scholarly journals A NEW ALGEBRAIC STRUCTURE OF FINITE QUANTUM SYSTEMS AND THE MODIFIED BESSEL FUNCTIONS

2007 ◽  
Vol 04 (07) ◽  
pp. 1205-1215 ◽  
Author(s):  
KAZUYUKI FUJII
Keyword(s):  
Quantum Mechanics ◽  
Algebraic Structure ◽  
Bessel Functions ◽  
Quantum Systems ◽  
Modified Bessel Functions ◽  
Level System ◽  
Integer Order ◽  
Pauli Matrices ◽  
Finite Quantum Systems

In this paper we present a new algebraic structure (a superhyperbolic system in our terminology) for finite quantum systems, which is a generalization of the usual one in the two-level system. It fits into the so-called generalized Pauli matrices, so they play an important role in theory. Some deep relation to the modified Bessel functions of integer order is pointed out. By taking a skillful limit finite quantum systems become quantum mechanics on the circle developed by Ohnuki and Kitakado.

The Modified Bessel Functions I n (x) of Integer Order

2008 ◽  
pp. 507-517
Author(s):  
Keith B. Oldham ◽  
Jan C. Myland ◽  
Jerome Spanier
Keyword(s):  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Integer Order

scholarly journals From Geometry to Coherent Dissipative Dynamics in Quantum Mechanics

2021 ◽  
Vol 3 (4) ◽  
pp. 664-683
Author(s):  
Hans Cruz-Prado ◽  
Alessandro Bravetti ◽  
Angel Garcia-Chung
Keyword(s):  
Quantum Mechanics ◽  
Hamiltonian Dynamics ◽  
Contact Manifold ◽  
Quantum Systems ◽  
Geometric Description ◽  
Level System ◽  
Quantum Processes ◽  
Continuous Processes ◽  
Novel Approach ◽  
Dissipative Quantum Systems

Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation by using appropriate contact Hamiltonian dynamics. We work out the case of finite-level systems for which it is shown, by means of the corresponding contact master equation, that the resulting dynamics constitute a viable alternative candidate for the description of this subclass of dissipative quantum systems. As a concrete application, motivated by recent experimental observations, we describe quantum decays in a 2-level system as coherent and continuous processes.

Asymptotic expansions and converging factors V. Lommel, Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions

1959 ◽  
Vol 249 (1257) ◽  
pp. 284-292 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Lommel Functions ◽  
Special Cases

A theory of Lommel functions is developed, based upon the methods described in the first four papers (I to IV) of this series for replacing the divergent parts of asymptotic expansions by easily calculable series involving one or other of the four ‘basic converging factors’ which were investigated and tabulated in I. This theory is then illustrated by application to the special cases of Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions.

(p, q)-Extended Bessel and Modified Bessel Functions of the First Kind

2017 ◽  
Vol 72 (1-2) ◽  
pp. 617-632 ◽  
Author(s):  
Dragana Jankov Maširević ◽  
Rakesh K. Parmar ◽  
Tibor K. Pogány
Keyword(s):  
Bessel Functions ◽  
Modified Bessel Functions

Oscillations in Finite Quantum Systems

Physics Today ◽  
1995 ◽  
Vol 48 (5) ◽  
pp. 68-69 ◽  
Author(s):  
G. F. Bertsch ◽  
R. A. Broglia ◽  
Herman Feshbach
Keyword(s):  
Quantum Systems ◽  
Finite Quantum Systems
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