Related papers: Quantization of the Szekeres System
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees…
A new semiclassical approach to linear (L) and nonlinear (NL) one-dimensional Schr\"odinger equation (SE) is presented. Unlike the usual WKB solution, our solution does not diverge at the classical turning point. For LSE, our zeroth-order…
We apply the ``consistent discretization'' technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and…
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
The classical limit for generalized partition functions is obtained using coherent states. In this framework it is presented a general procedure to obtain all the corrections to the classical limit. In particular, the first and second order…
A generalization of coherent states has been developed in the context of supersymmetric quantum mechanics. For many cases, no link has been made with the corresponding classical system. In this work, we consider simple superpotentials and…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
Equations of motion of low-energy effective theories of quantum electrodynamics include infinitely many interaction terms, which make them difficult to solve. The self-duality property has facilitated research on the solutions to these…
In a previous work, both the constants of motion of a classical system and the symmetries of the corresponding quantum version have been computed with the help of factorizations. As their expressions were not polynomial, in this paper the…
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential $V(\bfr)$. We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\ Lett. {\bf…