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

International Journal of Modern Physics B

PATH INTEGRAL DERIVATION OF THE GROUND STATE ENERGY OF THE INTERACTING PARTICLES IN A HARMONIC TRAP

K. Tayanasanti, Virulh Sa‐Yakanit

Published Dec 30, 2003• 0 citations
Publisher

Abstract

We show within the framework of Variational Path Integration that the density matrix and the ground state energy of the trapped Bose gas can be obtained in a simple way and it is in agreement with the result obtained by the variational Gross–Pitaevskii equation. The advantage of this method is the analytical result can be found for various forms of interaction between particles.

DOI
10.1142/s0217979203023215

Related papers

Solution of the ground state wave function of Bose-condensed gas in a harmonic trap based on the Gross-Pitaevskii function

Xu Zhi-Jun, Shi Jian-Qing, Li Zhen +2 more

Based on the Gross-Pitaevskii(G-P) energy functional and variational method, we present a new method to find the ground state wave function for Bose-condensed gas in a harmonic trap at zero temperature. With this method we are able to find the analytic expression of ground state wave function and explore the relevant quantities, such as energy, chemical potential and so on. These results agree well with previous ground state numerical solutions of the G-P equation given by Dalfovo et al. Under the large number of particles N limit for repulsive interaction, our results and Thomas-Fermi approximation model approach to reaching unanimity. This new method is simple compared to other methods used to solve numerically the G-P equation, and one can obtained the analytic and reliable results.

Acta Physica Sinica•Jan 1, 2006•1 citation

Ground State Properties for Bose-Condensed Gas in Anisotropic Traps

Xu Zhi-Jun, Haibin Li, Xin Xiao-Tian +2 more

Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross–Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 (1996) 2477] This new method is simple compared to other methods used to solve numerically the Gross–Pitaevskii equation, and one can obtain analytic and reliable results.

Chinese Physics Letters•May 30, 2006•2 citations

Determination of ground state energy and effective mass of bose systems in random potentials by path integration method

Wattana Lim, Wichit Sritrakool, Virulh Sa-yakanit

We apply Feynman's path integral theory to study Bose-Einstein condensates in a double well potential and in a random potential. The main idea of this thesis is to perform the mean field approximation in two body interaction by the path integral approach. Bose particles are confined in the double well which is taken as a harmonic potential with Gaussian or cosine barrier. Performing the variational calculations we obtain analytical results of the ground state energy, wave functions, and overlap integrals. The overlap integrals enable us to calculate the tunneling rates which are in good agreement with numerical values for the two-mode model of Gross-Pitaevskii's equation. We also consider the model of a Bose system consisting of N particles with finite interacting pair potentials under the influence of random potentials. The porosity or nonhomogeneity of the system can be represented by the density of porosity with amplitude of the fluctuation, and a correlation length. We obtain analytical results of the effective mass and the ground state energy which are in good agreement with that of Bugoliubov approach. The propagator of the system is used to calculate the partition function, specific heat, the critical temperature, condensate density, and the superfluid density of the system.

•Jan 1, 2007•0 citations

Bose-Einstein condensates in multiple well potentials from a variational path integral

Wattana Ratismith, Holger Hauptmann, Walter T. Strunz

We apply a path integral variational approach to obtain analytical expressions for condensate wave functions of an ultracold, interacting trapped Bose gases. As in many recent experiments, the particles are confined in a 1D or 3D harmonic oscillator trap which is superimposed by a periodic potential in one direction. Based on the first order cumulant expansion with respect to a harmonic trial action, and emplyoing a mean-field approximation, optimal variational parameters are obtained by minimizing an analytical expression for the ground state energy. Our largely analytical results for energy and condensate wave function are in good agreement with fully numerical calculations based on the Gross-Pitaevskii equation.

arXiv:1403.1474•Mar 6, 2014•0 citations

Path integration approach to charged bosons in an isotropic trap

Chakrit Nualchimplee, Virulh Sa-yakanit

In this thesis, the case of charged bosons confined in an isotropic magnetic trap is studied by using Feynman path integration. We show that the upper bound of the ground state energy can be evaluated by applying the variational path integral technique. Consequently, the approximated density matrix and wavefunction are obtained. The ground state energy is then compared with the result obtained by Ginzburg-Pitaevskii-Gross approach. it is shown that our result agrees with such an approach. Furthermore, from our result, when we neglect the effect of screened Coulomb potential in the ground state energy of the screened Coulomb case, the ground state energy of the Coulomb potential arises as expected.

•Jan 1, 2001•0 citations

GROUND STATE ENERGY OF BOSE-EINSTEIN CONDENSATION IN A DISORDERED SYSTEM

Virulh Sa‐Yakanit, Wattana Lim

A modeled Bose system consisting of N particles with two-body interaction confined within volume V under inhomogeneity of the system is investigated using the Feynman path integral approach. The two-body interaction energy is assumed to be dependent on the two-parameter interacting strength a and the correlation length l. The inhomogeneity of the system or the porosity can be represented as density [Formula: see text] with interacting strength b and correlation length L. The mean field approximation on the two-body interaction in the Feynman path integrals representation is performed to obtain the one-body interaction. This approximation is equivalent to the Hartree approximation in the many-body electron gas problem. This approximation has shown that the calculation can be reduced to the effective one-body propagator. Performing the variational calculations, we obtain analytical results of the ground state energy which is in agreement with that from Bugoliubov's approach.

International Journal of Modern Physics B•Oct 20, 2008•5 citations
We show within the framework of Variational Path Integration that the density matrix and the ground state energy of the trapped Bose gas can be obtained in a simple way and it is in agreement with the result obtained by the variational Gross–Pitaevskii equation. The advantage of this method is the analytical result can be found for various forms of interaction between particles.
Based on the Gross-Pitaevskii(G-P) energy functional and variational method, we present a new method to find the ground state wave function for Bose-condensed gas in a harmonic trap at zero temperature. With this method we are able to find the analytic expression of ground state wave function and explore the relevant quantities, such as energy, chemical potential and so on. These results agree well with previous ground state numerical solutions of the G-P equation given by Dalfovo et al. Under the large number of particles N limit for repulsive interaction, our results and Thomas-Fermi approximation model approach to reaching unanimity. This new method is simple compared to other methods used to solve numerically the G-P equation, and one can obtained the analytic and reliable results.
Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross–Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 (1996) 2477] This new method is simple compared to other methods used to solve numerically the Gross–Pitaevskii equation, and one can obtain analytic and reliable results.
We apply Feynman's path integral theory to study Bose-Einstein condensates in a double well potential and in a random potential. The main idea of this thesis is to perform the mean field approximation in two body interaction by the path integral approach. Bose particles are confined in the double well which is taken as a harmonic potential with Gaussian or cosine barrier. Performing the variational calculations we obtain analytical results of the ground state energy, wave functions, and overlap integrals. The overlap integrals enable us to calculate the tunneling rates which are in good agreement with numerical values for the two-mode model of Gross-Pitaevskii's equation. We also consider the model of a Bose system consisting of N particles with finite interacting pair potentials under the influence of random potentials. The porosity or nonhomogeneity of the system can be represented by the density of porosity with amplitude of the fluctuation, and a correlation length. We obtain analytical results of the effective mass and the ground state energy which are in good agreement with that of Bugoliubov approach. The propagator of the system is used to calculate the partition function, specific heat, the critical temperature, condensate density, and the superfluid density of the system.
We apply a path integral variational approach to obtain analytical expressions for condensate wave functions of an ultracold, interacting trapped Bose gases. As in many recent experiments, the particles are confined in a 1D or 3D harmonic oscillator trap which is superimposed by a periodic potential in one direction. Based on the first order cumulant expansion with respect to a harmonic trial action, and emplyoing a mean-field approximation, optimal variational parameters are obtained by minimizing an analytical expression for the ground state energy. Our largely analytical results for energy and condensate wave function are in good agreement with fully numerical calculations based on the Gross-Pitaevskii equation.
In this thesis, the case of charged bosons confined in an isotropic magnetic trap is studied by using Feynman path integration. We show that the upper bound of the ground state energy can be evaluated by applying the variational path integral technique. Consequently, the approximated density matrix and wavefunction are obtained. The ground state energy is then compared with the result obtained by Ginzburg-Pitaevskii-Gross approach. it is shown that our result agrees with such an approach. Furthermore, from our result, when we neglect the effect of screened Coulomb potential in the ground state energy of the screened Coulomb case, the ground state energy of the Coulomb potential arises as expected.
A modeled Bose system consisting of N particles with two-body interaction confined within volume V under inhomogeneity of the system is investigated using the Feynman path integral approach. The two-body interaction energy is assumed to be dependent on the two-parameter interacting strength a and the correlation length l. The inhomogeneity of the system or the porosity can be represented as density [Formula: see text] with interacting strength b and correlation length L. The mean field approximation on the two-body interaction in the Feynman path integrals representation is performed to obtain the one-body interaction. This approximation is equivalent to the Hartree approximation in the many-body electron gas problem. This approximation has shown that the calculation can be reduced to the effective one-body propagator. Performing the variational calculations, we obtain analytical results of the ground state energy which is in agreement with that from Bugoliubov's approach.