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Bulletin of the American Physical Society

Violation of time reversal invariance in ensembles with random interactions.

Volha Abramkina, Alexander Volya, Vladimir Zelevinsky

Published Mar 31, 2012• 0 citations
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The distributions of the diagonal elements of the Wigner's reaction [Formula: see text] matrix for open systems with violated time reversal T invariance in the case of large absorption are for the first time experimentally studied. The Wigner's reaction matrix links the properties of chaotic systems with the scattering processes in the asymptotic region. Microwave networks consisting of microwave circulators were used in the experiment to simulate quantum graphs with violated T invariance. The distributions of the diagonal elements of the reaction [Formula: see text] matrix were experimentally evaluated by measuring of the two-port scattering matrix [Formula: see text]. The violation of T invariance in the networks with large absorption was demonstrated by calculating the enhancement factor W of the matrix [Formula: see text]. Our experimental results are in very good agreement with the analytic ones attained for the Gaussian unitary ensemble in the random matrix theory. The obtained results suggest that the distributions P(ʋ) and P(u) of the imaginary and the real parts of the diagonal elements of the Wigner's reaction [Formula: see text] matrix together with the enhancement factor W can be used as a powerful tool for identification of systems with violated T symmetry and quantification of their absorption.
Time-reversal (TR) symmetry is crucial for understanding a wide range of physical phenomena, and plays a key role in constraining fundamental particle interactions and in classifying phases of quantum matter. In this work, we introduce an ensemble of random quantum circuits that are representative of the dynamics of generic TR-invariant many-body quantum systems. We derive a general statistical mechanics model describing entanglement, many-body quantum chaos, and quantum information dynamics in such TR-invariant circuits. As an example of application of our formalism, we study the universal properties of measurement-induced phase transitions in monitored TR-invariant systems, with measurements performed in a TR-invariant basis. We find that TR invariance of the unitary part of the dynamics does not affect the universality class, unless measurement outcomes are postselected to satisfy the global TR invariance of each quantum trajectory. We confirm these predictions numerically and find, for both generic and Clifford-based evolutions, critical exponents in the case of “strong,” i.e., global TR invariance where each quantum trajectory is TR invariant.