Related papers: Quantum and Arithmetical Chaos
We consider the several phenomena which are taking place in Quantum Dots (QD) and Quantum Rings (QR): The connection of the Quantum Chaos (QC) with the reflection symmetry of the QD, Disappearance of the QC in the tunnel coupled chaotic QD,…
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
Entanglement is a Hilbert-space based measure of nonseparability of states that leads to unique quantum possibilities such as teleportation. It has been at the center of intense activity in the area of quantum information theory and…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
Some of the so-called imponderables and counterintuitive puzzles associated with the Copenhagen interpretation of quantum mechanics appear to have alternate, parallel explanations in terms of nonlinear dynamics and chaos. These include the…
Lecture notes prepared for the EMS--IAMP Spring School ``Symmetries and Measurement in Quantum Field Theory''. This set of lecture notes covers four lectures: 1. Operator Algebras and Quantum Field Theory, 2. Tomita-Takesaki Modular Theory…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate…
Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
We consider a system in which a classical oscillator is interacting with a purely quantum mechanical oscillator, described by the Lagrangian $ L = \frac{1}{2} \dot{x}^2 + \frac{1}{2} \dot{A}^2 - \frac{1}{2} ( m^2 + e^2 A^2) x^2 \>, $ where…
This is the contribution to Quarks'2018 conference proceedings. This contribution is devoted to the holographic description of chaos and quantum complexity in the strongly interacting systems out of equilibrium. In the first part of the…
The presence of quantum chaos in nuclear mass systematics is analyzed by considering the differences between measured and calculated nuclear masses as a time series described by the power law 1/ f^alpha. While for the liquid droplet model…
This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation of chaos is shown…
We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the…
We propose an uncertainty principle for chaos, focusing on two key characteristics: alpha unpredictability and Lorenz sensitivity. This principle outlines a limitation on the relationship between two infinite sequences that underpin these…
Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and…