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

arXiv:nucl-th/9501020 · Physical Review Letters

Incorporation of Quantum Statistical Features in Molecular Dynamics

Akira Ohnishi A, Jørgen Randrup

Published Jul 24, 1995• 30 citations
arXivHTMLPDF

Abstract

We formulate a method for incorporating quantum fluctuations into molecular-dynamics simulations of many-body systems, such as those employed for energetic nuclear collision processes. Based on Fermi's golden rule, we allow spontaneous transitions to occur between the wave packets which are not energy eigenstates. The ensuing diffusive evolution in the space of the wave packet parameters exhibits appealing physical properties, including relaxation towards quantum statistical equilibrium.

DOI
10.1103/physrevlett.75.596

Related papers

Quantum Monte Carlo for molecules

William A. Lester, PETER J. REYNOLDS

An alternative approach to conventional quantum chemistry techniques for molecular studies is described.This approach uses the quantum Monte Carlo method, which was developed and used primarily in nuclear and condensed-matter physics.In this approach the many-body Schrodinger equation is re-interpreted as a diffusion equation.Simulation of the appropriate random walk process allows one to calculate expectation values of molecular properties.In principle these expectation values can be calculated exactly, subject only to statistical errors (which may be made arbitrarily small).In preliminary work on small molecules (H 2 , LiH, Li 2 , and H 2 0), we use a simple but accurate approximation to ease the treatment of Fermi statistics.In that approximation, the calculated total energy remains an upper bound to the true energy.How good the bound is, as well as the magnitude of the statistical error, depends on the quality of an "importance function" which guides the diffusion into more probable regions of phase space.With relatively simple importance functions, we obtain from 75-100% of the correlation energy of the above-mentioned molecules.

California Univ., Berkeley Report•May 1, 1983•3 citations

Fermi Molecular Dynamics

L. Wilets, William A Beck

classical many body models supplemented by repulsive momentum-dependent potentials to simulate the Pauli and Heisenberg principles have been use with some success for nuclear and atomic bound state and collision problems. They are capable of describing mean ground state properties, hydrodynamics, shocks (if warranted by the physics), viscosity, correlations, clustering, fragmentation, etc. We have become interested in the Feldmeier Gaussian packet formulation since it is based on a variational principle using trial wave functions. We discuss some limitations of the model and discuss further directions of investigation.

•Jan 1, 1991•0 citations

Simulation of quantum processes using entangled trajectory molecular dynamics

Arnaldo Donoso, Yujun Zheng, Craig C. Martens

In this paper, we describe a new method for simulating quantum processes using classical-like molecular dynamics. The approach is based on solving the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories in phase space. The nonlocality of quantum mechanics is incorporated in the trajectory representation as nonclassical interactions between the members of the ensemble, leading to an entanglement of their evolution. The statistical independence of the individual trajectories making up an ensemble in the classical limit is lost when quantum effects are included, and the entire state of the system must be propagated as a unified whole. We develop the formalism and its numerical implementation, and illustrate its application on two model problems of quantum mechanical tunneling: escape from a metastable well and wave packet penetration of the Eckhart barrier.

The Journal of Chemical Physics•Aug 21, 2003•85 citations

Quantum Enhancement of Thermalization

Yulong Qiao, Frank Großmann, Peter Schlagheck +1 more

Equilibrium properties of many-body systems with a large number of degrees of freedom are generally expected to be described by statistical mechanics. Such expectations are closely tied to the observation of thermalization, as manifested through equipartition in time-dependent observables, which takes place both in quantum and classical systems but may look very different in comparison. By studying the dynamics of individual lattice site populations in ultracold bosonic gases, we show that the process of relaxation toward equilibrium in a quantum system can be orders of magnitude faster than in its classical counterpart. Classical chaos quantifiers reveal that this is due to a wave packet in a quantum system being able to escape regions of inefficient classical transport by a mechanism akin to tunneling. Since the presented phenomenon takes place in a broad parameter range and persists in weakly disordered systems, we expect that it occurs in a variety of many-body systems and is amenable to direct experimental verification in state-of-the-art quantum simulation platforms.

arXiv:2410.06039•Physical Review Letters•Jul 21, 2025•5 citations

Using the wavelet transform to separate scales in the Schrödinger equation and subsequently derive the Boltzmann equation

A. P. Meilakhs

Here we continue our investigation aimed at the derivation of the Boltzmann equation from the first principles of quantum mechanics. The key difficulty that we overcome in this manuscript is the incompatibility between traditional methods employed in the derivation of classical mechanics from quantum mechanics and methods used to describe transitions between quantum states due to interaction. Here we use a novel technique that is similar to the wavelet transform method that originally appeared in the context of signal processing. With this method, we can simultaneously work with slowly varying potentials that give rise to classical-like wave-function behaviour, motion along a prescribed trajectory, and sharp potentials that lead to behaviour that is best understood in terms of quantum transitions. Working with smooth potentials in this framework, we derive the Liouville equation from the Schrödinger equation. When using this method for sharp potentials, we naturally obtain the description of system dynamics in terms of a transition-rate matrix. The transition rates between system states, which characterize the process, are determined by Fermi's golden rule. We observe that, through the Liouville equation, we can deduce the non-collision part of the Boltzmann equation, and that, through the transition-rate matrix, we can deduce the collision integral. We combine the results to derive the Boltzmann equation, the main formula of physical kinetics.

quant-pharXiv:2511.21601•Nov 27, 2025•0 citations

Molecular dynamics with quantum fluctuations

Ionuţ Georgescu, Vladimir A. Mandelshtam

A quantum dynamics approach, called Gaussian molecular dynamics, is introduced. As in the centroid molecular dynamics, the $N$-body quantum system is mapped to an $N$-body classical system with an effective Hamiltonian arising within the variational Gaussian wave-packet approximation. The approach is exact for the harmonic oscillator and for the high-temperature limit, accurate in the short-time limit and is computationally very efficient.

Physical Review B•Sep 9, 2010•12 citations
We formulate a method for incorporating quantum fluctuations into molecular-dynamics simulations of many-body systems, such as those employed for energetic nuclear collision processes. Based on Fermi's golden rule, we allow spontaneous transitions to occur between the wave packets which are not energy eigenstates. The ensuing diffusive evolution in the space of the wave packet parameters exhibits appealing physical properties, including relaxation towards quantum statistical equilibrium.
An alternative approach to conventional quantum chemistry techniques for molecular studies is described.This approach uses the quantum Monte Carlo method, which was developed and used primarily in nuclear and condensed-matter physics.In this approach the many-body Schrodinger equation is re-interpreted as a diffusion equation.Simulation of the appropriate random walk process allows one to calculate expectation values of molecular properties.In principle these expectation values can be calculated exactly, subject only to statistical errors (which may be made arbitrarily small).In preliminary work on small molecules (H 2 , LiH, Li 2 , and H 2 0), we use a simple but accurate approximation to ease the treatment of Fermi statistics.In that approximation, the calculated total energy remains an upper bound to the true energy.How good the bound is, as well as the magnitude of the statistical error, depends on the quality of an "importance function" which guides the diffusion into more probable regions of phase space.With relatively simple importance functions, we obtain from 75-100% of the correlation energy of the above-mentioned molecules.
classical many body models supplemented by repulsive momentum-dependent potentials to simulate the Pauli and Heisenberg principles have been use with some success for nuclear and atomic bound state and collision problems. They are capable of describing mean ground state properties, hydrodynamics, shocks (if warranted by the physics), viscosity, correlations, clustering, fragmentation, etc. We have become interested in the Feldmeier Gaussian packet formulation since it is based on a variational principle using trial wave functions. We discuss some limitations of the model and discuss further directions of investigation.
In this paper, we describe a new method for simulating quantum processes using classical-like molecular dynamics. The approach is based on solving the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories in phase space. The nonlocality of quantum mechanics is incorporated in the trajectory representation as nonclassical interactions between the members of the ensemble, leading to an entanglement of their evolution. The statistical independence of the individual trajectories making up an ensemble in the classical limit is lost when quantum effects are included, and the entire state of the system must be propagated as a unified whole. We develop the formalism and its numerical implementation, and illustrate its application on two model problems of quantum mechanical tunneling: escape from a metastable well and wave packet penetration of the Eckhart barrier.
Equilibrium properties of many-body systems with a large number of degrees of freedom are generally expected to be described by statistical mechanics. Such expectations are closely tied to the observation of thermalization, as manifested through equipartition in time-dependent observables, which takes place both in quantum and classical systems but may look very different in comparison. By studying the dynamics of individual lattice site populations in ultracold bosonic gases, we show that the process of relaxation toward equilibrium in a quantum system can be orders of magnitude faster than in its classical counterpart. Classical chaos quantifiers reveal that this is due to a wave packet in a quantum system being able to escape regions of inefficient classical transport by a mechanism akin to tunneling. Since the presented phenomenon takes place in a broad parameter range and persists in weakly disordered systems, we expect that it occurs in a variety of many-body systems and is amenable to direct experimental verification in state-of-the-art quantum simulation platforms.
Here we continue our investigation aimed at the derivation of the Boltzmann equation from the first principles of quantum mechanics. The key difficulty that we overcome in this manuscript is the incompatibility between traditional methods employed in the derivation of classical mechanics from quantum mechanics and methods used to describe transitions between quantum states due to interaction. Here we use a novel technique that is similar to the wavelet transform method that originally appeared in the context of signal processing. With this method, we can simultaneously work with slowly varying potentials that give rise to classical-like wave-function behaviour, motion along a prescribed trajectory, and sharp potentials that lead to behaviour that is best understood in terms of quantum transitions. Working with smooth potentials in this framework, we derive the Liouville equation from the Schrödinger equation. When using this method for sharp potentials, we naturally obtain the description of system dynamics in terms of a transition-rate matrix. The transition rates between system states, which characterize the process, are determined by Fermi's golden rule. We observe that, through the Liouville equation, we can deduce the non-collision part of the Boltzmann equation, and that, through the transition-rate matrix, we can deduce the collision integral. We combine the results to derive the Boltzmann equation, the main formula of physical kinetics.
A quantum dynamics approach, called Gaussian molecular dynamics, is introduced. As in the centroid molecular dynamics, the NNN-body quantum system is mapped to an NNN-body classical system with an effective Hamiltonian arising within the variational Gaussian wave-packet approximation. The approach is exact for the harmonic oscillator and for the high-temperature limit, accurate in the short-time limit and is computationally very efficient.