Related papers: The Role of Commuting Operators in Quantum Superin…
This work gives value to the importance of Hilbert-Schmidt operators in the formulation of a noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework.
We study some quantum systems described by noncanonical commutation relations formally expressed as [q,p]=ihbar(I + chi H), where H is the associated (harmonic oscillator-like) Hamiltonian of the system, and chi is a Hermitian (constant)…
We find the position-momentum decomposition of the quantum operators of the classic Meixner random variables. The position-momentum decomposition involves translation operators, which are used to give a new characterization of the Meixner…
The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have…
Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities -- energy, particles, electric charge, etc. -- that…
A system of $N$ non-canonical dynamically free 3D harmonic oscillators is studied. The position and the momentum operators (PM-operators) of the system do not satisfy the canonical commutation relations (CCRs). Instead they obey the weaker…
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function.…
In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of…
In this article we consider means of positive operators on a Hilbert space. We extend the theory of matrix power means to arbitrary operator means in the sense of Kubo-Ando. The basis of the extension is relying on ideas coming from…
Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions and star-products, following a technique developed earlier, {\it viz\/,} using the unitary…
Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…
Aim of this paper is trying to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics: More…
Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…
Quantum semitoric systems form a large class of quantum Hamiltonian integrable systems with circular symmetry which has received great attention in the past decade. They include systems of high interest to physicists and mathematicians such…
The isotropic harmonic oscillator in dimension 3 separates in several different coordinate systems. Separating in a particular coordinate system defines a system of three commuting operators, one of which is the Hamiltonian. We show that…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…