Related papers: A General Theory of Phase-Space Quasiprobability D…
In this paper we view the sigma-model couplings of appropriate vertex operators describing the interaction of string matter with a certain type of string solitons (0-branes) as the quantum phase space of a point particle. The sigma-model is…
We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
We determine a positive normalised phase space probability distribution $P$ with minimum mean square fractional deviation from the Wigner distribution $W$ .The minimum deviation, an invariant under phase space rotations, is a quantitative…
We define the Kirkwood-Dirac quasiprobability representation of quantum mechanics associated with the Fourier transform over second countable locally compact abelian groups. We discuss its link with the Kohn-Nirenberg quantization of the…
A generalization of the Weyl law to systems with a sharply divided mixed phase space is proposed. The ansatz is composed of the usual Weyl term which counts the number of states in regular islands and a term associated with sticky regions…
A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an…
In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…
Phase space quasi-probability functions provide powerful representations of quantum states and operators, as well as criteria for assessing quantum computational resources. In discrete, odd-dimensional systems (qudits), protocols involving…
Wilk's theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the…
For a general class of unitary quantum maps, whose underlying classical phase space is divided into several invariant domains of positive measure, we establish analogues of Weyl's law for the distribution of eigenphases. If the map has one…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
This paper is concerned with the construction of phase operators, phase states, vector phase states, and coherent states for a generalized Weyl-Heisenberg algebra. This polynomial algebra (that depends on real parameters) is briefly…
We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar Cartesian case are systematically…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
In solid state systems, group representation theory is powerful in characterizing the behavior of quasiparticles, notably the energy degeneracy. While conventional group theory is effective in answering yes-or-no questions related to…