相关论文: Semiclassical analysis of constrained quantum syst…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…
Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In…
We introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the…
Semiclassical approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are…
We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…
We apply the semi-classical limit of the generalized $SO(3)$ map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on $T^{\ast…
We obtain two-sided bounds on kinetic and potential energies of a bound state of a quantum particle in the semiclassical limit, as the Planck constant $\hbar\ri 0$. Proofs of these results rely on the generalized virial theorem obtained in…
A single wave component of a quantum particle can in principle be detected by the way that it interferes with itself, that is, through the local wave function correlation. The interpretation as the expectation of a local translation…
By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the…
We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be…
We analyze the strength of polarization correlations between two light beams that can be achieved in the semiclassical regime using statistical mixtures of coherent states and binary on/off detectors. Under certain symmetry assumptions, the…
We consider the classical limit of the quantum evolution, with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics. We prove that under appropriate conditions, even in the case of BV…
The semiclassical dynamics of atoms are theoretically studied, when the atoms are confined inside a standing-wave high-finesse resonator. The atoms are cooled by scattering processes in which the photons of a transverse laser are coherently…
The definition of a length operator in quantum cosmology is usually influenced by a~quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of…
States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing…
In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
We study the propagation of wave packets for nonlinear nonlocal Schrodinger equations in the semi-classical limit. When the kernel is smooth, we construct approximate solutions for the wave functions in subcritical, critical and…