Related papers: Stationary quantum Markov process for the Wigner f…
Unbounded potentials are always utilized to strictly confine quantum dynamics and generate bound or stationary states due to the existence of quantum tunneling. However, the existed accurate Wigner solvers are often designed for either…
Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the…
In this paper, we study the set of stationary solutions of the Vlasov-Fokker-Planck (VFP) equation. This equation describes the time evolution of the probability distribution of a particle moving under the influence of a double-well…
The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner…
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a…
Classical molecular dynamics (MD) is a well established and powerful tool in various fields of science, e.g. chemistry, plasma physics, cluster physics and condensed matter physics. Objects of investigation are few-body systems and…
We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform…
We study a (relativistic) Wiener process on a complexified (pseudo-)Riemannian manifold. Using Nelson's stochastic quantization procedure, we derive three equivalent descriptions for this problem. If the process has a purely real quadratic…
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…
The time evolution of the one-point probability vector of stochastic processes and quantum processes for $N$-level systems have been unified. Hence, quantum states and quantum operations can be regarded as generalizations of the one-point…
This paper extends the Karhunen-Loeve representation from classical Gaussian random processes to quantum Wiener processes which model external bosonic fields for open quantum systems. The resulting expansion of the quantum Wiener process in…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum…
We prescribe a formulation of the particle production with real-time Stochastic Quantization. To construct the retarded and the time-ordered propagators we decompose the stochastic variables into positive- and negative-energy parts. In this…
We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard…
In this paper, the ground state Wigner function of a many-body system is explored theoretically and numerically. First, an eigenvalue problem for Wigner function is derived based on the energy operator of the system. The validity of finding…