Related papers: Higher Order Correlations in Quantum Chaotic Spect…
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…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by…
The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…
We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the…
The authors review the evidence for the applicability of random--matrix theory to nuclear spectra. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately: quantum chaos) in nuclei whenever random--matrix…
The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic…
The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…
Within random matrix theory for quantum dots, both the dot's one-particle eigenlevels and the dot-lead couplings are statistically distributed. While the effect of the latter on the conductance is obvious and has been taken into account in…
This chapter discusses the conditions and timescales under which isolated many-body quantum systems, initially far from equilibrium, ultimately reach thermal equilibrium. We also examine quantities that, during the relaxation process,…
We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
This is a review of the properties of spectral fluctations in disordered metals, their relation with Random Matrix Theory and semiclassical picture. We also review the physics of persistent currents in mesoscopic isolated rings, the…
The spectral statistic $\delta_n$ measures the fluctuations of the number of energy levels around its mean value. It has been shown that chaotic quantum systems display $1/f$ noise (pink noise) in the power spectrum $S(f)$ of the $\delta_n$…
Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. They have been previously shown to distinguish standard model coupling parameters as…