Quantum initial condition sampling for linearized density matrix dynamics: Vibrational pure dephasing of iodine in krypton matrices

This paper reviews the linearized path integral approach for computing time dependent properties of systems that can be approximated using a mixed quantum-classical description. This approach is applied to studying vibrational pure dephasing of ground state molecular iodine in a rare gas matrix. The Feynman-Kleinert optimized harmonic approximation for the full system density operator is used to sample initial conditions for the bath degrees of freedom. This extremely efficient approach is compared with alternative initial condition sampling techniques at low temperatures where classical initial condition sampling yields dephasing rates that are nearly an order of magnitude too slow compared with quantum initial condition sampling and experimental results.Comment: 20 pages and 8 figure

Investigating interaction-induced chaos using time-dependent density functional theory

Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbour level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.Comment: 8 pages, 4 figure

Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation

We study the low temperature behaviour of path integrals for a simple one-dimensional model. Starting from the Feynman-Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the occupation times of Brownian motions constrained to stay within boxes with finite sizes. From that representation, we infer a kind of ergodic approximation, which only involves double ordinary integrals. As shown by its applications to different confining potentials, the ergodic approximation turns out to be quite efficient, especially in the low-temperature regime where other usual approximations fail

Wigner functions for angle and orbital angular momentum: Operators and dynamics

Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S^1 x R, i.e. for the canonical pair angle and angular momentum, was presented (arXiv:1601.02520), main properties of those functions derived, discussed and their usefulness illustrated by examples. The present paper is a continuation which compares properties of the new Wigner functions for cylindrical phase spaces with those of the well-known Wigner functions on planar ones in more detail. Furthermore, the mutual (Weyl) correspondence between Hilbert space operators and their phase space functions is discussed. The star product formalism is shown to be completely implementable. In addition basic dynamical laws for the new Wigner and Moyal functions are derived as generalized quantum Liouville and energy equations. They are very similar to those of the planar case, but also show characteristic differences.Comment: 14 pages, continuation of paper Phys. Rev. A 94, 062113 (2016