相关论文: Statistics and Quantum Chaos
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
The application of a random modulation of a system parameter usually increases decoherence effects. Here we show how, employing an appropriate stochastic modulation, it is instead possible to preserve the quantum coherence of a system.
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
We investigate the role of quantum monitoring in the dynamical manifestations of Hamiltonian quantum chaos. Specifically, we analyze the generalized spectral form factor, defined as the survival probability of a coherent Gibbs state under…
By modeling quantum chaotic dynamics with ensembles of random operators, we explore howmachine learning learning algorithms can be used to detect pseudorandom behavior in qubit systems.We analyze samples consisting of pieces of correlation…
In this dissertation, we analyze equilibrium and out-of-equilibrium quantum phase transitions present in quantum spin-$\frac{1}{2}$ models, using a quantum information approach through quantum correlations and phase space formalism, and a…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
In this work, the term ``quantum chaos'' refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using e.g.~the spectral form factor, which…
Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Effects of quantum statistics are clearly seen in the final states of high-energy multiparticle production processes. These effects are being widely used to obtain information about the regions where the final state hadrons are produced.…
It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
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 study the statistical properties of the time delay matrix $Q$ in the context of quantum transport through a chaotic cavity, in the absence of time-reversal invariance. First, we approach the problem from the point of view of random…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by…
By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction…
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,…