相关论文: Sample-size dependence of the ground-state energy …
We study the distribution of the $n$-th energy level for two different one-dimensional random potentials. This distribution is shown to be related to the distribution of the distance between two consecutive nodes of the wave function. We…
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 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…
We derive analytically the full distribution of the ground-state energy of $K$ non-interacting fermions in a disordered environment, modelled by a Hamiltonian whose spectrum consists of $N$ i.i.d.~random energy levels with distribution…
We consider the homogenization of parabolic equations with large spatially-dependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We…
We investigate the statistics of eigenstates in a weak self-affine disordered potential in one dimension, whose Gaussian fluctuations grow with distance with a positive Hurst exponent $H$. Typical eigenstates are superlocalized on samples…
We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the…
The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$…
We study numerically the effects of short- and long-range correlations on the localization properties of the eigenstates in a one-dimensional disordered lattice characterized by a random non-Hermitian Hamiltonian, where the imaginary part…
This paper studies the localization behaviour of Bose-Einstein condensates in disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a bounded interval. In the regime of weak particle interaction, we are able to quantify…
Localized states in one-dimensional open disordered systems and their connection to the internal structure of random samples have been studied. It is shown that the localization of energy and anomalously high transmission associated with…
We show that a quantum particle in $\mathbb{R}^d$, for $d \geq 1$, subject to a white-noise potential, moves super-ballistically in the sense that the mean square displacement $\int \|x\|^2 \langle \rho(x,x,t) \rangle ~dx$ grows like…
We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $\xi$. We employ Non-perturbative Functional…
Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This…
The resonance states of one- and two-particle Hamiltonians are studied using variational expansions with real basis-set functions. The resonance energies, $E_r$, and widths, $\Gamma$, are calculated using the density of states and an…
The density of states for the Schroedinger equation with a Gaussian random potential is calculated in a space of dimension d=4-epsilon in the entire energy range including the vicinity of a mobility edge. Leading terms in 1/epsilon are…
We study localization properties of electronic states in one-dimensional lattices with nearest-neighbour interaction. Both the site energies and the hopping amplitudes are supposed to be of arbitrary form. A few cases are considered in…
The Gaussian chain in a quenched random potential (which is characterized by the disorder strength $\Delta$) is investigated in the $d$ - dimensional space by the replicated variational method. The general expression for the free energy…
We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or…
Zero-field magnetic noise, characterised by the magnetic autocorrelation function $S_s(t)$, has been observed, perhaps surprisingly, to depend on sample shape $s$. The reasons for this are identified and general expressions are derived that…