Related papers: Crossover from Poisson to Wigner-Dyson Level Stati…
Certain frustrated systems, including spin ice and dimer models, exhibit a Coulomb phase at low temperatures, with power-law correlations and fractionalized monopole excitations. Transitions out of this phase, at which the effective gauge…
By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
Using a new class of exactly solvable models based on the pairing interaction, we show that it is possible to construct integrable Hamiltonians with a Wigner distribution of nearest neighbor level spacings. However, these Hamiltonians…
We analyze numerically ensembles of tight-binding Hamiltonians describing highly-symmetric graphene nanoflakes with weak diagonal disorder induced by random electrostatic potential landscapes. When increasing the disorder strength,…
We present a systematic analysis of quantum Heisenberg-, XY- and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating…
We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of…
We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with…
We investigate the dependence of the structural phase transitions in an infinite quasi-one-dimensional system of repulsively interacting particles on the profile of the confining channel. Three different functional expressions for the…
Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase of the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behavior may be misinterpreted as a…
We study measures on random partitions, arising from condensing stochastic particle systems with stationary product distributions. We provide fairly general conditions on the stationary weights, which lead to Poisson-Dirichlet statistics of…
We propose a novel framework to analyze symmetry breaking in dynamical systems through the lens of entropy and information transfer. Information transfer quantifies the directional exchange of entropy between observables, allowing us to…
Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically…
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…
We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random…
Employing Monte-Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing…
The energy level statistics of 2D electrons with spin-orbit scattering are considered near the disorder induced metal-insulator transition. Using the Ando model, the nearest-level-spacing distribution is calculated numerically at the…
The universal behavior of magnetic impurities in a metal is proved with the help of skeleton diagrams. The energy scales are derived from the structure of the skeleton diagrams. A minimal set of skeleton diagrams is sorted out that scales…
We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the…
Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this…