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Acta Physica Polonica A

Atomic Nucleus as Chaotic Quantum Many-Body System

Vladimir Zelevinsky

Published Dec 1, 2015• 1 citation
Publisher

Abstract

Quantum many-body chaos is described as a practical (theoretical, experimental, and computational) instrument in physics of mesoscopic systems of interacting particles.Using mainly nuclear physics applications, it is shown that interactions of constituents create stationary states of high complexity with respect to the nean-field basis with observable properties smoothly changing along the spectrum.Both local Gaussian orthogonal ensemble type features and the global evolution along the spectrum are used to understand the many-body physics and define thermodynamic properties of isolated mesoscopic objects.Among the examples discussed, especially interesting is a chaotic enhancement of weak perturbations illustrated by a large parity violation in neutron resonances on heavy nuclei.Artificially introduced chaotic elements are used to explore the nuclear landscape and predict phase transformations.

DOI
10.12693/aphyspola.128.1008

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Quantum many-body chaos is described as a practical (theoretical, experimental, and computational) instrument in physics of mesoscopic systems of interacting particles.Using mainly nuclear physics applications, it is shown that interactions of constituents create stationary states of high complexity with respect to the nean-field basis with observable properties smoothly changing along the spectrum.Both local Gaussian orthogonal ensemble type features and the global evolution along the spectrum are used to understand the many-body physics and define thermodynamic properties of isolated mesoscopic objects.Among the examples discussed, especially interesting is a chaotic enhancement of weak perturbations illustrated by a large parity violation in neutron resonances on heavy nuclei.Artificially introduced chaotic elements are used to explore the nuclear landscape and predict phase transformations.
Many-body quantum chaos results from interparticle interactions in mesoscopic systems at sufficiently high level density. A short review shows that, going beyond generic properties of local spectral statistics, the ideas of many-body quantum chaos serve as a rich source of new theoretical approaches, computational and experimental tools. Chosen examples include the enhancement of weak perturbations, thermalization in finite systems, exponential convergence of large Hamiltonian matrices and correlations between the states of different symmetry.
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded (two-body) random matrix ensembles and their various deformations. These ensembles predict that the smoothed form of matrix elements of a transition operator between the chaotic eigenstates weighted by the densities at the two ends (i.e. the bivariate strength density) will be a bivariate Gaussian with the bivariate correlation coefficient arising out of the non-commutability of the hamiltonian and the transition operator involved. The ensemble theory extends to systems with a mean-field and a chaos generating two-body interaction (as in nuclei, atoms and diffusive quantum dots). These developments in many-body quantum chaos are described with special reference to one-body transition operators.
In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures, reflecting the distinction between chaotic, mixed or integrable classical dynamics, and the corresponding quantum properties. Well established techniques dealing with ergodic wave interference in the usual semiclassical limit ℏ→0\hbar \to 0ℏ→0, where the classical limit is given by Hamiltonian mechanics of particles, constitute a now standard part of the toolkit of theoretical physics. During the last years, these ideas have been extended into the field theoretical domain of systems composed of NNN indistinguishable particles, aka quantum fields, displaying a different type of semiclassical limit ℏeff=1/N→0\hbar_{\rm eff}=1/N \to 0ℏeff​=1/N→0 and accounting for genuine many-body quantum interference. The foundational concept behind this idea of many-body interference, the many-body version of the van Vleck-Gutzwillers semiclassical propagator, is explained in detail. Based on this the corresponding semiclassical many-body theory is reviewed. It provides a unified framework for understanding a variety of quantum chaotic phenomena addressed, including random-matrix spectral correlations in many-body systems, the universal morphology of many-body eigenstates, interference effects kin to mesoscopic weak localization, and the key to the scrambling of many-body correlations characterized by out-of-time-order correlators.
Experimental progress in the miniaturization of electronic devices has made routinely available in the laboratory small electronic systems, on the micrometre or sub-micrometre scale, which at low temperature are sufficiently well isolated from their environment to be considered as fully coherent. Some of their most important properties are dominated by the interaction between electrons. Understanding their behaviour therefore requires a description of the interplay between interference effects and interactions. The goal of this review is to address this relatively broad issue and more specifically to address it from the perspective of the quantum chaos community. I will therefore present some of the concepts developed in the field of quantum chaos which may be applied to the study of many-body effects in mesoscopic and nanoscopic systems. Their implementation is illustrated in a few examples of experimental relevance such as persistent currents, mesoscopic fluctuations of Kondo properties or Coulomb blockade. I will furthermore try to bring out, from the various physical illustrations, some of the specific advantages on more general grounds of the quantum chaos based approach.
Highly excited many-particle states in quantum systems (nuclei, atoms, quantum dots, spin systems, quantum computers) can be ‘chaotic’ superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is a result of the very high energy level density of many-body states which can be easily mixed by a residual interaction between particles. We consider the time dynamics of wave functions and increase of entropy in such chaotic systems. As an example, we present the time evolution in a closed quantum computer. A time scale for the entropy S ( t ) increase is t c ~&tgr; 0 /( n log 2 n ), where &tgr; 0 is the qubit ‘lifetime’, n is the number of qubits, S (0) = 0 and S ( t c )=1. At t _ t c the entropy is small: S ~ nt 2 J 2 log 2 (1/ t 2 J 2 ), where J is the inter-qubit interaction strength. At t > t c the number of ‘wrong’ states increases exponentially as 2 S ( t ) . Therefore, t c may be interpreted as a maximal time for operation of a quantum computer. At t >> t c the system entropy approaches that for chaotic eigenstates.