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2023

Microcanonical Truncations of Observables in Quantum Chaotic Systems

Iniguez, Fernando, Srednicki, Mark

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We consider the properties of an observable (such as a single spin component that squares to the identity) when expressed as a matrix in the basis of energy eigenstates, and then truncated to a microcanonical slice of energies of varying width.

For a quantum chaotic system, we model the unitary or orthogonal matrix that relates the spin basis to the energy basis as a random matrix selected from the appropriate Haar measure.
We find that the spectrum of eigenvalues is given by a centered Jacobi distribution that approaches the Wigner semicircle of a random hermitian matrix for small slices.
For slices that contain more than half the states, there is a set of eigenvalues of exactly $\pm 1$.

Microcanonical Truncations of Observables in Quantum Chaotic Systems · Around

Built on

Quantum statistical mechanics in a closed system
J. M. Deutsch · 1991
Earlier work this paper cites.
Chaos and quantum thermalization
Mark Srednicki · 1994
Earlier work this paper cites.
Thermal fluctuations in quantized chaotic systems
Mark Srednicki · 1996
Earlier work this paper cites.
The approach to thermal equilibrium in quantized chaotic systems
Mark Srednicki · 1999
Earlier work this paper cites.
Random Matrices
Madan Lal Mehta · 2004
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