The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Phase space representation of quantum dynamics
Open accessAbstract
Abstract We discuss a phase space representation of quantum dynamics of systems with many degrees of freedom. This representation is based on a perturbative expansion in quantum fluctuations around one of the classical limits. We explicitly analyze expansions around three such limits: (i) corpuscular or Newtonian limit in the coordinate–momentum representation, (ii) wave or Gross–Pitaevskii limit for interacting bosons in the coherent state representation, and (iii) Bloch limit for the spin systems. We discuss both the semiclassical (truncated Wigner) approximation and further quantum corrections appearing in the form of either stochastic quantum jumps along the classical trajectories or the nonlinear response to such jumps. We also discuss how quantum jumps naturally emerge in the analysis of non-equal time correlation functions. This representation of quantum dynamics is closely related to the phase space methods based on the Wigner–Weyl quantization and to the Keldysh technique. We show how such concepts as the Wigner function, Weyl symbol, Moyal product, Bopp operators, and others automatically emerge from the Feynmann's path integral representation of the evolution in the Heisenberg representation. We illustrate the applicability of this expansion with various examples mostly in the context of cold atom systems including sine-Gordon model, one- and two-dimensional Bose–Hubbard model, Dicke model and others.
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Citations
Cites
On the Quantum Correction For Thermodynamic Equilibrium
Wigner, E. (1932) · Physical Review · doi:10.1103/physrev.40.749 · Cited by 9,283
Non-adiabatic crossing of energy levels
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Quantum mechanics as a statistical theory
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Quantum annealing in the transverse Ising model
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Trotzky, S., Cheinet, P., Fölling, S., Feld, M., Schnorrberger, U., Rey, A. M., Polkovnikov, A., Demler, E. A., Lukin, M. D., & Bloch, I. (2008) · Science · doi:10.1126/science.1150841 · Cited by 698
Self-citationDynamical quantum noise in trapped Bose-Einstein condensates
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Decoherence, chaos, and the correspondence principle
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Self-citation
Cited by
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems
Polkovnikov, A., Sengupta, K., Silva, A., & Vengalattore, M. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.863 · Cited by 2,562
Self-citationFrom quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
D'Alessio, L., Kafri, Y., Polkovnikov, A., & Rigol, M. (2016) · Advances in Physics · doi:10.1080/00018732.2016.1198134 · Cited by 2,330
Self-citationGeometry and non-adiabatic response in quantum and classical systems
Kolodrubetz, M., Sels, D., Mehta, P., & Polkovnikov, A. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.07.001 · Cited by 326
Self-citationQuantum Many-Body Dynamics in Optomechanical Arrays
Ludwig, M., & Marquardt, F. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.073603 · Cited by 321
Quantum walk of two interacting bosons
Lahini, Y., Verbin, M., Huber, S. D., Bromberg, Y., Pugatch, R., & Silberberg, Y. (2012) · Physical Review A · doi:10.1103/physreva.86.011603 · Cited by 99
Metadata
- Authors
- Polkovnikov, A.
- Venue
- Annals of Physics
- Publisher
- Elsevier BV
- Published
- 2010-08
- Volume
- 325
- Issue
- 8
- Pages
- 1790-1852
- ISSN
- 0003-4916 (ISSN-L)
- OpenAlex
- W1969827863
- Cited by
- 595
- References
- 8
- FWCI
- 9.82
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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