Related papers: Nonclassical phase-space trajectories for the damp…
We present a perturbation analysis of the semiclassical Wigner equation which is based on the interplay between configuration and phase spaces via Wigner transform. We employ the so-called harmonic approximation of the Schrodinger…
Instead of imposing the Schr\"{o}dinger equation to obtain the configuration space propagator $\csprop$ for a quantum mechanical nonlinear sigma model, we directly evaluate the phase space propagator $\psprop$ by expanding the exponent and…
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time…
The semiclassical propagation of spin coherent states is considered in complex phase space. For two time-independent systems we find the appropriate classical trajectories and show that their combined contributions are able to describe…
Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
White noise analysis is used to derive the propagator of an open quantum system consisting of a harmonic oscillator which is coupled to an environment consisting of N multimode harmonic oscillators. The quantum propagators are obtained…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
Using the path integral representation of the density matrix propagator of quantum Brownian motion, we derive its asymptotic form for times greater than the localization time, $ (\hbar / \gamma k T )^{\half}$, where $\gamma$ is the…
We study the dissipative quantum harmonic oscillator with general non-thermal preparations of the harmonic oscillator bath. The focus is on equilibration of the oscillator in the long-time limit and the additional requirements for…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs…
The quantum harmonic oscillator with parity-time ($\mathcal{PT}$) symmetry, obtained from the ordinary (Hermitian) quantum harmonic oscillator by an imaginary displacement of the spatial coordinate, provides an important and…
A bouncing droplet on a vibrated bath can couple to the waves it generates, so that it becomes a propagative walker. Its propulsion at constant velocity means that a balance exists between the permanent input of energy provided by the…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Extended phase space (EPS) formulation of quantum statistical mechanics treats the ordinary phase space coordinates on the same footing and thereby permits the definite the canonical momenta conjugate to these coordinates . The extended…
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
We study a particular form of interaction Hamiltonian between qubits and quantum harmonic oscillators, whose closed system dynamics results in qubit controlled displacement operations. We show how this interaction is realizable in many…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…