Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques

By P. B. Blakie, Ashton S. Bradley, M. Davis, R. Ballagh, C. Gardiner. 2008

467 citations recorded by the source corpus.

We review phase-space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross–Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develop versions of the formalism appropriate at zero temperature, where quantum fluctuations can be important, and at finite temperature where thermal fluctuations dominate. The numerical techniques necessary for implementing the formalism are discussed in detail, together with methods for extracting observables of interest. Numerous applications to a wide range of phenomena are presented.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9aa1d75eab9c8b160b9898c2779c530438d8f86a

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Phase space representation of quantum dynamics (2009, background): “…finding the initial Wigner function can be avoided by either doing various approximations to the initial state like the Bogoliubov’s approximation (Blakie et al., 2008) or by starting from a simple initial state and then adiabatically evolving the Hamiltonian in time so that the couplings reach…”
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems (2010, background): “Cold atom experiments also prompted rapid developments in phase space methods, where quantum dynamics is represented as an evolution in the classical phase space (Blakie et al., 2008; Polkovnikov, 2010).”
Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space (2014, background): “The quantum uncertainty in the initial state is accounted for by an average over different initial conditions [17, 18] determined by a continuous Wigner function.”