Related papers: Energy transitions driven by phase space reflectio…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
The Wigner function W(q,p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are…
We show that classicality emerges during quantum phase transitions due to parametric interactions without coupling to environments. The Wigner functions are explicitly calculated for the Gaussian vacuum, number, and thermal states of a free…
Semiclassical approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in phase space, but it is not available for chaotic systems. An analogous evolution surface underlies semiclassical…
Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…
An analysis of the Wigner function for identical particles is presented. Four situations have been considered. i) A scattering process between two indistinguishable electrons described by a minimum uncertainty wave packets showing the…
Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. The Shannon differential entropy of the Wigner function of such states -- called Wigner entropy for…
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any…
In this work we provide a complete model of semiclassical theories by including back-reaction and correlation into the picture. We specially aim at the interaction between light and a two-level atom, and we also illustrate it via the…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
Bifractional displacement operators, are introduced by performing two fractional Fourier transforms on displacement operators. They are shown to be special cases of elements of the group G, that contains both displacements and squeezing…
Macroscopic Wigner islands present an interesting complementary approach to explore the properties of two-dimensional confined particles systems. In this work, we characterize theoretically and experimentally the interaction between their…