Related papers: Minimal Length Uncertainty Relations and New Shape…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…
This paper extends the construction of invariants for virtual knots to virtual long knots and introduces two new invariant modules of virtual long knots. Several interesting features are described that distinguish virtual long knots from…
We present a general framework and procedure to derive uncertainty relations for observables of quantum systems in a covariant manner. All such relations are consequences of the positive semidefiniteness of the density matrix of a general…
We study the properties of {\bf exact} (all level $k$) quantum coherent states in the context of string theory on a group manifold (WZWN models). Coherent states of WZWN models may help to solve the unitarity problem: Having positive norm,…
In the supersymmetric quantum mechanics formalism, the shape invariance condition provides a sufficient constraint to make a quantum mechanical problem solvable; i.e., we can determine its eigenvalues and eigenfunctions algebraically. Since…
Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied…
Given any unoriented link diagram, a group of new knot invariants are constructed. Each of them satisfies a generalized 4 term skein relation. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations…
The role of gauge invariance is reconsidered by "deriving it without assuming it" within an autonomous approach to interactions of Standard Model particles. In this approach, the renormalizable interactions are purely constrained by quantum…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
We examine shape invariant potentials (excluding those that are obtained by scaling) in supersymmetric quantum mechanics from the stand-point of periodic orbit theory. An exact trace formula for the quantum spectra of such potentials is…
Uncertainty relations express the fundamental incompatibility of certain observables in quantum mechanics. Far from just being puzzling constraints on our ability to know the state of a quantum system, uncertainty relations are at the heart…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
We construct creation and annihilation operators for harmonic oscillators with minimal length uncertainty relations. We discuss a possible generalization to a large class of deformations of cannonical commutation relations. We also discuss…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
Four new exactly solvable, real and shape-invariant potentials associated with a position-dependent effective mass are generated within the concept of shape-invariant potentials using a specific ansatz for superpotential. The accompanying…
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
Quantum mechanical models with a minimal length are often described by modifying the commutation relation between position and momentum. Although this represents a small complication when described in momentum space, at least formally, the…