scholarly journals Signatures of Quantum Mechanics in Chaotic Systems

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 618 ◽  
Author(s):  
Kevin M. Short ◽  
Matthew A. Morena
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Chaotic Systems ◽  
Measurement Problem ◽  
Quantum Systems ◽  
Analytical Tool ◽  
Quantum Mechanical ◽  
Unstable Periodic Orbits ◽  
Classical Correspondence ◽  
Quantum Mechanical Systems

We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, various entropy definitions, the superposition of states, and the measurement problem. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. We also discuss several characteristics of quantum systems that are not fully compatible with chaotic entanglement and that make quantum entanglement unique.

scholarly journals ${\mathcal N}$-FOLD SUPERSYMMETRIC QUANTUM MECHANICS WITH REFLECTIONS

2012 ◽  
Vol 27 (19) ◽  
pp. 1250102 ◽  
Author(s):  
TOSHIAKI TANAKA
Keyword(s):  
Quantum Mechanics ◽  
Hermitian Matrix ◽  
Mechanical Systems ◽  
Quantum Systems ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Quantum Mechanical ◽  
Quantum Mechanical Systems ◽  
Ordinary Quantum

We formulate [Formula: see text]-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of [Formula: see text]-fold supersymmetry, namely, almost isospectrality and weak quasi-solvability. We construct explicitly the most general one- and two-fold supersymmetric quantum mechanical systems with reflections. In the case of [Formula: see text], we find that there are seven inequivalent such systems, three of which are characterized by three arbitrary functions having definite parity while the other four characterized by two arbitrary functions. In addition, four of the seven inequivalent systems do not reduce to ordinary quantum systems without reflections. Furthermore, in certain particular cases, they are essentially equivalent to the most general two-by-two Hermitian matrix two-fold supersymmetric quantum systems obtained previously by us.

Constructing deterministic models for quantum mechanical systems

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040007
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Quantum Mechanics ◽  
Essential Element ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
Final States ◽  
Deterministic Models ◽  
Quantum Theories ◽  
Initial States ◽  
Quantum Mechanical Systems ◽  
Entire Theory

A sharper formulation is presented for an interpretation of quantum mechanics advocated by the author. We claim that only those quantum theories should be considered for which an ontological basis can be constructed. In terms of this basis, the entire theory can be considered as being deterministic. An example is illustrated: massless, noninteracting fermions are ontological. Subsequently, as an essential element of the deterministic interpretation, we put forward conservation laws concerning the ontological nature of a variable, and the uncertainties concerning the realization of states. Quantum mechanics can then be treated as a device that combines statistics with mechanical, deterministic laws, such that uncertainties are passed on from initial states to final states.

scholarly journals Generalized Probabilistic Theories in a New Light

2021 ◽  
Author(s):  
Raed Shaiia
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Quantum Mechanical ◽  
Infinite Dimensional ◽  
Classical Systems ◽  
Generalized Probabilistic Theories ◽  
Deterministic Description ◽  
New Formulation ◽  
The Universe ◽  
Probabilistic Theories

Abstract In this paper we will present a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, and give the guidelines to how to extend this work to infinite dimensional Hilbert spaces. Moreover, this new formulation which we will call extended operational-probabilistic theories, applies not only to quantum systems, but also equally well to classical systems, without violating Bell’s theorem, and at the same time solves the measurement problem. This is why we will see that the question of why our universe is quantum mechanical rather than classical is misplaced. The only difference that exists between a classical universe and a quantum mechanical one lies merely in which observables are compatible and which are not. Besides, this extended probability theory which we present in this paper shows that it is non-determinacy, or to be more precise, the non-deterministic description of the universe, that makes the laws of physics the way they are. In addition, this paper shows us that what used to be considered as purely classical systems and to be treated that way are in fact able to be manipulated according to the rules of quantum mechanics –with this new understanding of these rules- and that there is still a possibility that there might be a deterministic level from which our universe emerges, which if understood correctly, may open the door wide to applications in areas such as quantum computing. In addition to all that, this paper shows that without the use of complex vector spaces, we cannot have any kind of continuous evolution of the states of any system.

Quantum Mechanics

2021 ◽  
Author(s):  
Arjun Berera ◽  
Luigi Del Debbio
Keyword(s):  
Mechanical Properties ◽  
Quantum Mechanics ◽  
Angular Momentum ◽  
Quantum Information ◽  
Quantum Entanglement ◽  
Quantum States ◽  
Quantum Mechanical ◽  
Mathematical Skills ◽  
Key Concepts ◽  
Modern Textbook

Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.

THERMAL PHASES IN FINITE QUANTUM SYSTEMS

2003 ◽  
Vol 17 (28) ◽  
pp. 5093-5100
Author(s):  
D. J. DEAN
Keyword(s):  
Mechanical Systems ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Body System ◽  
Many Body ◽  
Finite Quantum Systems ◽  
Quantum Mechanical Systems ◽  
Increasing Temperature

I will describe the behaviour of two different quantum-mechanical systems as a function of increasing temperature. While these systems are somewhat different, the questions addressed are very similar, namely, how does one describe transitions in phase of a finite many-body system; how does one recognise these transitions in practical calculations; and how may one obtain the order of the transition.

Shifted 1/N expansion for confined quantum systems

2000 ◽  
Vol 78 (2) ◽  
pp. 141-152 ◽  
Author(s):  
Anjana Sinha ◽  
Rajkumar Roychoudhury ◽  
Y P Varshni
Keyword(s):  
Mechanical Systems ◽  
Expansion Method ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Spherically Symmetric ◽  
Hulthén Potential ◽  
Hulthen Potential ◽  
Screening Parameter ◽  
Quantum Mechanical Systems ◽  
Confined Quantum Systems

In this paper we formulate the shifted 1/N expansion method for constrained quantum mechanical systems with spherically symmetric potentials. As an example, we apply our technique to the confined Hulthén potential V(r) = –Zδ[e -δr/(1 –e-δr)] for different values of the confinement parameter b and the screening parameter δ. It is found that the agreement between our results and the exact numerical values is reasonably good.PACS No.: 03.65Ge

scholarly journals Causality in Schwinger’s Picture of Quantum Mechanics

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 75
Author(s):  
Florio M. Ciaglia ◽  
Fabio Di Di Cosmo ◽  
Alberto Ibort ◽  
Giuseppe Marmo ◽  
Luca Schiavone ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Von Neumann Algebra ◽  
Operator Algebras ◽  
Quantum Mechanical ◽  
Von Neumann ◽  
Triangular Operator ◽  
Quantum Mechanical Systems ◽  
Causal Structures ◽  
Incidence Theorem

This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin’s incidence theorem will be proved and some illustrative examples will be discussed.

scholarly journals THE MAIN LEITMOTIFS OF CHINESE MEDICINE IN THE CONTEXT OF THE DEVELOPMENT OF MODERN SCIENCE

2020 ◽  
Vol 73 (5) ◽  
pp. 1000-1003
Author(s):  
Ihor A. Sniehyrov ◽  
Inna А. Plakhtiienko ◽  
Viktoriia O. Kurhanska ◽  
Yurii V. Smiianov
Keyword(s):  
Quantum Mechanics ◽  
Qualitative Difference ◽  
Modern Science ◽  
Periodic Wave ◽  
Dissipative Structures ◽  
Living System ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Quantum Mechanical Systems ◽  
Integral Quantum

The aim: To demonstrate the limitations of pharmacological (chemical) therapy and the atomistic paradigm of science (in particular medicine) on the methodological basis of modern interdisciplinary directions (the theory of dissipative structures, chaos, autopoiesis), quantum mechanics, as well as the basic patterns of oriental medicine. Materials and methods: The principles used in the article include self-organization, emergence, quantum mechanics (the Heisenberg uncertainty principle), the principle of consistency; principles of using coherent millimeter waves of low power, etc. Theoretical methods of analysis and synthesis, idealization, abstraction, induction and deduction are also used. Сonclusions: The concept of “integrable system” is equivalent to the concept of “integral quantum-mechanical system”; Integral quantum-mechanical systems (nuclei, atoms, molecules, living objects) in the ground state are described by periodic wave functions of the type exp (jwt); The traditional paradigm, for the most part, eliminates the qualitative difference between living and dead matter; Any living system functioning as a whole is simultaneously a macroscopic quantum-mechanical object and a millimeter-wave laser.

Exploring Chaos and Entanglement in the Hénon–Heiles System Using Squeezed Coherent States

2016 ◽  
Vol 26 (03) ◽  
pp. 1650052
Author(s):  
Sijo K. Joseph ◽  
Miguel A. F. Sanjuán
Keyword(s):  
Quantum Entanglement ◽  
Local Structure ◽  
Coherent States ◽  
Quantum Systems ◽  
Initial Condition ◽  
Chaotic Orbit ◽  
Chaotic Orbits ◽  
Classical Correspondence ◽  
Squeezed Coherent State ◽  
Classical Phase Space

Quantum entanglement in the Hénon–Heiles system is analyzed using the squeezed coherent state. Enhancement of quantum entanglement via squeezing is explored in connection with chaotic and regular dynamics of the system. It is found that the entanglement enhancement via squeezing is implicitly linked to the local structure of the classical phase-space and it shows a clear quantum-classical correspondence. In particular, the entanglement enhancement via squeezing is found to be negligible for a highly chaotic orbit compared to the regular and weakly chaotic orbits, and shows a clear correspondence to the degree of chaos present in the classical initial condition. We believe that these results might be useful to develop efficient strategies to enhance entanglement in quantum systems.

scholarly journals Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems indDimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Richard L. Hall ◽  
Alexandra Lemus Rodríguez
Keyword(s):  
Quantum Mechanics ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Natural Basis ◽  
Boson Systems ◽  
Spanning Set

It is shown that the spanning set forL2([0,1])provided by the eigenfunctions{2sin(nπx)}n=1∞of the particle in a box in quantum mechanics provides a very effective variational basis for more general problems. The basis is scaled to[a,b], whereaandbare then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box inRdturns out to be appropriate also for problems that are softly confined byU-shaped potentials, including those with strong singularities atr=0. Specific examples are discussed in detail, along with some boundN-boson systems.

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