Localization in a one-dimensional disordered model

Numerical investigation of a random, one dimensional Kronig-Penny-like model is performed using long chains and large ensembles. Dependence of the inverse localization length α on randomness, irreproducibility of resistance measurements and the dependence of the standard deviation of α on α and the length of the chain were studied. For energies, E=k² close to the zone boundary k=π, we have found α～(π-k).     

Depinning of a metastable disordered vortex lattice

We report on experiments investigating the depinning dynamics of a strongly pinned vortex lattice in 2H-NbSe2. We find that the depinning process starts at currents that are well below the critical current of the entire lattice and that it is governed by the formation of contiguous channels of mobile vortices connecting the sample edges. We obtain the formation time of the first channel by monitoring the delayed voltage response to a driving current step and by measuring the ramping rate dependence of the critical current. The subsequent increase in the number of moving vortices is determined from the temporal evolution of the voltage response and the critical current.     

Delocalization of quasiparticles in quasi-two-dimensional disordered superconductors with s-wave pairing

We investigate localization behavior of quasiparticles in disordered multi-plane superconductors with s-wave pairing. By introducing disorder with random site energies, the spatial fluctuations of Bogoliubov-de Gennes pairing potential are self-consistently determined. The size dependence of rescaled localization length for a long bar is calculated by using the transfer-matrix method. From the finite-size scaling analysis we show that there exists a critical point of the disorder strength W_c which separates the extended and localized quasiparticle states in such quasi-two-dimensional systems. The associated critical behavior is studied and the relationship of the results to the number of planes is discussed.     

Berry phase effects on the dynamics of quasiparticles in a superfluid with a vortex

We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms' momentum distribution around a vortex.     

New quasiparticles hystons and coherent photoinduced dynamics of molecules in polar disordered media

Using methods of statistical thermodynamics, it is shown that after pulse excitation the evolution of a “polar luminescent probe—polar disordered medium” system is described by an equation of damping vibrations. This allows the conclusion that in the solvate shell of the probe molecule synchronous rotational vibrations (librations) of the molecules of the medium occur, whose damping is caused by dielectric friction. Such a collective synchronous motion is considered as a motion of a quasiparticle called a hyston. The moment of inertia J_n and mass M_h of a hyston are defined as J_h=2m² ₁a^-3Ω₀ ^-2(ε-1)/(2ε+1), M_h=J_hM_s/J_s, where m₁ is the dipole moment of the probe molecule in the excited S₁-stute; a is the Onsager radius; Ω₀ is the cyclic frequency of harmonic vibrations of the hyston; ε is the dielectric constant; M_s and J_s are the mass and moment of inertia of a molecule of the medium, respectively. The correlation function of the motion of the molecules c(t) is a solution of the equation of hyston motion. The fluorescence response s(t) in measurements with time resolution coincides with the correlation function: s(t)=c(t). The concepts concerning hystons make it possible to describe macroscopic photoinduced coherent motion that is manifested against a background of thermal motion of the medium molecules. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnei Spektroskopii, Vol 65, No. 2, pp. 176–183, March–April, 1998.     

Localization in disordered systems with interactions

We present an improved numerical approach to the study of disorder and interactions in quasi-1D systems which combines aspects of the transfer matrix method and the density matrix renormalization group which have been successfully applied to disorder and interacting problems respectively. The method is applied to spinless fermions in 1D and a generalization to finite cross-sections is outlined.      

Localization lengths in disordered Peierls systems

We have studied the influence of bond- and site-type impurities on the ground state properties of one-dimensional Peierls systems. Using a functional integral formalism with both commuting and anticommuting variables we have calculated the averaged Green's function which determines the electronic density of states and localization length (Thouless formula). Some limiting cases can be solved analytically. To apply our model to doped polymers we derive the connection between doping concentration and disorder strengths D_j. For illustration we present the results with parameters appropriate for polyacetylene.     

Mode-locking behaviour: ac response of a driven disordered vortex lattice

Using random pinning force simulations, we study numerically the alternating current (ac) response of the driven disordered vortex lattice. In the presence of a superimposed ac force, mode-locking steps are observed in the velocity－direct current (dc) force characteristics at high dc forces, where a smectic order occurs. The step width shows damped oscillations with the strength of interaction between vortices, in good agreement with recent experiments.     

Absence of an elastic vortex glass in disordered HTS

Analyses of standard current–voltage (I–V) characteristics of disordered high-temperature superconductors (HTS) indicate that the vortex phase at high magnetic fields H should be an elastic vortex glass, where the vortex pinning barriers diverge at low current densities, whereas dc magnetization relaxation measurements reveal the presence of nondiverging (plastic) pinning barriers in a wide H–T domain. We show that the different conclusions concerning the nature of the vortex phase at high H in disordered HTS seem to be due to the ordering effect of the driving force existing in various experiments.     

Dynamical phase transition of a driven vortex lattice with disordered pinning

We have numerically solved the overdamped equation of vortex motion in a two-dimensional driven vortex lattice with disordered pinning, in which the driving Lorentz force, the pinning force due to point defects, the intervortex interacting force, and the thermal fluctuation force are taken into account. It is found that the vortex density and pinning strength are two important factors of affecting the melting transition of a vortex lattice. At low magnetic fields, there exist hysteresis loops of the average vortex velocity and the average pinning force vs. the driving force, from which the feature of a first-order melting transition of the vortex motion can be clearly seen. As the magnetic field is increased beyond a critical value, the hysteresis loops disappear and the melting transition is replaced by a second-order glass transition. We have also studied the influence of intervortex interactions on the vortex melting transition by comparing several forms of repulsive forces between the vortices.     

Localization in disordered,nonlinear dynamical systems

We study localization and wave trapping in disordered, nonlinear dynamical systems. For some models of classical, disordered anharmonic crystal lattices, we prove that, with large probability, there are quasiperiodic lattice vibrations of finite total energy which lie on some infinite-dimensional, compact invariant tori in phase space. Such vibrations remain localized, for all times, and there is no transport of energy through the lattice. Our general concepts and techniques extend to other systems, such as disordered, nonlinear Schrödinger equations, or randomly coupled rotors.     

Localization of surface states in disordered step lattices

The character of the surface state wave function on regularly stepped Cu(111) is reinvestigated. It is shown that the qualitative change at terrace lengths around 17 A observed previously by Ortega et al. [Phys. Rev. Lett. 84, 6110 (2000)]] must necessarily be described as a change from a propagating superlattice state to a terrace-confined quasi-one-dimensional state. This reconciles previous, apparently contradictory experimental results and sheds new light on the behavior of nearly free electrons in nanostructures. Possible mechanisms driving the localization are discussed on the basis of the surface state bulk penetration depth, which has been measured in both regimes.     

Localization of the phonon-polarization in disordered ionic crystals

Using diagrammatic Green function methods we show that the criterion for localization of the phonon-polariton in ionic crystals containing randomly distributed dielectric spheres can be satisfied. The localization characteristics are discussed. It is proposed that effects of the phonon-polariton localization can be observed in optical absorption experiments.     

Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z ^d , 〈,〉 denotes nearest neighbors inZ ^d ;J>0 andh={h(x)>0,x∈Z ^d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h ^?δ dμ(h)<∞ for some δ>0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z ^d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _x,h,J <∞.     

Localization properties of driven disordered one-dimensional systems

We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.