Phase space representation of quantum dynamics

A quantum mechanical representation in phase space

A quantum mechanical representation suitable for studying the time evolution of quantum densities in phase space is proposed and examined in detail. This representation on 2'2 (2) phase space is based on definitions of the operators P and Q in phase space that satisfy various correspondences for the Liouville equation in classical and quantum phase space, as well as quantum position and momentu...

Phase space dynamics of overdamped quantum systems

The phase space dynamics of dissipative quantum systems in strongly condensed phase is considered. Based on the exact path integral approach it is shown that the Wigner transform of the reduced density matrix obeys a time evolution equation of Fokker-Planck type valid from high down to very low temperatures. The effect of quantum fluctuations is discussed and the accuracy of these findings is t...

Quantum phase space distributions in thermofield dynamics

It is shown that the the quantum phase space distributions corresponding to a density operator ρ can be expressed, in thermofield dynamics, as overlaps between the state | ρ > and ”thermal” coherent states. The usefulness of this approach is brought out in the context of a master equation describing a nonlinear oscillator for which exact expressions for the quantum phase distributions for an ar...

Phase space representation of quantum dynamics . Lecture notes . Boulder Summer School , 2013

Quantum dynamics in phase space: From coherent states to the Gaussian representation

We give an outlook on the future of coherence theory and manybody quantum dynamics as experiments develop in the arena of ultra-cold atoms. Novel results on quantum heating of center-of-mass temperature in evaporative cooling and simulation methods for long-range interactions are obtained, using positive-P phase-space techniques. 1 Coherence theory in the 21st century One recognition of importa...