Related papers: Individual energy level distributions for one-dime…
We study the sample-size dependence of the ground-state energy in a one-dimensional localization problem, based on a supersymmetric quantum mechanical Hamiltonian with random Gaussian potential. We determine, in the form of bounds, the…
Numerical study of the one-dimensional Frenkel Hamiltonian with on-site randomness is carried out. We focus on the statistics of the energy levels near the lower exciton band edge, i. e. those determining optical response. We found that the…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
We study the energy distribution of maxima and minima of a simple one-dimensional disordered Hamiltonian. We find that in systems with short range correlated disorder there is energy separation between maxima and minima, such that at fixed…
We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric…
Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this…
We study the full distribution $P(E)$ of the ground-state energy of a single quantum particle in a potential $V(\boldsymbol{x}) = V_0(\boldsymbol{x}) + \sqrt{\epsilon} \, v_1(\boldsymbol{x})$, where $V_0(\boldsymbol{x})$ is a deterministic…
The one-dimensional supersymmetric random Hamiltonian $H_{susy}=-\frac{d^2}{dx^2}+\phi^2+\phi'$, where $\phi(x)$ is a Gaussian white noise of zero mean and variance $g$, presents particular spectral and localization properties at low…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…
We consider an Ising model with quenched surface disorder, the disorder average of the free energy is the main object of interest. Explicit expressions for the free energy distribution are difficult to obtain if the quenched surface spins…
We study the energy distribution function $\rho (E)$ for interfaces in a random field environment at zero temperature by summing the leading terms in the perturbation expansion of $\rho (E)$ in powers of the disorder strength, and by taking…
We investigate the charging energy level statistics of disordered interacting electrons in quantum dots by numerical calculations using the Hartree approximation. The aim is to obtain a global picture of the statistics as a function of…
A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics…
We investigate two one-dimensional tight-binding models with disorder that have extended states at zero energy. We use exact and partial diagonalisation of the Hamiltonian to obtain the eigenmodes and the associated participation ratios,…
We consider a single particle spectrum as given by the eigenvalues of the Wigner-Dyson ensembles of random matrices, and fill consecutive single particle levels with n fermions. Assuming that the fermions are non-interacting, we show that…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential $\phi(x)$ is a random telegraph process is solved exactly. Both the localization length and the…
We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price…
The dynamics of individual colloidal particles in random potential energy landscapes were investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a…
We study the Sinai model for the diffusion of a particle in a one dimensional quenched random energy landscape. We consider the particular case of discrete energy landscapes made of random +/- 1 jumps on the semi infinite line Z+ with a…