Related papers: Negativity witness for the quantum ergodic conject…
The presence of unique quantum correlations is the core of quantum information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using…
Non-Gaussian quantum states, described by negative valued Wigner functions, are important both for fundamental tests of quantum physics and for emerging quantum information technologies. However, they are vulnerable to dissipation. It is…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
In this paper, we study within the structure of Symplectic Quantum Mechanics a bi-dimensional non-relativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which…
For any state in a $D$-dimensional Hilbert space with a choice of basis, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents the state on a discrete phase space. The Wigner function…
The concept of ergodicity---the convergence of the temporal averages of observables to their ensemble averages---is the cornerstone of thermodynamics. The transition from a predictable, integrable behavior to ergodicity is one of the most…
The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their…
We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a cross-over from…
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators, which is a distribution uniquely characterized by the property that the marginals for all linear combinations of the given operators agree with the…
We present a method for calculating expectation values of operators in terms of a corresponding c-function formalism which is not the Wigner--Weyl position-momentum phase-space, but another space. Here, the quantity representing the quantum…
An observer at rest with the expanding universe experiences some extra noise in the quantum vacuum, and so does an accelerated observer in a vacuum at rest (in Minkowski space). The literature mainly focuses on the ideal cases of…
This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid [2020], is to interpret the phase…
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a…
In this manuscript, the behavior of the Wigner function of accelerated and non-accelerated two qubit system passing through different noisy channels is discussed. The decoherence of the initial quantum correlation due to the noisy channels…
Liouville theorem (LT) reveals robust incompressibility of distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., LT is only conditionally true (e.g., for…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
A coarse grained Wigner distribution p_{W}(x,u) obeying positivity derives out of information-theoretic considerations. Let p(x,u) be the unknown joint PDF (probability density function) on position- and momentum fluctuations x,u for a pure…
We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…
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.…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…