Related papers: Quantum chaos and level dynamics
The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics…
We investigate quantum systems perturbed by noise in the form of repeated interactions between the system and the environment. As the number of interactions (aka time steps) tends to infinity, we show, following the works by Pellegrini,…
Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
We present an experimental study of missing level statistics of three-dimensional chaotic microwave cavities. The investigation is reinforced by the power spectrum of level fluctuations analysis which also takes into account the missing…
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…
Recent studies have shown that there is a strong interplay between quantum complexity and quantum chaos. In this work, we consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems to…
Quantized chaotic systems are generically characterized by two energy scales: the mean level spacing $\Delta$, and the bandwidth $\Delta_b\propto\hbar$. This implies that with respect to driving such systems have an adiabatic, a…
We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter is shown to…
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
We present a robust analysis of the spectral fluctuations exhibited by the light meson spectrum. This analysis provides information about the degree of chaos in light mesons and may be useful to get some insight on the underlying…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls level repulsion exponent $\beta$ and range $h$ of interactions between eigenvalues is shown to reproduce…
Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
In quantum engineering, faults may occur in a quantum control system, which will cause the quantum control system unstable or deteriorate other relevant performance of the system. This note presents an estimator-based fault-tolerant control…
We consider nonequilibrium probabilistic dynamics in logistic-like maps $x_{t+1}=1-a|x_t|^z$, $(z>1)$ at their chaos threshold: We first introduce many initial conditions within one among $W>>1$ intervals partitioning the phase space and…
A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…