Statistical properties of nuclear energy levels and nuclear transitions have long been juxtaposed to the limit of random matrix theory. A novel practical measure of chaos onset, the ratio of ...consecutive energy spacings, that does not require the unfolding of energy levels, was previously introduced for all three canonical random matrix ensembles, along with the expressions for the regular and chaotic limits. In this study, an expression for this ratio interpolating between the regular and chaotic limits is introduced and applied to the energy levels calculated in the realistic nuclear shell model and in the interacting boson model. The results are consistent with those extracted from the traditional statistics of nearest-neighbor spacings with unfolding; we find the relation between the ways of convergence to the chaotic limit.
Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral ...correlations. Based on recent progress in the application of spectral analysis to non-Hermitian quantum systems, we show that local level statistics, which probe the dynamics around the Heisenberg time, of a non-Hermitianq-body Sachdev-Ye-Kitev (nHSYK) model withNMajorana fermions, and its chiral and complex-fermion extensions, are also well described by random matrix theory forq>2, while forq=2, they are given by the equivalent of Poisson statistics. For that comparison, we combine exact diagonalization numerical techniques with analytical results obtained for some of the random matrix spectral observables. Moreover, depending onqandN, we identify 19 out of the 38 non-Hermitian universality classes in the nHSYK model, including those corresponding to the tenfold way. In particular, we realize explicitly 14 out of the 15 universality classes corresponding to non-pseudo-Hermitian Hamiltonians that involve universal bulk correlations of classesAI†andAII†, beyond the Ginibre ensembles. These results provide strong evidence of striking universal features in nonunitary many-body quantum chaos, which in all cases can be captured by nHSYK models withq>2.
We compare the entire classical and quantum evolutions of the Dicke model in its regular and chaotic domains. This is a paradigmatic interacting spin-boson model of great experimental interest. By ...studying the classical and quantum survival probabilities of initial coherent states, we identify features of the long-time dynamics that are purely quantum and discuss their impact on the equilibration times. We show that the ratio between the quantum and classical asymptotic values of the survival probability serves as a metric to determine the proximity to a separatrix in the regular regime and to distinguish between two manifestations of quantum chaos: scarring and ergodicity. In the case of maximal quantum ergodicity, our results are analytical and show that quantum equilibration takes longer than classical equilibration.
It has been recently proposed by Maldacena and Qi that an eternal traversable wormhole in a two-dimensional anti–de Sitter space is the gravity dual of the low temperature limit of two ...Sachdev-Ye-Kitaev (SYK) models coupled by a relevant interaction (which we will refer to as spin operator). We study spectral and eigenstate properties of this coupled SYK model. We find that level statistics in the tail of the spectrum, and for a sufficiently weak coupling, show substantial deviations from random matrix theory, which suggests that traversable wormholes are not quantum chaotic. By contrast, for sufficiently strong coupling, corresponding to the black hole phase, level statistics are well described by random matrix theory. This transition in level statistics coincides approximately with a previously reported Hawking-Page transition for weak coupling. We show explicitly that this thermodynamic transition turns into a sharp crossover as the coupling increases. Likewise, this critical coupling also corresponds to the one at which the overlap between the ground state and the thermofield double state (TFD) is smallest. In the range of sizes we can reach by exact diagonalization, the ground state is well approximated by the TFD only in the strong coupling limit. This is due to the fact that the ground state is close to the eigenstate of the spin operator corresponding to the lowest eigenvalue which is an exact TFD at infinite temperature. In this region, the spectral density is separated into blobs centered around the eigenvalues of the spin operator. For weaker couplings, the exponential decay of coefficients in a tensor product basis, typical of the TFD, becomes power law. Finally, we also find that the total Hamiltonian has an additional discrete symmetry which has not been reported previously.
We present a semiclassical calculation, based on classical action correlations implemented by means of a matrix integral, of all moments of the Wigner–Smith time delay matrix, Q, in the context of ...quantum scattering through systems with chaotic dynamics. Our results are valid for broken time reversal symmetry and depend only on the classical dwell time and the number of open channels, M, which is arbitrary. Agreement with corresponding random matrix theory reduces to an identity involving some combinatorial concepts, which can be proved in special cases.
•Implements an efficient semiclassical approach in terms of a matrix integral.•Computes general statistics of time delay in quantum chaotic systems.•Advances a new conjecture in the theory of symmetric polynomials.
PDF
