scholarly journals Random matrix theory of the isospectral twirling

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Salvatore Francesco Emanuele Oliviero ◽  
Lorenzo Leone ◽  
Francesco Caravelli ◽  
Alioscia Hamma
Keyword(s):  
Mutual Information ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Quantum Dynamics ◽  
Matrix Theory ◽  
Probability Distributions ◽  
Equilibrium States ◽  
Many Body ◽  
Many Body Systems ◽  
Integrable Dynamics

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref. [1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCs, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.

scholarly journals Spectral decoupling in many-body quantum chaos

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jordan Cotler ◽  
Nicholas Hunter-Jones
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Energy Eigenvalue ◽  
Time Dependent ◽  
Late Time ◽  
Many Body ◽  
Many Body Systems

Abstract We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding ensemble of disordered Hamiltonians. We find that late time correlation functions approximately factorize into a time-dependent piece, which only depends on spectral statistics of the Hamiltonian ensemble, and a time-independent piece, which only depends on the data of the constituent operators of the correlation function. We call this phenomenon “spectral decoupling”, which signifies a dynamical onset of random matrix theory in correlation functions. A key diagnostic of spectral decoupling is k-invariance, which we refine and study in detail. Particular emphasis is placed on the role of symmetries, and connections between k-invariance, scrambling, and OTOCs. Disordered Pauli spin systems, as well as the SYK model and its variants, provide a rich source of disordered quantum many-body systems with varied symmetries, and we study k-invariance in these models with a combination of analytics and numerics.

scholarly journals Nonuniversality of compact support probability distributions in random matrix theory

1999 ◽  
Vol 60 (5) ◽  
pp. 5287-5292 ◽  
Author(s):  
G. Akemann ◽  
G. M. Cicuta ◽  
L. Molinari ◽  
G. Vernizzi
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Compact Support ◽  
Matrix Theory ◽  
Probability Distributions

scholarly journals QUANTUM DYNAMICS AND RANDOM MATRIX THEORY

2002 ◽  
Vol 16 (14n15) ◽  
pp. 2003-2008 ◽  
Author(s):  
HERVÉ KUNZ
Keyword(s):  
Probability Distribution ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Survival Probability ◽  
Quantum Dynamics ◽  
Matrix Theory ◽  
Symmetry Class ◽  
Initial State

We compute the survival probability of an initial state, with an energy in a certain window, by means of random matrix theory. We determine its probability distribution and show that is is universal, i.e. characterised only by the symmetry class of the hamiltonian and independent of the initial state.

RANDOM MATRIX THEORY AND ITS APPLICATION TO THE DECAY OUT OF A SUPERDEFORMED BAND

2008 ◽  
Vol 17 (supp01) ◽  
pp. 292-303 ◽  
Author(s):  
JIANZHONG GU
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
Quantum Systems ◽  
Many Body ◽  
Superdeformed Band ◽  
Eigenvalues And Eigenfunctions ◽  
Physical Problems

Originally, random matrix theory (RMT) was designed by Wigner to deal with the statistics of eigenvalues and eigenfunctions of complex many-body quantum systems in 1950s. During the last two decades, the RMT underwent an unexpected and rapid development: The RMT has been successfully applied to an ever increasing variety of physical problems, and it has become an important tool to attack many-body problems. In this contribution I briefly outline the development of the RMT and introduce its basics. Its application to the decay out of a Superdeformed band and a comparison of the approach used in Ref. 34 with that proposed by Vigezzi et al are presented. Current theoretical activities on the decay out problem are reviewed, and the influence of the degree of chaoticity of the normally deformed states on the decay out intensity is examined systematically.

scholarly journals Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Pavel Kos ◽  
Marko Ljubotina ◽  
Tomaž Prosen
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Many Body
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