scholarly journals Leading off-diagonal contribution to the spectral form factor of chaotic quantum systems

2003 ◽  
Vol 36 (30) ◽  
pp. L455-L462 ◽  
Author(s):  
Marko Turek ◽  
Klaus Richter
Keyword(s):  
Form Factor ◽  
Quantum Systems ◽  
Spectral Form

scholarly journals Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 127 ◽  
Author(s):  
Aurélia Chenu ◽  
Javier Molina-Vilaplana ◽  
Adolfo del Campo
Keyword(s):  
Form Factor ◽  
Random Matrix ◽  
Exponential Growth ◽  
Energy Levels ◽  
System Size ◽  
Quantum Systems ◽  
Entangled State ◽  
Spectral Form ◽  
Work Distribution ◽  
Loschmidt Echo

Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.

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

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 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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