An exponentially increasing semiclassical spectral form factor for a class of chaotic systems

1994 ◽  
Vol 27 (6) ◽  
pp. 1967-1979 ◽  
Author(s):  
R Aurich ◽  
M Sieber
Keyword(s):  
Form Factor ◽  
Chaotic Systems ◽  
Spectral Form

scholarly journals Universal spectral form factor for chaotic dynamics

2004 ◽  
Vol 37 (3) ◽  
pp. L31-L37 ◽  
Author(s):  
Stefan Heusler ◽  
Sebastian Müller ◽  
Petr Braun ◽  
Fritz Haake
Keyword(s):  
Form Factor ◽  
Chaotic Dynamics ◽  
Spectral Form

Semiclassical form factor for chaotic systems with spin ½

1999 ◽  
Vol 32 (50) ◽  
pp. 8863-8880 ◽  
Author(s):  
Jens Bolte ◽  
Stefan Keppeler
Keyword(s):  
Form Factor ◽  
Chaotic Systems

Spectral form factor near the Ehrenfest time

2006 ◽  
Vol 74 (6) ◽  
Author(s):  
Piet W. Brouwer ◽  
Saar Rahav ◽  
Chushun Tian
Keyword(s):  
Form Factor ◽  
Spectral Form ◽  
Ehrenfest Time

scholarly journals Spectral form factor in non-Gaussian random matrix theories

2019 ◽  
Vol 100 (2) ◽  
Author(s):  
Adwait Gaikwad ◽  
Ritam Sinha
Keyword(s):  
Form Factor ◽  
Random Matrix ◽  
Spectral Form ◽  
Non Gaussian

scholarly journals Semiclassical form factor for spectral and matrix element fluctuations of multidimensional chaotic systems

2005 ◽  
Vol 71 (1) ◽  
Author(s):  
Marko Turek ◽  
Dominique Spehner ◽  
Sebastian Müller ◽  
Klaus Richter
Keyword(s):  
Form Factor ◽  
Matrix Element ◽  
Chaotic Systems

scholarly journals Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Paul Romatschke
Keyword(s):  
Form Factor ◽  
High Temperature ◽  
Low Temperature ◽  
Energy Level ◽  
Harmonic Oscillator ◽  
Anharmonic Oscillator ◽  
Chaotic Behavior ◽  
Quantum Mechanical ◽  
Spectral Form ◽  
Quartic Potential

Abstract Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems. In this work, I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential, which is classically integrable and has a Poisson-like energy-level distribution. For low temperature, OTOCs are periodic in time, similar to results for the harmonic oscillator and the particle in a box. For high temperature, OTOCs exhibit a rapid (but power-like) rise at early times, followed by saturation consistent with 2〈x2〉T〈p2〉T at late times. At high temperature, the spectral form factor decreases at early times, bounces back and then reaches a plateau with strong fluctuations.

scholarly journals Spectral form factor for time-dependent matrix model

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Arkaprava Mukherjee ◽  
Shinobu Hikami
Keyword(s):  
Form Factor ◽  
Matrix Model ◽  
Random Matrix ◽  
Quantum Chaos ◽  
Numerical Evaluation ◽  
Time Dependent ◽  
Spectral Form ◽  
Random Matrix Model ◽  
Large Size ◽  
Analytic Expression

Abstract The quantum chaos is related to a Gaussian random matrix model, which shows a dip-ramp-plateau behavior in the spectral form factor for the large size N. The spectral form factor of time dependent Gaussian random matrix model shows also dip-ramp-plateau behavior with a rounding behavior instead of a kink near Heisenberg time. This model is converted to two matrix model, made of M1 and M2. The numerical evaluation for finite N and analytic expression in the large N are compared for the spectral form factor.

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