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Cited by 164Cold Atom Physics and Bose-Einstein CondensatesStrong Light-Matter InteractionsQuantum, superfluid, helium dynamics

Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential

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Gardiner, C. W., Zoller, P.·1997·Physical Review A
DOI 10.1103/physreva.55.2902
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Abstract

A quantum kinetic master equation (QKME) for bosonic atoms is formulated. It is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas, and describes the behavior and formation of Bose condensation. The key assumption in deriving the QKME is a Markov approximation for the atomic collision terms. In the present paper the basic structure of the theory is developed, and approximations are stated and justified to delineate the region of validity of the theory. Limiting cases of the QKME include the quantum Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an equation analogous to the Gross-Pitaevskii equation.

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  • 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 [145]

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Research works printed but not linked: 7

  1. [40]C. W. Gardiner, Quantum Noise (Springer-Verlag, Berlin Heidelberg, 1991).
  2. [41]Bose-Einstein Condensation , edited by A. Griffin, D. W. Snoke, and S. Stringari (Cambridge University Press, Cambridge, 1995).
  3. [42]L.W. Nordheim, Proc. Roy. Soc. A, 119 , 689 (1928); F. Bloch, Z. Phys. 52 , 555, (1928); (Initial derivations of the Uehling Uhlenbeck equation); S. Kikuchi and L. Nordheim, Z. Phys. 60 , 652 (1930); (More rigorous derivation of the Uehling
  4. Uhlenbeck equation); E. A. Uehling and G.E. Uhlenbeck, Phys. Rev. 43, 552 (1933) (Application of the Uehling Uhlenbeck equation to transport phenomena in quantum gases.) L. P. Kadanoff and G. Baym, Quantum statistical mechanics : Green's function methods in equilibrium and nonequilibrium (Addison-Wesley, 1962). See also [52] for a more recent derivation, and references to other contemporary work.
  5. [46]E.M. Lifshitz and L.P. Pitaevskii, Statistical Physics Part 2, Landau and Lifshitz Course of Theoretical Physics Vol. 9 (Pergamon Press, Oxford 1980)
  6. [47]J. Dalibard, Y. Castin, and K. Mølmer, Phys. Rev. Lett. 68 , 580 (1992); C. W. Gardiner, A. S. Parkins, and P. Zoller, Phys. Rev. A 46 , 4363 (1992); H.J.Carmichael, An Open Systems Approach to Quantum Optics , Lectures Notes in Physics m18 (Springer, Berlin, 1993).
  7. [49]A.J. Leggett, in Bose-Einstein Condensation , Eds. A. Griffin, D.W. Snoke and S. Stringari (Cambridge University Press, Cambridge 1995), p. 452. see, for example, Ref. [45]

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Authors
Gardiner, C. W., & Zoller, P.
Affiliations
  • Victoria University of Wellington (NZ)
  • Universität Innsbruck (AT)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
1997-04-01
Volume
55
Issue
4
Pages
2902-2921
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.55.2902
OpenAlex
W2561215647
Cited by
164
References
53
Citations by year
2026: 1 · 2025: 1 · 2023: 1 · 2022: 1 · 2021: 3 · 2020: 2 · 2018: 6 · 2017: 25 · 2016: 4 · 2015: 5 · 2014: 4 · 2013: 2 · 2012: 11
FWCI
7.98
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
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 › Strong Light-Matter Interactions
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum, superfluid, helium dynamics
Keywords
Bose-Einstein condensation, weakly interacting Bose gas, Markov approximation, dilute quantum gases, Gross-Pitaevskii equation, quantum kinetic theory

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