quantum effects into more realistic systems, such as those that describe magnetic materials.

•Aug 19, 2025•0 citations

Quasiclassical approximation for the spin-boson Hamiltonian with counterrotating terms

G. A. Finney, Julio R. Gea-Banacloche

We derive quasiclassical (approximately factorizable) trajectories for the spin-boson Hamiltonian without the rotating-wave approximation (RWA) and show how they may be used to calculate the evolution of the fully quantized system when the initial state of the oscillator (boson field) is a coherent state with sufficiently large amplitude. We give a general prescription to obtain such trajectories for other systems. We study how well-known features of the model in the RWA are modified by the counterrotating terms and explore some of the new phenomenology introduced by these terms.

Physical Review A•Sep 1, 1994•25 citations

Dynamical behavior of the dissipative two-state system

Klaus Voelker

We investigate the dynamical correlation function of a quantum-mechanical two-state system that is coupled to a bosonic heat bath, utilizing the equivalence between the spin-boson Hamiltonian and the ${1/r}^{2}$ Ising model. The imaginary-time correlation function is obtained from Monte Carlo simulations on the Ising system and then continued to real time by a Pad\'e approximation. In the unbiased system, the transition from oscillatory to strongly damped behavior is found to occur at a coupling strength close to $\ensuremath{\alpha}=1/2$. The biased system favors coherent relaxation and displays a significantly larger crossover value ${\ensuremath{\alpha}}_{c}.$ We introduce the quasiparticle picture to describe the relevant behavior at intermediate time scales. Within this approximation, we map out phase diagrams for the unbiased and biased systems.

arXiv:cond-mat/9712080•Physical review. B, Condensed matter•Jul 15, 1998•37 citations
Statistical and dynamical properties of a quasiparticle coupled to polarization vibrations in a dimer model are investigated using a full quantum-mechanical approach. The propagation of the system is described in terms of spin-boson coherent states and compared to various quasiclassical descriptions of the system. The spectrum of the energy eigenvalues and the level spacing distributions of the system are calculated and turn out to be almost regular, especially in the strong coupling limit. It is demonstrated that the usual quasiclassical approach to this problem is not quite satisfactory. This is because the quantum fluctuations in the spin variable give rise to entangled states and correlations which hence should be included in a quasiclassical description. We show that a limited but satisfactory quasiclassical approximation may be given using a suitable integrable reference Hamiltonian.
The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu- tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn- amical Born-Oppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.
A semiclassical time-dependent self-consistent-field approach for the description of dissipative quantum phenomena is proposed. The total density operator is approximated by a semiclassical ansatz, which couples the system degrees of freedom to the bath degrees of freedom in a self-consistent manner, and is thus in the spirit of a classical-path description. The capability of the approach is demonstrated by comparing semiclassical calculations for a spin–boson model with an Ohmic bath to exact path-integral calculations. It is shown that the semiclassical model nicely reproduces the complex dissipative behavior of the spin–boson model for a large range of model parameters. The validity and accuracy of the semiclassical approach is discussed in some detail. It is shown that the method is essentially based on the assumption of complete randomization of nuclear phases. In particular, the assumption of phase randomization allows one to perform the trace over the bath variables through quasiclassical sampling of the nuclear initial conditions without invoking any further approximation.
We study a new model for treating quantum dissipative systems, in which the bath is modeled as a collection of spins coupled to the system of interest. We develop a quasiclassical method to study this model, approximating the quantum Heisenberg equations by the classical ones, supplemented with stochastic initial conditions carefully chosen so that the results obtained from the classical equations are as close as possible to the quantum results. Using this method we compare the dynamics of such a spin–spin system with that of a spin–boson system, in which the bath is modeled as a collection of harmonic oscillators. We verify numerically that when the system-bath coupling is spread over many bath spins (the Brownian motion limit), the spin–spin model can be mapped on the spin–boson model (although with a temperature dependent spectral density). We also demonstrate that the two dissipative models are qualitatively very different in a non-Brownian motion regime.
An understanding of strongly coupled open quantum systems is crucial for the realisation of many of today’s emerging quantum technologies. However, actually simulating a quantum system that strongly interacts, or couples, with its environment is no easy task. This thesis tackles a number of topics in the field of strongly coupled open quantum systems. Given the computational challenges of solving the full open system dynamics, we first discuss how and why a quasiclassical stochastic approach can be used to simulate the dynamics of a quantum harmonic oscillator that is strongly coupled to its environment. We build upon the established analytical agreement by implementing the quasiclassical stochastic case numerically in the SpiDy.jl Julia package. Motivated by the applications to magnetic modelling, we then solve the full open quantum systems model for a single spin coupled arbitrarily strongly to multiple heat baths. In doing so, we find that the presence of multiple baths can actually increase the system-environment entanglement in the steady state. We also compare this to a fully classical approach and find that, for isotropic environmental coupling, the environment-induced effects in the equilibrium state only appear quantum mechanically. Finally, we couple these two topics together by considering the quasiclassical stochastic simulation of a single quantum spin, helping to understand the regimes of validity beyond the linear harmonic oscillator. This is with the larger aim to eventually be able to encode quantum effects into more realistic systems, such as those that describe magnetic materials.
We derive quasiclassical (approximately factorizable) trajectories for the spin-boson Hamiltonian without the rotating-wave approximation (RWA) and show how they may be used to calculate the evolution of the fully quantized system when the initial state of the oscillator (boson field) is a coherent state with sufficiently large amplitude. We give a general prescription to obtain such trajectories for other systems. We study how well-known features of the model in the RWA are modified by the counterrotating terms and explore some of the new phenomenology introduced by these terms.
We investigate the dynamical correlation function of a quantum-mechanical two-state system that is coupled to a bosonic heat bath, utilizing the equivalence between the spin-boson Hamiltonian and the 1/r2{1/r}^{2}1/r2 Ising model. The imaginary-time correlation function is obtained from Monte Carlo simulations on the Ising system and then continued to real time by a Pad\'e approximation. In the unbiased system, the transition from oscillatory to strongly damped behavior is found to occur at a coupling strength close to $\ensuremath{\alpha}=1/2$. The biased system favors coherent relaxation and displays a significantly larger crossover value ${\ensuremath{\alpha}}_{c}.$ We introduce the quasiparticle picture to describe the relevant behavior at intermediate time scales. Within this approximation, we map out phase diagrams for the unbiased and biased systems.