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The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices is valid only if the spectra are desymmetrized. This implies that the fluctuation properties of the spectra are affected by the discrete symmetries of the system. In this work, it is shown that in the chaotic limit the fluctuation characteristics and symmetry structure for any arbitrary sequence of measured or computed levels can be inferred from its higher-order spectral statistics without desymmetrization. In particular, we consider a spectrum composed of $k>0$ independent level sequences with each sequence having the same level density. The $k$-th order spacing ratio distribution of such a composite spectrum is identical to its nearest neighbor counterpart with modified Dyson index $k$. This is demonstrated for the spectra obtained from random matrices, quantum billiards, spin chains and experimentally measured nuclear resonances with disparate symmetry features.
We derive a general scheme to obtain quantum fluctuation relations for dynamical observables in open quantum systems. For concreteness we consider Markovian non-unitary dynamics that is unraveled in terms of quantum jump trajectories, and exploit tec
In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation functions
We perform an in-depth comparison of quantum annealing with several classical optimisation techniques, namely thermal annealing, Nelder-Mead, and gradient descent. We begin with a direct study of the 2D Ising model on a quantum annealer, and compare
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of states viol
We address the problem of the minus sign sampling for two electron systems using the path integral approach. We show that this problem can be reexpressed as one of computing free energy differences and sampling the tails of statistical distributions.