Related papers: Resonances in one-dimensional Disordered Chain
The first work of Dyson relating to random matrix theory, "The dynamics of a disordered linear chain", is reviewed. Contained in this work is an exact solution of a so-called Type I chain in the case of the disorder variables being given by…
We investigate the sharp density $\rho(t,x; y)$ of the solution $u(t,x)$ to stochastic partial differential equation $\frac{\partial }{\partial t} u(t,x)=\frac12 \Delta u(t,x)+u\diamond \dot W(t,x)$, where $\dot W$ is a general Gaussian…
Much of the discussion in the literature of the low frequency part of the density of states of amorphous solids was dominated for years by comparing measured or simulated density of states to the classical Debye model. Since this model is…
We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric…
In this paper, by introducing a new type asymptotic coupling by reflection, we explore the long time behavior of random probability measure flows associated with a large class of one-dimensional McKean-Vlasov SDEs with common noise.…
Disorder hyperuniformity (DHU) is a recently discovered exotic state of many-body systems that possess a hidden order in between that of a perfect crystal and a completely disordered system. Recently, this novel DHU state has been observed…
We compute the density of states (d.o.s.) in N coupled chains with random hopping. At zero energy, the d.o.s. shows a singularity that strongly depends on the parity of N. For odd N, the d.o.s. is proportional to 1/(E (\ln |E|)^3), with and…
The self averaging properties of conductance $g$ are explored in random resistor networks with a broad distribution of bond strengths $P(g)\simg^{\mu-1}$. Distributions of equivalent conductances are estimated numerically on hierarchical…
Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the…
We study self avoiding random walks in an environment where sites are excluded randomly, in two and three dimensions. For a single polymer chain, we study the statistics of the time averaged monomer density and show that these are well…
We study the wave transport through a disordered system inside a waveguide. The expectation value of the complex reflection and transmission coefficients (the coherent fields) as well as the transmittance and reflectance are obtained…
We study the stochastic Allen-Cahn equation driven by a noise term with intensity $\sqrt{\varepsilon}$ and correlation length $\delta$ in two and three spatial dimensions. We study diagonal limits $\delta, \varepsilon \to 0$ and describe…
We determine the statistical properties of wave functions in disordered quantum systems by exact diagonalization of one-, two- and quasi-one dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we find that the tails of…
We study the creation and distribution of entanglement in disordered $XY$-type spin-$1/2$ chains for the paradigmatic case of a single flipped spin prepared on a fully polarized background. The local magnetic field is set to follow a…
We thoroughly study the persistent current of noninteracting electrons in one, two, and three dimensional thin rings. We find that the results for noninteracting electrons are more relevant for individual mesoscopic rings than hitherto…
The phenomenon of random intensity patterns, for waves propagating in the presence of disorder, is well known in optics and in mesoscopic physics. We study this phenomenon for cold atomic gases expanding, by a diffusion process, in a weak…
We study the interaction among dispersion, nonlinearity, and disorder effects in the context of wave transmission through a discrete periodic structure, subjected to continuous harmonic excitation in its stop band. We consider a damped…
Anomalies near the conductance threshold of nearly perfect semiconductor quantum wires are explained in terms of singlet and triplet resonances of conduction electrons with a single weakly-bound electron in the wire. This is shown to be a…
We perform a detailed numerical study of the conductance $G$ through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies $\epsilon$ of the tight-binding Hamiltonian are…
We reconsider the study of persistent currents in a disordered one-dimensional ring threaded by a magnetic flux, using he one-band tight-binding model for a ring of N-sites with random site energies. The secular equation for the…