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Quantum Chaos and Dissipation in Finite Fermi Systems

Sergiy Radionov

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We address the problem of the dissipative character of collective motion in finite Fermi systems. We study this problem from the point of view of chaotic features of the fermionic degrees of freedom of the many-body Fermi systems. Our main aim is of two kinds: first, we investigate how quantum chaos sets in in many-body systems and then, we try to relate quantum many-body chaos of the intrinsic fermionic degrees of freedom to the corresponding dissipative properties of the macroscopic collective motion. The main focus is on the role of two-body interaction between fermions in onset of the quantum many-body chaos and collective dissipation.

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We address the problem of the dissipative character of collective motion in finite Fermi systems. We study this problem from the point of view of chaotic features of the fermionic degrees of freedom of the many-body Fermi systems. Our main aim is of two kinds: first, we investigate how quantum chaos sets in in many-body systems and then, we try to relate quantum many-body chaos of the intrinsic fermionic degrees of freedom to the corresponding dissipative properties of the macroscopic collective motion. The main focus is on the role of two-body interaction between fermions in onset of the quantum many-body chaos and collective dissipation.
In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the basis of non-interacting particles. In order to demonstrate the most important aspects of this approach, the matrix model of two-body random interaction between Fermi-particles has been used. Different problems have been considered such as the onset of chaos and statistical equilibrium, the relation between the structure of eigenstates and distribution of occupation numbers, the emergence of the Fermi-Dirac distribution in isolated systems of finite number of particles and many others. The application of the approach to dynamical systems with the classical limit is discussed as well.
We discuss the possibility of having "quantum dissipation" due to the interaction with chaotic degrees of freedom. We define the conditions that should be satisfied in order to have a dissipative effect similar to the one due to an interaction with a (many body) bath. We also compare with the case where the environment is modeled by a random matrix model. In the case of interaction with "chaos" we observe a regime where the relaxation process is nonuniversal and reflects the underlaying semiclassical dynamics. As an example we consider a two level system (spin) that interacts with a two-dimensional anharmonic oscillator.
The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many-body system, a set of coupled dynamical equations for the collective classical variable and the quantum mechanical occupancies of the intrinsic nuclear states is derived in the limit of weak coupling of the collective and intrinsic subsystems. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed.
Quantum chaos concerns the emergence of universal statistical and dynamical prop- erties in quantum systems whose classical counterparts exhibit chaotic behavior. Unlike classical chaos, which can be characterized by sensitivity to initial conditions and exponential divergence of trajectories, quantum chaos manifests itself through a variety of indirect diagnostics, including spectral correlations, operator growth, and information scrambling. Understanding how these signatures arise from microscopic dynamics, and how they can be accessed in realistic many-body systems, is a central challenge in modern physics. This thesis investigates quantum chaos from complementary theoretical and practical perspectives. On the theoretical side, it develops effective descriptions of chaotic dy- namics in many-body systems with approximate symmetries, focusing on how weak symmetry breaking controls the exploration of Hilbert space and the crossover to random-matrix universality. Using perturbative arguments, numerical simulations, and a nonlinear sigma-model formulation, we identify a regime of Hilbert-space dif- fusion in which chaotic dynamics unfolds through a slow, collective spreading across nearly decoupled symmetry sectors. On the practical side, the thesis addresses the question of how paradigmatic chaotic models can be realized and probed in controlled experimental platforms. In partic- ular, it explores quantum simulation schemes for Sachdev–Ye–Kitaev (SYK) models using cavity quantum electrodynamics. By employing time-dependent disorder and Trotterized evolution in single-mode optical cavities, we demonstrate how low-rank interactions can be systematically promoted to effective all-to-all randomness, re- producing the spectral and dynamical signatures of SYK physics. Extensions to open-system dynamics are discussed, including Lindbladian realizations and the role of dissipation. The thesis thus highlights the connections between effective descriptions of quantum chaos and their implementation in controlled quantum simulation settings.