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

Journal of Guangxi University of Technology

Time-dependent variational approach to the phonon dispersion relation of the quantum FPU model

Hong Zhong

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The phonon dispersion relation of the quantum FPU model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction.The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction.Under the condition of minimum uncertainty relation,equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation.It is shown that the harmonically coupling strength is strengthened and the width of the phonon band is broadened due to the quantum fluctuations in comparison with those of the classical FPU model.In addition,the harmonically coupling strength and the width of the phonon band increase with increasing the quantum fluctuations and quartic coupling strength.

Related papers

Time-Dependent Variational Approach to the Phonon Dispersion Relation of the Commensurate Quantum Frenkel–Kontorova Model

Hong-Wei Zhong, Yi Ping Tang

The phonon dispersion relation of the commensurate quantum Frenkel–Kontorova model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction for the particles. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the strength of the substrate potential and the phonon excitation gap are reduced due to the quantum fluctuations in comparison with those of the classical model. We also compare our results with those previously obtained by using the path-integral molecular dynamics.

Chinese Physics Letters•Jul 21, 2006•4 citations

Time-dependent variational approach to dispersion relation of the quantum Klein-Gordon model

Hong Zhong

The phonon dispersion relation of the quantum Klein-Gordon model with symmetric single-well anharmonic substrate potential is studied by means of the time-dependent variational principle combined with Hartree-type trial wavefunction for system and Jackiw-Kerman wavefunction for single particle.Under the condition of minimum uncertainty relation,equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation.It is shown that the coefficient of square term of the substrate potential is strengthened and the band gap is broadened due to the quantum fluctuations in comparison with those of the classical model.In addition,the coefficient of square term and the band gap increase with increasing the quantum fluctuations and the coefficient of quartic term of the substrate potential.

Journal of Guangxi University of Technology•Jan 1, 2009•0 citations

Time-Dependent Variational Approach to the Ground State of the Quantum FPU Model

Xiuyan Zhang

The ground state of the quantum FPU model is studied by virtue of Dirac's time-dependent variational principle together with a Hartree-type many-body trial wave function.The single-particle state is taken to be Jackiw-Kerman wave function.The effective classical Hamiltonian for the system and coupled equations for the particle's expectation values and quantum fluctuations are derived.The expectation values,the quantum fluctuations and the energy for the ground state are obtained.

Journal of Guangxi University of Technology•Jan 1, 2011•0 citations

Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

Hong-Wei Zhong, Haiqing Xu, Ping-Hua Huang

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle's expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.

Chinese Physics Letters•Jul 29, 2008•3 citations

Simple variational approach to the quantum Frenkel-Kontorova model

Choon-Lin Ho, Chung-I Chou

We present a simple and complete variational approach to the one-dimensional quantum Frenkel-Kontorova model. Dirac's time-dependent variational principle is adopted together with a Hartree-type many-body trial wave function for the atoms. The single-particle state is assumed to have the Jackiw-Kerman form. We obtain an effective classical Hamiltonian for the system, which is simple enough for a complete numerical solution for the static ground state of the model. Numerical results show that our simple approach captures the essence of the quantum effects first observed in quantum Monte Carlo studies.

arXiv:cond-mat/0008142•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Dec 18, 2000•12 citations

Dissipation Effect of Quantum Fluctuation on Envelope Soliton in Fermi-Pasta-Ulam Model

Dan Liang

In this paper,the time-dependent variational principle(TDVP) is applied to study the one-dimensional Fermi-Pasta-Ulam(FPU) model,and the dynamic equation of particles in the chain is obtained by TDVP.In the semi-quantal study,the considered quantum effect is quantum fluctuation.The Jackiw-Kerman wave function is used for the single particle.The research results show that quantum fluctuation can disperse,blur and even destroy the nonlinear excitation of FPU model,envelope soliton.The effect of quantum fluctuation has the quasi-exponentional relationship with the effective Plank constant.Furthermore,it is found that coupling the effective Plank constant the anharmonic coupling strength has the joint effect on quantum dissipation.The uniquely joint effect may be induced by the unique Hamiltonian of the FPU chain.

Journal of Guangxi Normal University•Jan 1, 2012•0 citations
The phonon dispersion relation of the quantum FPU model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction.The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction.Under the condition of minimum uncertainty relation,equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation.It is shown that the harmonically coupling strength is strengthened and the width of the phonon band is broadened due to the quantum fluctuations in comparison with those of the classical FPU model.In addition,the harmonically coupling strength and the width of the phonon band increase with increasing the quantum fluctuations and quartic coupling strength.
The phonon dispersion relation of the commensurate quantum Frenkel–Kontorova model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction for the particles. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the strength of the substrate potential and the phonon excitation gap are reduced due to the quantum fluctuations in comparison with those of the classical model. We also compare our results with those previously obtained by using the path-integral molecular dynamics.
The phonon dispersion relation of the quantum Klein-Gordon model with symmetric single-well anharmonic substrate potential is studied by means of the time-dependent variational principle combined with Hartree-type trial wavefunction for system and Jackiw-Kerman wavefunction for single particle.Under the condition of minimum uncertainty relation,equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation.It is shown that the coefficient of square term of the substrate potential is strengthened and the band gap is broadened due to the quantum fluctuations in comparison with those of the classical model.In addition,the coefficient of square term and the band gap increase with increasing the quantum fluctuations and the coefficient of quartic term of the substrate potential.
The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle's expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.
We present a simple and complete variational approach to the one-dimensional quantum Frenkel-Kontorova model. Dirac's time-dependent variational principle is adopted together with a Hartree-type many-body trial wave function for the atoms. The single-particle state is assumed to have the Jackiw-Kerman form. We obtain an effective classical Hamiltonian for the system, which is simple enough for a complete numerical solution for the static ground state of the model. Numerical results show that our simple approach captures the essence of the quantum effects first observed in quantum Monte Carlo studies.
In this paper,the time-dependent variational principle(TDVP) is applied to study the one-dimensional Fermi-Pasta-Ulam(FPU) model,and the dynamic equation of particles in the chain is obtained by TDVP.In the semi-quantal study,the considered quantum effect is quantum fluctuation.The Jackiw-Kerman wave function is used for the single particle.The research results show that quantum fluctuation can disperse,blur and even destroy the nonlinear excitation of FPU model,envelope soliton.The effect of quantum fluctuation has the quasi-exponentional relationship with the effective Plank constant.Furthermore,it is found that coupling the effective Plank constant the anharmonic coupling strength has the joint effect on quantum dissipation.The uniquely joint effect may be induced by the unique Hamiltonian of the FPU chain.