Amplitude scaling behavior of band center states of Frenkel exciton chains with correlated off-diagonal disorder

We report the amplitude scaling behavior of Frenkel exciton chains with nearest-neighbor correlated off-diagonal random interactions. The band center spectrum and its localization properties are investigated through the integrated density of states and the inverse localization length. The correlated random interactions are produced through a binary sequence similar to the interactions in spin glass chains. We produced sets of data with different interaction strength and “wrong” sign concentrations that collapsed after scaling to the predictions of a theory developed earlier for Dirac fermions with random-varying mass. We found good agreement as the energy approaches the band center for a wide range of concentrations. We have also established the concentration dependence of the lowest order expansion coefficient of the scaling amplitudes for the correlated case. The correlation causes unusual behavior of the spectra, i.e., deviations from the Dyson-type singularity.     

Localization and off-diagonal disorder

The question of localization is examined in the framework of a tight-binding Hamiltonian with randomness in the off-diagonal matrix elements. It is shown that the mobility edges, although they may move initially inwards into the band with increasing off-diagonal randomness, eventually move outwards leaving always a region of extended states around the middle of the band.     

Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres

We propose and demonstrate a "bottom-up" approach to constructing photonic structures for photon manipulation. Supermonodispersive polymer microspheres are used as building blocks and a size uniformity better than 0.05% could be obtained by sorting the spheres using spectroscopic methods. The spheres are positioned in a V groove on a silicon substrate and form a photonic chain with resonant coupling of the optical whispering-gallery modes. Photonic band modes are clearly observed in fluorescence and resonant scattering spectra, and an excellent agreement with a tight-binding model calculation is found. Heavy photon states and a group index as high as 40 are obtained.     

Effective-medium theory for goldstone systems with off-diagonal disorder

An effective medium theory for low temperature phonons and other Goldstone excitations with diagonal and off-diagonal disorder is developed which preserves the herglotz property of the self-energy and is correct in both dilute limits c→0 and c→1.     

Localization and transmission coefficient for two coupled metal chains with disorder

The equation for distribution of probabilities for the transmission coefficient T has been obtained for an electron passing through the finite section of the length L, consisting of two coupled disordered chains. The behavior of the mean 〈lnT〉 = - L/l_loc suggests localization of the electron on the length l, which depends on the coupling energy t between the chains. The ratio l_loc(t =)/l_loc(t?v_F/l) is found to be equal to 1 ? 1/π.     

CPA conductivity of a binary alloy with off-diagonal disorder

D.c.-conductivity of a binary alloy A_xB_y with off-diagonal disorder is calculated, assuming Shiba's condition for the random transfer integrals, by means of a modified CPA, i.e.,the renormalization propagator formalism developed elsewhere by one of the authors (K.N.).     

Current in a quantum driven thermostatted system with off-diagonal disorder

We analyze a one dimensional quantum model with off-diagonal disorder, consisting of a sequence of potential energy barriers whose width is a random variable either uniformly or “half-normally” distributed, subjected to an external electric field. We shed light on how the microscopic disorder affects the value of the transmission coefficient and on the structure of the fluctuations around the solutions corresponding to the regular lattice configuration. We also characterize the asymptotic limit obtained by letting the number of barriers diverge. Thus, we explain the novelty of our method with respect to the standard thermodynamic limit discussed in the literature and also evidence the onset of a large deviation principle for the transmission coefficient.     

Perturbation expansion for a one-dimensional Anderson model with off-diagonal disorder

The weak disorder expansion for a random Schrödinger equation with off-diagonal disorder in one dimension is studied. The invariant measure, the density of states, and the Lyapunov exponent are computed. The most interesting feature in this model appears at the band center, where the differentiated density of states diverges, while the Lyapunov exponent vanishes. The invariant measure approaches an atomic measure concentrated on zero and infinity. The results extend previous work of Markos to all orders of perturbation theory.     

Anderson localization in different one-dimensional systems with off-diagonal disorder and spin-dependence

The localization properties of certain spin-dependent, one-dimensional electronic systems with only off-diagonal disorder are studied. In higher dimensions (d=2,3) the models considered would correspond to different universality classes, whereas ford=1 no qualitative difference is found: ForE=0, all eigenstates are exponentially localized, whereas forE0 the localization length diverges logarithmically, such that exactly atE=0 the geometric average of the transmission coefficient would decay with increasing chain lengthL as exp (-const. ·L ^1/2), instead of the usual, exponential decay.ForE=0, in the interior of the band, the localization lengthr ₀ diverges W ₂ ^–2 in the limit of weak disorder (W ₂0), whereas just at the band edge one has roughlyr ₀W ₂ ^–2/3. A universal recursion relation, depending only on the energy and on certain randomly distributed determinants, determines the localization length and the density of states for all systems considered.     

Superfluid-insulator transition in a commensurate one-dimensional bosonic system with off-diagonal disorder

We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of a large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and the applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.     

Numerical results for electron localization with site-diagonal and off-diagonal disorder

Numerical calculations of eigenfunctions and the participation ratio P are carried out for a two-dimensional square lattice where the site diagonal and/or off-diagonal matrix elements of a one-electron Hamiltonian are disordered. We show that, for purely off-diagonal disorder, states near the centre of the band will never be localized but states in the wings of the band are localized. We also see that the combined effects of diagonal and off-diagonal disorder yield several interesting results. Moreover, we confirm that, as suggested by Economou and Antoniou, the mobility-edge surface takes a bottle-neck shape in the three-dimensional space defined by energy E, the degree of diagonal randomness Γ and the degree of off-diagonal randomness V₁.     

Localization of vibrational modes in a layered lattice with diagonal and off-diagonal disorder

This paper discusses the possibility of weak localization of the phonon modes in a nonideal harmonic crystal lattice whose separate layers are weakly coupled to each other. An expression is obtained for the diffusivity tensor. The role of inverse coherent scattering processes is studied. It is established that, when such processes occur under conditions of strong diagonal disorder in the region of relatively low frequencies, where the dispersion law of the phonon modes exhibits two-dimensional properties, substantial renormalization of the diffusivity can take place. The paper analyzes the situation that occurs under conditions of off-diagonal disorder when resonant-scattering impurity centers are present in the lattice. The question of the possible nature of the low-temperature plateau in the thermal conductivity of the complex crystals BSCCO and BSYCO is discussed. Zh. éksp. Teor. Fiz. 113, 930–954 (March 1998)     

Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with nondecaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.     

Near band centre states for one-dimensional off-diagonal disordered systems

We study and characterize the eigenstates near the centre of the band of a one-dimensional tight binding model with off-diagonal disorderW _T . We report a new exponent for the localization length on an energy-dependent range of disorderW _T . We correlate this feature with a change of structure of the wave-function displayed by the behaviour of its density-density correlation function.     

Numerical results for Anderson localisation in the presence of off-diagonal disorder

Numerical calculations of the inverse participation ratio have been performed for the diamond cubic lattice with nearest neighbour interactions, and both diagonal and off-diagonal disorder. We confirm the prediction of Economou and Antoniou that off-diagonal disorder cannot, per se, produce an Anderson transition, although it reduces the amount of diagonal disorder necessary for the transition. In the presence of off-diagonal disorder alone we do not detect any substantial localisation even in the wings of the band.     

Absence of localization on the 2d model with long-range correlated off-diagonal disorder

We study the one-electron eigenstates in atwo-dimensional (2d) Anderson model with long-range correlated off-diagonaldisorder, generated by a 2ddiscrete Fourier method. The dynamics of an initiallylocalized wave packet is investigated by numerically solving the2d time-dependent Schrödinger equation. In additional the participation number and itsscaling behavior was obtained through direct diagonalization. Our numerical data suggest that the systemexhibits a ballistic dynamics in the stronglycorrelated disorder regime. Moreover, the scaling analysis of mean participation number around the band centeralso indicates the presence of extended states for high degree of correlations.