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 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 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.

scholarly journals Integrability and spectral form factor in Chern–Simons formulation

2020 ◽  
Vol 35 (24) ◽  
pp. 2050143
Author(s):  
Chen-Te Ma ◽  
Hongfei Shu
Keyword(s):  
Form Factor ◽  
Random Matrix ◽  
Integrable Model ◽  
Toda Chain ◽  
Simons Theory ◽  
Spectral Form ◽  
Higher Spin ◽  
Chain Theory ◽  
Matrix Spectrum ◽  
Chern Simons

We study the integrability from the spectral form factor in the Chern–Simons formulation. The effective action in the higher spin sector was not derived so far. Therefore, we begin from the SL(3) Chern–Simons higher spin theory. Then the dimensional reduction in this Chern–Simons theory gives the SL(3) reparametrization invariant Schwarzian theory, which is the boundary theory of an interacting theory between the spin-2 and spin-3 fields at the infrared or massless limit. We show that the Lorentzian SL(3) Schwarzian theory is dual to the integrable model, SL(3) open Toda chain theory. Finally, we demonstrate the application of open Toda chain theory from the SL(2) case. The numerical result shows that the spectral form factor loses the dip-ramp-plateau behavior, consistent with integrability. The spectrum is not a Gaussian random matrix spectrum. We also give an exact solution of the spectral form factor for the SL(3) theory. This solution provides a similar form to the SL(2) case for [Formula: see text]. Hence the SL(3) theory should also do not have a Gaussian random matrix spectrum.

scholarly journals Spectral form factor in a random matrix theory

1997 ◽  
Vol 55 (4) ◽  
pp. 4067-4083 ◽  
Author(s):  
E. Brézin ◽  
S. Hikami
Keyword(s):  
Form Factor ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Spectral Form

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

Sign in / Sign up

Export Citation Format

Share Document