Related papers: Quantum Markov Process on a Lattice
We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a…
Quantum link models are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. Quantum link models not only reproduce the standard features of Wilson's lattice gauge…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
In the beginning of the 1950's, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum…
We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and…
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…
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…
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 concept of quantum phase space offers a view on quantum mechanics, which is different from the standard Hilbert space approach, but which more closely resembles the classical phase space. Due to the properties of quantum mechanics there…
Within the framework of stochastic one-body approach a simulation procedure to study the Vlasov dynamics for fermi system on phase space lattice is presented. To deal with fermions on lattice, the phase cell occupancy factors are taken to…
Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution…
This work develops and applies the concept of mollification in order to smooth out highly oscillatory exponentials. This idea, known for quite a while in the mathematical community (mollifiers are a means to smooth distributions), is new to…
Starting from a general relativistic kinetic equation, a self-consistent mean-field equation for fermions is derived within a covariant density matrix approach of QED plasmas in strong external fields. A Schr\"odinger picture formulation on…
The quantum smoothing theory [Tsang, Phys. Rev. Lett. 102, 250403 (2009); Phys. Rev. A, in press (e-print arXiv:0906.4133)] is extended to account for discrete jumps in the classical random process to be estimated, discrete variables in the…
We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…
We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact…
We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel…
The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval…
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum…
The exact solution of the Lindblad equation with a quadratic Hamiltonian and linear coupling operators was derived within the chord representation, that is, for the Fourier transform of the Wigner function, also known as the characteristic…