Related papers: Effective potentials from semiclassical truncation…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
We derive the semi-classical Lindblad master equation in phase space for both canonical and non-canonical Poisson brackets using the Wigner-Moyal formalism and the Moyal star-product. The semi-classical limit for canonical dynamical…
A comparison of structural features of quantum and classical physical theories, such as the information capacity of systems subject to these theories, requires a common formal framework for the presentation of corresponding concepts (such…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
I develop a theory of classicality from quantum systems. This theory stems from the study of classical and quantum stationary stochastic processes. The stochastic processes are characterized by polyhedral (classical) and semidefinite…
This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…
We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…
Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…
We implement in systems of fermions the formalism of pseudoclassical paths that we recently developed for systems of bosons and show that quantum states of fermionic fields can be described, in the Heisenberg picture, as linear combinations…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective…
We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
Quasiclassical methods for non-adiabatic quantum dynamics can reveal new features of quantum effects, such as tunneling evolution, that are harder to reveal in standard treatments based on wave functions of stationary states. Here, these…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and…