Related papers: Quantum Liouville-space trajectories for dissipati…
A novel derivation of quantum propagator of a system described by a general quadratic Lagrangian is presented in the framework of Heisenberg equations of motion. The general corresponding density matrix is obtained for a derived quantum…
In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic…
A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both first-order dissipative phase transitions…
We extend a recent formulation of quantum continuum mechanics [J. Tao et. al, Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a magnetic field. To accomplish this, we propose a modified Lagrangian approach, in…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
We illustrate how non-relativistic quantum mechanics may be recovered from a dynamical Weyl geometry on configuration space and an `ensemble' of trajectories (or `worlds'). The theory, which is free of a physical wavefunction, is presented…
Langevin (stochastic differential) equations are routinely used to describe particle-laden flows. They predict Gaussian probability density functions (PDFs) of a particle's trajectory and velocity, even though experimentally observed…
In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix…
Exact and nonperturbative quantum master equation can be constructed via the calculus on path integral. It results in hierarchical equations of motion for the reduced density operator. Involved are also a set of well--defined auxiliary…
We present a quantum-kinetic scheme for the calculation of non-equilibrium transport properties in nanoscale systems. The approach is based on a Liouville-master equation for a reduced density operator and represents a generalization of the…
Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as by an ideal photodetector. Here we derive (non-Markovian) quantum trajectories for realistic…
We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and…
The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the…
We propose a hierarchical dynamics approach for evaluation of nonequilibrium dynamic response properties of quantum impurity systems. It is based on a hierarchical equations of motion formalism, in conjunction with a linear response theory…
We present a new method to derive transport equations for quantum many-particle systems. This method uses an equation-of-motion technique and is applicable to systems with bosons and fermions, arbitrary interactions and time-dependent…
An equation of motion for open quantum systems incorporating memory effects and initial correlations with the environment is presented in terms of an effective Liouville operator that solely acts on states of the system. The environment can…
We consider quantum nonlinear systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas are derived in order to evaluate…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville von Neumann methodology is used to…
The quantum-classical Liouville equation offers a rigorous approach to nonadiabatic quantum dynamics based on surface hopping type trajectories. However, in practice the applicability of this approach has been limited to short times owing…