TEMPORAL QUANTUM CHAOS

1999 ◽  
Vol 13 (18) ◽  
pp. 2361-2369 ◽  
Author(s):  
R. AURICH ◽  
F. STEINER
Keyword(s):  
Quantum Chaos ◽  
Chaotic Systems ◽  
Quantum Systems ◽  
Time Behavior ◽  
Classical Dynamics ◽  
Long Time Behavior ◽  
Initial State ◽  
Numerical Tests ◽  
Weyl Sum ◽  
Long Time

We study the long-time behavior of bound quantum systems whose classical dynamics is chaotic and put forward two conjectures. Conjecture A states that the autocorrelation function C(t)=<Ψ(0)|Ψ(t)> of a delocalized initial state |Ψ(0)> shows characteristic fluctuations, which we identify with a universal signature of temporal quantum chaos. For example, for the (appropriately normalized) value distribution of S~|C(t)| we predict the distribution P(S)=(π/2)Se-πS2/4. Conjecture B gives the best possible upper bound for a generalized Weyl sum and is related to the extremely large recurrence times in temporal quantum chaos. Numerical tests carried out for numerous chaotic systems confirm nicely the two conjectures and thus provide strong evidence for temporal quantum chaos.

scholarly journals Long-time behavior of macroscopic quantum systems

2010 ◽  
Vol 35 (2) ◽  
pp. 173-200 ◽  
Author(s):  
S. Goldstein ◽  
J. L. Lebowitz ◽  
R. Tumulka ◽  
N. Zanghì
Keyword(s):  
Quantum Systems ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Macroscopic Quantum ◽  
Long Time ◽  
Macroscopic Quantum Systems

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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