Related papers: Wigner flow reveals topological order in quantum p…
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…
Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian, $H^{W}(q,\,p)$, constrained by the $\partial ^2 H^{W} / \partial q \partial p = 0$ condition are analytically obtained in terms of Wigner…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Extending the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum, gaussian functions are identified as the quantum ground state. Once a Hamiltonian, $H^{W}(q,\,p)$,…
The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory…
We presented the topological current of Ehrenfest definition of phase transition. It is shown that different topology of the configuration space corresponds to different phase transition, it is marked by the Euler number of the interaction…
Instability features associated to topological quantum domains which emerge from the Weyl-Wigner (WW) quantum phase-space description of Gaussian ensembles driven by Aubry-Andr\'e-Harper (AAH) Hamiltonians are investigated. Hyperbolic…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
The quasilinear theory of the Wigner-Poisson system in one spatial dimension is examined. Conservation laws and properties of the stationary solutions are determined. Quantum effects are shown to manifest themselves in transient periodic…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse fields. In regard to the special characteristics of such field types we derive modified…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
Quantum trajectories defined in the de Broglie--Bohm theory provide a causal way to interpret physical phenomena. In this Letter, we use this formalism to analyze the short time dynamics induced by unstable periodic orbits in a classically…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
The paper scrutinizes both the similarities and the differences between the classical optics and quantum mechanical theories in phase space, especially between the Wigner distribution functions defined in the respective phase spaces.…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…