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Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitaevskii Breather. PHYSICS 2022. [DOI: 10.3390/physics4010002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored, indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculation, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.
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Edwards JP, Gerber U, Schubert C, Trejo MA, Weber A. Integral transforms of the quantum mechanical path integral: Hit function and path-averaged potential. Phys Rev E 2018; 97:042114. [PMID: 29758645 DOI: 10.1103/physreve.97.042114] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2017] [Indexed: 11/07/2022]
Abstract
We introduce two integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories measuring respectively the relative contribution to the path integral from paths crossing a given spatial point (the hit function) and the likelihood of values of the line integral of the potential along a path in the ensemble (the path-averaged potential).
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Affiliation(s)
- James P Edwards
- Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Apdo. Postal 2-82, C.P. 58040, Morelia, Michoacán, Mexico
| | - Urs Gerber
- Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Apdo. Postal 2-82, C.P. 58040, Morelia, Michoacán, Mexico.,Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de Mexico, A.P. 70-543, C.P. 04510 Ciudad de México, Mexico
| | - Christian Schubert
- Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Apdo. Postal 2-82, C.P. 58040, Morelia, Michoacán, Mexico
| | - Maria Anabel Trejo
- Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Apdo. Postal 2-82, C.P. 58040, Morelia, Michoacán, Mexico.,Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Axel Weber
- Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Apdo. Postal 2-82, C.P. 58040, Morelia, Michoacán, Mexico
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Lemmens LF, Brosens F, Devreese JT. Many-body diffusion and path integrals for identical particles. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:4467-4476. [PMID: 9964779 DOI: 10.1103/physreve.53.4467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Caffarel M, Ceperley DM, Kalos MH. Comment on "Feynman-Kac path-integral calculation of the ground-state energies of atoms". PHYSICAL REVIEW LETTERS 1993; 71:2159. [PMID: 10054598 DOI: 10.1103/physrevlett.71.2159] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Korzeniowski A, Fry JL, Orr DE, Fazleev NG. Korzeniowski et al. reply. PHYSICAL REVIEW LETTERS 1993; 71:2160-2161. [PMID: 10054599 DOI: 10.1103/physrevlett.71.2160] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Foulkes WM. Comment on "Feynman-Kac path-integral calculation of the ground-state energies of atoms". PHYSICAL REVIEW LETTERS 1993; 71:2158. [PMID: 10054597 DOI: 10.1103/physrevlett.71.2158] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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