Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series SEM-LPTM-UCP
Subjects math-ph
Date Thursday 6 May 2021
Time 14:00
Institute LPTM
Seminar Room Distanciel TEAMS
Speaker's Last Name De Luca
Speaker's First Name Andrea
Speaker's Email Address
Speaker's Institution LPTM, CY CPU, CNRS, Cergy Pontoise
Title Spectral statistics in the thermodynamic limit of extended many-body quantum systems
Abstract Defining the chaotic properties of quantum systems is a notoriously difficult problem, because of the fundamental fact that in quantum mechanics trajectories are not well-defined. A historically very productive direction has been the investigation of spectral properties of quantum Hamiltonian in a statistical way: it emerges that chaos is associated with strong repulsion between energy levels. When one tries to apply this recipe to many-body systems, it is clear that a hierarchy of energy/time scales can emerge due to the interplay of farther components of the system which are less and less correlated. Recently, the use of quantum circuits composed by random gates has allowed explicit calculations clarifying to what extent chaos emerges for spatially extended systems. In this talk, I will review some recent advances in the field with an emphasis on the strong success of a "Wick rotation" which exchanges space and time. Thanks to this formulation, we have been able to connect spectral properties to a spectrum of Lyapunov exponents, which emerge from the infinite product of random operators in the space direction.
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