Hamiltonian Structure of the Schrödinger Classical Dynamical System

2016 ◽  
Vol 46 (9) ◽  
pp. 1127-1167 ◽  
Author(s):  
Massimo Tessarotto ◽  
Michael Mond ◽  
Davide Batic
Keyword(s):  
Dynamical System ◽  
Hamiltonian Structure ◽  
Classical Dynamical System

scholarly journals ON BARYON NUMBER NONCONSERVATION IN TWO-DIMENSIONAL O(2N+1) QCD

2010 ◽  
Vol 25 (06) ◽  
pp. 1253-1266
Author(s):  
TAMAR FRIEDMANN
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Matrix Models ◽  
Gauge Group ◽  
Baryon Number ◽  
Two Dimensional ◽  
Infinite Dimensional ◽  
Field Approach ◽  
Large N ◽  
Classical Dynamical System

We construct a classical dynamical system whose phase space is a certain infinite-dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O (2N+1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.

scholarly journals Bifurcation and anomalous spectral accumulation in an oval billiard

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
Hironori Makino
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Limited Region ◽  
Classical Dynamical System ◽  
Classical Trajectories ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Spectral Statistics ◽  
Math Phys ◽  
Good Agreement

Abstract The spectral statistics of a quantum oval billiard whose classical dynamical system shows bifurcations is numerically investigated in terms of the two-point correlation function (TPCF), which is defined as the probability density of finding two levels at a specific energy interval. The eigenenergy levels at the bifurcation point are found to show anomalous accumulation, which is observed as a periodic spike oscillation of the TPCF. We analyzed the eigenfunctions localizing onto the various classical trajectories in the phase space and found that the oscillation is supplied from a limited region in the phase space that contains the bifurcating orbit. We also show that the period of the oscillation is in good agreement with the period of a contribution from the bifurcating orbit to the semiclassical TPCF obtained by Gutzwiller’s trace formula [J. Math. Phys. 12, 343 (1971)].

ON SUPERSYMMETRIC NONLINEAR σ MODELS AND CLASSICAL DYNAMICAL SYSTEMS

1996 ◽  
Vol 11 (06) ◽  
pp. 1101-1115
Author(s):  
ANTTI J. NIEMI ◽  
KAUPO PALO
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Partition Function ◽  
Integrable Systems ◽  
Morse Theory ◽  
General Class ◽  
Loop Space ◽  
Two Dimensional ◽  
Hamiltonian Flow ◽  
Classical Dynamical System

We construct a two-dimensional nonlinear σ model that describes the Hamiltonian flow in the loop space of a classical dynamical system. This model is obtained by equivariantizing the standard N=1 supersymmetric nonlinear σ model by the Hamiltonian flow. We use localization methods to evaluate the corresponding partition function for a general class of integrable systems, and find relations that can be viewed as generalizations of standard relations in classical Morse theory.

scholarly journals Analogous Hawking radiation in butterfly effect

2021 ◽  
Author(s):  
Takeshi Morita
Keyword(s):  
Dynamical System ◽  
Lyapunov Exponent ◽  
Hawking Radiation ◽  
Quantum Fluctuations ◽  
Thermal Fluctuations ◽  
Classical Dynamical System ◽  
Butterfly Effect

We propose that Hawking radiation-like phenomena may be observed in systems that show butterfly effects. Suppose that a classical dynamical system has a Lyapunov exponent \lambda_LλL, and is deterministic and non-thermal (T=0T=0). We argue that, if we quantize this system, the quantum fluctuations may imitate thermal fluctuations with temperature $T _L/2 $ in a semi-classical regime, and it may cause analogous Hawking radiation. We also discuss that our proposal may provide an intuitive explanation of the existence of the bound of chaos proposed by Maldacena, Shenker and Stanford.

scholarly journals ON STRONG ERGODIC PROPERTIES OF QUANTUM DYNAMICAL SYSTEMS

2009 ◽  
Vol 12 (04) ◽  
pp. 551-564 ◽  
Author(s):  
FRANCESCO FIDALEO
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Ergodic Property ◽  
Invariant State ◽  
C Algebras ◽  
Quantum Dynamical ◽  
Ergodic Properties ◽  
Classical Dynamical System ◽  
Amalgamated Free Product ◽  
Quantum Dynamical Systems

We show that the shift on the reduced C*-algebras of RD-groups, including the free group on infinitely many generators, and the amalgamated free product C*-algebras, enjoys the very strong ergodic property of the convergence to the equilibrium. Namely, the free shift converges, pointwise in the weak topology, to the conditional expectation onto the fixed-point subalgebra. Provided the invariant state is unique, we also show that such an ergodic property cannot be fulfilled by any classical dynamical system, unless it is conjugate to the trivial one-point dynamical system.

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