Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation

We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover the truncated Wigner approximation, where the evolution is still classical but the initial conditions are distributed according to the Wigner transform of the initial density matrix. Further corrections can be characterized as quantum scattering events, which appear in the form of a nonlinear response of the observable to an infinitesimal displacement of the field along its classical evolution. At the end of the paper we give a few numerical examples to test the formalism.Comment: published versio

Low-temperature dynamical simulation of spin-boson systems

The dynamics of spin-boson systems at very low temperatures has been studied using a real-time path-integral simulation technique which combines a stochastic Monte Carlo sampling over the quantum fluctuations with an exact treatment of the quasiclassical degrees of freedoms. To a large degree, this special technique circumvents the dynamical sign problem and allows the dynamics to be studied directly up to long real times in a numerically exact manner. This method has been applied to two important problems: (1) crossover from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K is Kondo's parameter.Comment: Phys. Rev. B (in press), 28 pages, 6 figure

The quantum density of states of the helium-3. Wigner approach in path integral Monte Carlo

A new path integral representation of the quantum density of states (DOS) and distribution functions of strongly correlated fermions are derived in the Wigner formulation of quantum mechanics. A new path integral Monte Carlo approach to calculate DOS and thermodynamic functions is suggested. Using helium-3 as an interesting example, we calculate the DOS, internal energy distrubution (IED), momentum distribution functions (MDFs), spin--resolved radial distribution functions at different densities and temperatures. The physical meaning and parameters of exchange-- correlation holes, the quantum oscillations of IEDs and DOS as well as the high--momentum asymptotic (``quantum tails'') of MDFs have been considered and explained

Quantum dynamics of strongly coupled particles in phase space

The new numerical approach for investigation of strongly coupled systems including a subsystem of quantum particles and a subsystem of classical particles has been developed. The advanced approach combines and generalizes molecular dynamics and path integral Monte Carlo methods and allows investigating the dynamic and thermodynamic properties of degenerate particle systems. Numerical results for energy, pressure, pair correlation functions and frequency dependencies of tensor of electron conductivity