相关论文: Signatures of Randomness in Quantum Chaos
We investigate toy dynamical models of energy - level repulsion in quantum (quasi)energy eigenvalue sequences.
We identify parametric (radial) Bessel-Ornstein-Uhlenbeck stochastic processes as primitive dynamical models of energy level repulsion in irregular quantum systems. Familiar GOE, GUE, GSE and non-Hermitian Ginibre universality classes of…
We study the response of the quasi-energy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
Dissipative quantum chaos plays a central role in the characterization and control of information scrambling, non-unitary evolution, and thermalization, but it still lacks a precise definition. The Grobe-Haake-Sommers conjecture, which…
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We study statistical properties of excited levels of the E x (b_1+b_2) Jahn-Teller model. The multitude of avoided crossings of energy levels is generally claimed to be a testimony of quantum chaos. We found that apart from two limiting…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
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…
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices. We…
We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$…
We study the asymptotic behavior of continuous-time, time-inhomogeneous Markovian quantum dynamics in a stationary random environment. Under mild faithfulness and eventually positivity-improving assumptions, the normalized evolution…
We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite size system with many degrees of freedom. For the case of a direct cascade the energy and norm pumping takes place at low…
This statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions: eigenvalues of random matrices, non-crossing random walks and trapped fermions. These systems share many links, which can…
Discerning chaos in quantum systems is an important problem as the usual route of Lyapunov exponents in classical systems is not straightforward in quantum systems. A standard route is the comparison of statistics derived from model…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…