scholarly journals Manifestations of chaos in relativistic quantum systems - A study based on out-of-time-order correlator

Physics Open ◽  
2019 ◽  
Vol 1 ◽  
pp. 100001 ◽  
Author(s):  
Chen-Di Han ◽  
Hong-Ya Xu ◽  
Liang Huang ◽  
Ying-Cheng Lai
Keyword(s):  
Relativistic Quantum ◽  
Quantum Systems ◽  
Time Order

scholarly journals Some effects on relativistic quantum systems due to a weak gravitational field

2005 ◽  
Vol 35 (4b) ◽  
pp. 1110-1112 ◽  
Author(s):  
Geusa de A. Marques ◽  
Sandro G. Fernandes ◽  
V. B. Bezerra
Keyword(s):  
Gravitational Field ◽  
Relativistic Quantum ◽  
Quantum Systems ◽  
Weak Gravitational Field

On hyper‐relativistic quantum systems

1987 ◽  
Vol 28 (1) ◽  
pp. 79-84
Author(s):  
Awele Maduemezia
Keyword(s):  
Relativistic Quantum ◽  
Quantum Systems

Generalized Electromagnetic Fields Associated with the Hydrogen-Like Atom Problem

2018 ◽  
Vol 74 (1) ◽  
pp. 43-50 ◽  
Author(s):  
S.A. Bruce ◽  
J.F. Diaz-Valdes
Keyword(s):  
Quantum Mechanics ◽  
Electromagnetic Coupling ◽  
Relativistic Quantum ◽  
Scalar Potential ◽  
Symmetry Algebra ◽  
Dynamical Symmetry ◽  
Canonical Commutation Relation ◽  
Quantum Systems ◽  
Minimal Coupling ◽  
Exactly Solvable

AbstractIt is known that the principle of minimal coupling in quantum mechanics determines a unique interaction form for a charged particle. By properly redefining the canonical commutation relation between (canonical) conjugate components of position and momentum of the particle, e.g. an electron, we restate the Dirac equation for the hydrogen-like atom problem incorporating a generalized minimal electromagnetic coupling. The corresponding interaction keeps the $1/\left|\mathbf{q}\right|$ dependence in both the scalar potential $V\left({\left|\mathbf{q}\right|}\right)$ and the vector potential $\mathbf{A}\left(\mathbf{q}\right)$ ($\left|{\mathbf{A}\left(\mathbf{q}\right)}\right|\sim 1/\left|\mathbf{q}\right|$). This problem turns out to be exactly solvable; moreover, the eigenstates and eigenvalues can be obtained in an elementary fashion. Some feasible models within this approach are discussed. Then we make a few remarks about the breaking of supersymmetry. Finally, we briefly comment on the possible Lie algebra (dynamical symmetry algebra) of these relativistic quantum systems.

scholarly journals Non-relativistic quantum systems on topological defects spacetimes

2002 ◽  
Vol 19 (5) ◽  
pp. 985-995 ◽  
Author(s):  
Geusa de A Marques ◽  
Valdir B Bezerra
Keyword(s):  
Relativistic Quantum ◽  
Topological Defects ◽  
Quantum Systems

scholarly journals Generalized Cramér–Rao relations for non-relativistic quantum systems

2012 ◽  
Vol 25 (11) ◽  
pp. 1689-1694 ◽  
Author(s):  
J.S. Dehesa ◽  
A.R. Plastino ◽  
P. Sánchez-Moreno ◽  
C. Vignat
Keyword(s):  
Relativistic Quantum ◽  
Quantum Systems

scholarly journals Correlation Functions of Quantum Artin System

Universe ◽  
2020 ◽  
Vol 6 (7) ◽  
pp. 91
Author(s):  
Hrachya Babujian ◽  
Rubik Poghossian ◽  
George Savvidy
Keyword(s):  
Dynamical System ◽  
Correlation Functions ◽  
Modular Group ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Temperature Dependent ◽  
Chaotic Dynamical System ◽  
Classical Chaos ◽  
Time Order ◽  
Point Correlation

It was conjectured by Maldacena, Shenker and Stanford that the classical chaos can be diagnosed in thermal quantum systems by using an out-of-time-order correlation function. The Artin dynamical system defined on the fundamental region of the modular group SL(2,Z) represents a well defined example of a highly chaotic dynamical system in its classical regime. We investigated the influence of the classical chaotic behaviour on the quantum–mechanical properties of the Artin system calculating the corresponding out-of-time-order thermal quantum–mechanical correlation functions. We demonstrated that the two- and four-point correlation functions of the Liouiville-like operators decay exponentially with temperature dependent exponents and that the square of the commutator of the Liouiville-like operators separated in time grows exponentially.

ON THE INDEPENDENCE OF LOCAL ALGEBRAS IN QUANTUM FIELD THEORY

1990 ◽  
Vol 02 (02) ◽  
pp. 201-247 ◽  
Author(s):  
STEPHEN J. SUMMERS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relativistic Quantum ◽  
Mathematical Formulation ◽  
Quantitative Measure ◽  
Quantum Systems ◽  
Statistical Independence ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
C Algebra

A review is made of the multitude of different mathematical formalizations of the physical concept ‘two observables (or two systems) are independent’ that have been proposed in quantum theories, particularly relativistic quantum field theory. The most basic mathematical formulation of independence in any quantum theory is what one may call kinematical independence: the two observables, resp. the observables of the two quantum systems, which are represented by elements of a C*-algebra, resp. two subalgebras of a C*-algebra, are required to commute. This is related to a mathematical formulation of the notion of the coexistence (or compatibility) of two observables. Another basic notion of independence, generally called statistical independence in the literature, is, roughly speaking, two quantum systems are said to be statistically independent if each can be prepared in any state, how ever the other system has been prepared. There are numerous mathematical formulations of this notion and their interrelationships are explained. Statistical independence and kinematical independence are shown to be logically independent. Additional notions such as strict locality and their relation to statistical independence are discussed. The mathematics of a more quantitative measure of statistical independence, Bell’s inequalities, is reviewed and its relations with previously introduced notions are indicated. All of these notions are then viewed in application to relativistic quantum field theory.

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