Weak Random Potential Research Articles

Density-matrix renormalization-group studies for one-dimensional polarized Anderson–Hubbard model

By using the density-matrix renormalization-group method, we study impurity effects on the pair correlation function of the one-dimensional spin-imbalanced Anderson–Hubbard model. In strongly-attractive interacting cases in the presence of weak random potentials, we find that the Fulde–Ferrell–Larkin–Ovchinnikov type pair correlation function with nodes decays slower than that of Bardeen–Cooper–Schrieffer type one without nodes. This means that the former type pairing is unexpectedly more robust against randomness in the strong coupling regime.

INTERACTING BOSONIC ATOMS WITH RANDOM POTENTIAL IN OPTICAL LATTICES

In this paper, we study the ultracold atoms in optical lattice with a weak random external potential by an extended Bose–Hubbard model. When the on-site interaction is strong enough, the model can be mapped to the XXZ model. Then the mean-field theory is applied and we get the zero- and finite-temperature phase diagrams in different optical parameters. The differences between the systems with and without disorder were found, and the Bose-glass phase may exist in the system with disorder.

Superuid and insulator of dirty Bose-Fermi mixture

One-dimensional Bose-Fermi mixture systems in a random potential are numerically investigated with focus on their superfluidity and localization properties. It is known that one-dimensional bosons and fermions behave differently in a weak random potential: Interacting bosons in a weak random potential exhibit superfluidity if the interactions are repulsive and not too strong, while interacting fermions with repulsive forces are localized in the presence of randomness. So the question is what happens if weakly interacting bosons and fermions are mixed in a random potential, which might be actually realized by the technique of trapping atoms on a random optical lattice. To answer this question we performed quantum Monte Carlo simulations of bosons and fermions on a one-dimensional lattice with random site energies. The result showed that when the boson-fermion interactions were attractive, both bosons and fermions tended to be localized. However when the boson- fermion interactions were repulsive and relatively weak, the superfluidity of bosons was enhanced and the fermions were delocalized.

Excitations of One-Dimensional Bose-Einstein Condensates in a Random Potential

We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as l(omega) approximately 1/omega(alpha). We show that the well-known result alpha=2 applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, alpha starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, alpha=1. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.

Coincidence of Lyapunov exponents for random walks in weak random potentials

We investigate the free energy of nearest-neighbor random walks on ℤd, endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the ballistic regime in dimensions d≥4, at which we show that quenched and annealed Lyapunov exponents are equal as soon as the strength of the potential is small enough.

Slowly moving matter–wave gap soliton propagation in weak random nonlinear potential

We systematically investigate the motion of slowly moving matter–wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross–Pitaevskii equation.

Boltzmann Limit and Quasifreeness for a Homogenous Fermi Gas in a Weakly Disordered Random Medium

We discuss some basic aspects of the dynamics of a homogenous Fermi gas in a weak random potential, under negligence of the particle pair interactions. We derive the kinetic scaling limit for the momentum distribution function with a translation invariant initial state and prove that it is determined by a linear Boltzmann equation. Moreover, we prove that if the initial state is quasifree, then the time evolved state, averaged over the randomness, has a quasifree kinetic limit. We show that the momentum distributions determined by the Gibbs states of a free fermion field are stationary solutions of the linear Boltzmann equation; this includes the limit of zero temperature.

Enhancement of Localization in One-Dimensional Random Potentials with Long-Range Correlations

We experimentally study the effect of enhancement of localization in weak one-dimensional random potentials. Our experimental setup is a single-mode waveguide with 100 tunable scatterers periodically inserted into the waveguide. By measuring the amplitudes of transmitted and reflected waves in the spacing between each pair of scatterers, we observe a strong decrease of the localization length when white-noise scatterers are replaced by a correlated arrangement of scatterers.

Density correlations in cold atomic gases: Atomic speckles in the presence of disorder

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 random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.

Collective oscillations in trapped Bose-Einstein-condensed gases in the presence of weak disorder

The influence of a weak random potential on the collective modes of a trapped interacting Bose-Einstein condensate at zero temperature is calculated in the limit when the correlation length of the disorder is smaller than the healing length of the superfluid. The problem is solved in the Thomas-Fermi limit by generalizing the superfluid hydrodynamic equations to allow for the presence of weak disorder. We find that the disorder-induced frequency-shifts of the low-energy excitations can be of the same order of magnitude as the beyond mean-field corrections in the normal interaction recently observed experimentally.

Effects of weak impurity potential on the quasi-particle states in high- Tc superconductors

Using the Bogoliubov-de Gennes equation for d-wave superconductors, we investigate the effects of weak impurity potential on the quasi-particle states. The weak nonlocal potential has little effect on low energy spectrum (i.e. ∣ E∣ < 0.2 Δ), while the spectrum around ∣ E∣ ∼ Δ becomes strongly position dependent. We believe most of the inhomogeneity seen in recent STM studies is due to the weak scatterers modeled in the present analysis. The results shows inhomogeneity of superconducting order parameter which is observed by scanning tunneling experiments, may be attributed to the weak random dopant potential.

Anderson localization of elementary excitations in a one-dimensional Bose-Einstein condensate

We study the elementary excitations of a transversely confined Bose-Einstein condensate in presence of a weak axial random potential. We determine the localization length (i) in the hydrodynamical low energy regime, for a domain of linear densities ranging from the Tonks-Girardeau to the transverse Thomas-Fermi regime, in the case of a white noise potential and (ii) for all the range of energies, in the ``one-dimensional mean field regime'', in the case where the randomness is induced by a series of randomly placed point-like impurities. We discuss our results in view of recent experiments in elongated BEC systems.

Microwave resonance susceptibility of a two-dimensional hole system in a weak random potential

The electric susceptibility of a high-quality two-dimensional hole system is investigated experimentally by means of radio frequency techniques in the magnetically induced solid phase. The experiments were carried out with a heterodyne spectrometer that allows us to measure both the changes in absorption and dispersion. For frequencies between 0.2 and $4\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ the spectrum exhibits a series of four sharp resonances identified as pinned magnetophonon modes of the Wigner solid. Anomalous behavior around the Landau level filling factor of $1∕5$ indicates bulk and shear moduli variations that are not monotonic. The sharpness of the resonances and the correlation of the pinning frequency with the threshold field measured in dc transport experiments are not in agreement with the results of earlier experiments in two-dimensional electron systems. The results presented here allow for the determination of the dominant source of disorder, and indicate that long-range order remains in the hole solid despite the presence of impurities.

Density of states for theπ-flux state with bipartite real random hopping only: A weak disorder approach

Gade [R. Gade, Nucl. Phys. B \textbf{398}, 499 (1993)] has shown that the local density of states for a particle hopping on a two-dimensional bipartite lattice in the presence of weak disorder and in the absence of time-reversal symmetry(chiral unitary universality class) is anomalous in the vicinity of the band center $\epsilon=0$ whenever the disorder preserves the sublattice symmetry. More precisely, using a nonlinear-sigma-model that encodes the sublattice (chiral) symmetry and the absence of time-reversal symmetry she argues that the disorder average local density of states diverges as $|\epsilon|^{-1}\exp(-c|\ln\epsilon|^\kappa)$ with $c$ some non-universal positive constant and $\kappa=1/2$ a universal exponent. Her analysis has been extended to the case when time-reversal symmetry is present (chiral orthogonal universality class) for which the same exponent $\kappa=1/2$ was predicted. Motrunich \textit{et al.} [O. Motrunich, K. Damle, and D. A. Huse, Phys. Rev. B \textbf{65}, 064206 (2001)] have argued that the exponent $\kappa=1/2$ does not apply to the typical density of states in the chiral orthogonal universality class. They predict that $\kappa=2/3$ instead. We confirm the analysis of Motrunich \textit{et al.} within a field theory for two flavors of Dirac fermions subjected to two types of weak uncorrelated random potentials: a purely imaginary vector potential and a complex valued mass potential. This model is believed to belong to the chiral orthogonal universality class. Our calculation relies in an essential way on the existence of infinitely many local composite operators with negative anomalous scaling dimensions.

Anderson localization in Hubbard ladders

The effect of a weak random potential on two-leg Hubbard ladders is investigated. The random potential is shown to induce Anderson localization except for attractive enough interactions, suppressing completely d-wave superconductivity. These localization effects remain very strong even for many ladders coupled by Josephson coupling. Both DC and AC conductivities and localization lengths are obtained. Consequences for the superconducting ladder compound Sr x Ca 14− x Cu 24O 41+ δ are discussed.

Transport in a nearly periodic potential with a magnetic field

A two-dimensional gas of non-interacting quasiparticles in a nearly periodic potential and a perpendicular magnetic field is studied. The potential is a superposition of a periodic potential, induced, for example, by a charge-density wave or a vortex lattice of a type-II superconductor, and a weak random potential due to impurities. Approximating this model by Dirac fermions with random mass, random energy, and random vector potential, we evaluate the density of states and the Hall conductivity using a self-consistent approximation. We obtain a singular average density of states , where decreases with the strength of the randomness. The Hall conductivity has a plateau which is destroyed for strong tunnelling through the saddle points of the nearly periodic potential.

Coherent propagation of interacting particles in a random potential: The mechanism of enhancement

Coherent propagation of two interacting particles in a one-dimensional weak random potential is considered. An accurate estimate of the matrix element of the interaction in the basis of localized states leads to a mapping onto the relevant matrix model. This mapping allows one to clarify the mechanism of enhancement of the localization length, which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with ${l}_{2}{/l}_{1}\ensuremath{\sim}{l}_{1}^{\ensuremath{\gamma}},$ where ${l}_{1}$ and ${l}_{2}$ are the one- and two-particle localization lengths and the exponent $\ensuremath{\gamma}$ depends on the strength of the interaction. In particular, in the limit of a strong particle-particle interaction there is no enhancement of the coherent propagation at all ${(l}_{2}\ensuremath{\approx}{l}_{1})$.

Transport in channels and films with rough surfaces.

We present a simple and versatile description of transport of almost ballistic particles near rough boundaries with an emphasis on thin films and narrow channels. The main effects are associated with chaotization of motion as a result of repeated scattering from random walls. We show that the problem contains an additional mesoscopic length scale which is expressed explicitly via the amplitude and correlation radius (or the correlation function) of surface inhomogeneities, and the ratio of the particle wavelength to the correlation radius. The calculations are performed with the help of a canonical coordinate transformation which reduces a transport problem with rough random walls to a completely equivalent problem with ideal flat walls, but with some random bulk distortions. This problem is treated on the basis of a kinetic equation with a perturbative collision integral. In addition to the application of the Boltzmann transport equation for (quasi)particles with an arbitrary degree of degeneracy of the distribution function, we also include the results for a single-particle diffusion on the basis of the Focker-Plank equation. We calculate different transport coefficients for (quasi)particles with an arbitrary spectrum \ensuremath{\epsilon}(p) with a bulk of calculations for particles with quadratic, ${\mathit{p}}^{2}$/2m, and linear, cp, spectra. The calculations are made in classic and WKB regimes as well as in the case of quantized motion across the film.All the transport coefficients are expressed via the first two angular harmonics of the correlation function of surface inhomogeneities which play the role of an effective transport cross section. The results include the effects of bulk impurities and changes in potential relief near the walls. We also calculate the quantum interference corrections to conductivity and localization and mesoscopic effects associated with reflections from random surface inhomogeneities, and the density of states in low-dimensional films. The mesoscopic properties are especially simple in the case of strong quantization of motion across the d-dimensional films when the problem becomes effectively equivalent to localization of d-1-dimensional motion in weak random potential. We discuss possible future applications of our method such as for porous media, boundary slip, etc.

Strong vertex corrections from weak disorder in 2D d-wave superconductors

We show that weak static random potentials have pronounced effects on the quasiparticle states of a 2Dd-wave superconductor close to a node. We prove that the vertex correction coming from the simplest crossed diagram is important even for a nonmagnetic potential. The leading frequency and momentum dependent logarithmic singularities in the self-energy are calculated exactly to second order in perturbation theory. The self-energy corrections lead to a modified low energy density of states which depends strongly on the type of random potential and which can be measured in experiments. There is an exceptional case for a potential with extremely local scatterers and opposite nodes separated by (π, π) where an exact cancelation takes place eliminating the leading frequency dependent singularity in the simplest crossed diagram. A comparison of the perturbative results with a self-consistent CPA (coherent potential approximation) for the nonmagnetic disorder reveals qualitative differences in the self-energy at the smallest energies which are due to the neglectance of vertex corrections in CPA.

Effects of disorder in a dilute Bose gas.

We discuss the effects of a weak random external potential on the properties of the dilute Bose gas at zero temperature. The results recently obtained by Huang and Meng for the depletion of the condensate and of the superfluid density are recovered. Results for the shift of the velocity of sound as well as for its damping due to collisions with the external field are presented. The damping of phonons is calculated also for dense superfluids. (submitted to Phys.Rev.B)