Quantum kinetic theory. II. Simulation of the quantum Boltzmann master equation
Open accessAbstract
We present results of simulations of a quantum Boltzmann master equation (QBME) describing the kinetics of a dilute Bose gas confined in a trapping potential in the regime of Bose condensation. The QBME is the simplest version of a quantum kinetic master equation derived in previous work. We consider two cases of trapping potentials: a three-dimensional square-well potential with periodic boundary conditions and an isotropic harmonic oscillator. We discuss the stationary solutions and relaxation to equilibrium. In particular, we calculate particle distribution functions, fluctuations in the occupation numbers, the time between collisions, and the mean occupation numbers of the one-particle states in the regime of onset of Bose condensation.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In regimes whose properties are difficult to deduce by classical methods, many relevant models become hypersensitive to perturbations, and even small levels of noise may spoil completely the results of the quantum simulation.
“In these regimes, however, many relevant models become hypersensitive to perturbations [145, 146], and even small levels of noise may spoil completely the results of the quantum simulation.”
From Can one trust quantum simulators? (2012) · cites this paper as [146]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
JONES, J. E. (1971) · Nature · doi:10.1038/233571b0 · Cited by 956 · see citing works
Evaporative Cooling of Trapped Atoms
Ketterle, W., & van Druten, N. J. (1996) · Advances in atomic, molecular, and optical physics · doi:10.1016/s1049-250x(08)60101-9 · Cited by 597 · see citing works
Starzak, M. E. (1989) · Springer eBooks · doi:10.1007/978-1-4899-2082-9_7 · Cited by 474 · see citing works
Bose-Einstein condensation in an external potential
Bagnato, V. S., Pritchard, D. E., & Kleppner, D. (1987) · Physical Review A · doi:10.1103/physreva.35.4354 · Cited by 437 · see citing works
Kinetic theory of the evaporative cooling of a trapped gas
Luiten, O. J., Reynolds, M. W., & Walraven, J. T. M. (1996) · Physical Review A · doi:10.1103/physreva.53.381 · Cited by 328 · see citing works
SEMIKOZ, D. V., & Tkachev, I. I. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.3093 · Cited by 203 · see citing works
Gardiner, C. W., & Zoller, P. (1997) · Physical Review A · doi:10.1103/physreva.55.2902 · Cited by 164 · see citing works
Self-citationHolland, M., Burnett, K. R., Gardiner, C. W., Cirac, J. I., & Zoller, P. (1996) · Physical Review A · doi:10.1103/physreva.54.r1757 · Cited by 150 · see citing works
Self-citationMicrocanonical fluctuations of a Bose system’s ground state occupation number
Großmann, S., & Holthaus, M. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.54.3495 · Cited by 100 · see citing works
Bose-Einstein condensation: Kinetic evolution obtained from simulated trajectories
Holland, M., Williams, J. H., & Cooper, J. (1997) · Physical Review A · doi:10.1103/physreva.55.3670 · Cited by 65 · see citing works
Trajectory simulation of kinetic equations for classical systems
Holland, M., Williams, J., Coakley, K. J., et al. (1996) · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · doi:10.1088/1355-5111/8/3/019 · Cited by 25 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Can one trust quantum simulators?
Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I., & Lewenstein, M. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/8/082401 · Cited by 315 · see citing works
Quantum kinetic theory. III. Quantum kinetic master equation for strongly condensed trapped systems
Gardiner, C. W., & Zoller, P. (1998) · Physical Review A · doi:10.1103/physreva.58.536 · Cited by 108 · see citing works
Self-citationJaksch, D., Gardiner, C. W., Gheri, K. M., & Zoller, P. (1998) · Physical Review A · doi:10.1103/physreva.58.1450 · Cited by 74 · see citing works
Self-citation
- Authors
- Jaksch, D., Gardiner, C. W., & Zoller, P.
- Affiliations
- Universität Innsbruck (AT)
- Victoria University of Wellington (NZ)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1997-07-01
- Volume
- 56
- Issue
- 1
- Pages
- 575-586
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1982682321
- Cited by
- 128
- References
- 11
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 3 · 2023: 1 · 2022: 2 · 2021: 2 · 2020: 4 · 2018: 5 · 2017: 26 · 2016: 2 · 2015: 2 · 2014: 1 · 2013: 2 · 2012: 6
- FWCI
- 7.49
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Marsden Fund
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum, superfluid, helium dynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
- Keywords
- quantum kinetic theory, Bose-Einstein condensation, dilute Bose gas, square-well potential, isotropic harmonic oscillator, stationary solutions, relaxation to equilibrium, particle distribution function
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
