Thermal States on Mittag-Leffler Fock Space of the Slitted Plane

TL;DR

This paper develops the mathematical framework for studying number and thermal states on the Mittag-Leffler Fock space of the slitted plane, extending quantum state analysis beyond traditional Fock spaces.

Contribution

It constructs and analyzes number and thermal states on the Mittag-Leffler Fock space, a recent generalization of the usual Fock space, opening avenues for exploring more complex quantum states.

Findings

Construction of number states on ML Fock space.

Analysis of thermal states in the ML Fock space.

Foundation for studying non-Gaussian quantum states on ML Fock spaces.

Abstract

Number states and thermal states form an important class of physical states in quantum theory. A mathematical framework for studying these states is that of a Fock space over an appropriate Hilbert space. Several generalizations of the usual Bosonic Fock space have appeared recently due to their importance in many areas of mathematics and other scientific domains. One of the most prominent generalization of Fock spaces is the Mittag-Leffler (ML) Fock space of the slitted plane. Natural generalizations of the basic operators of quantum theory can be obtained on ML Fock spaces. Following the construction of the creation and annihilation operators in the Mittag-Leffler Fock space of the slitted plane by Rosenfeld, Russo, and Dixon, (J. Math. Anal. Appl. 463, 2, 2018). We construct and study the number states and thermal states on the ML Fock space of the slitted plane. Thermal states on usual Fock space form an important subclass of the so called quantum gaussian states, an analogous theory of more general quantum states (like squeezed states and Bell states) on ML Fock spaces is an area open for further exploration.