Phonon transmission and thermal conductance in one-dimensional system with on-site potential disorder

The role of on-site potential disorder on phonon transmission and thermal conductance of one-dimensional system is investigated. We found that the on-site potential disorder can lead to the localization of phonons, and has great effect on the phonon transmission and thermal conductance of the system. As on-site potential disorder W increases, the transmission coefficients decrease, and approach zero at the band edges. Corresponding, the thermal conductance decreases drastically, and the curves for thermal conductance exhibit a series of steps and plateaus. Meanwhile, when the on-site potential disorder W is strong enough, the thermal conductance decreases dramatically with the increase of system size N. We also found that the efficiency of reducing thermal conductance by increasing the on-site potential disorder strength is much better than that by increasing the on-site potential?s amplitude.     

Level statistics and localization: A study of the 1D Anderson model

The level statistics and the localization of a particle in a one-dimensional random potential are investigated numerically. First, we study the level spacing distributionP(S) as a function of the system lengthN and of the disorderw of the system. We show that in addition to the localized and delocalized regimes a third regime can be distinguished: For large disorder a resonance appears inP(S), which is caused by a local level repulsion effect. Second, we investigate the distribution of the localization lengths within the Anderson chain as a function ofN andw. Here, we identify the localization length with the rms spread of the wave functions and we show that this measure for the localization of the eigenstates is not a self-averaging quantity.     

Multichanel localization and magnetic impurities

The behaviour of an electron in N-coupled conducting chains of the length L is studied in the presence of magnetic impurities. The electron flow can be expanded in an orthonormal set of 2N channels. Each channel has its own transmission coefficient T_n(L). Spontaneous breaking of the symmetry between channels results in 2N different exponential dependences T_n(L) ～ exp (—L/l¹_n) where l¹_n is a localization length in the nth channel. Low frequency kinetic behaviour depends on the channel with the maximum localization length l¹₀.     

Ginzburg–Landau expansion in strongly disordered attractive Anderson–Hubbard model

We have studied disordering effects on the coefficients of Ginzburg–Landau expansion in powers of superconducting order parameter in the attractive Anderson–Hubbard model within the generalized DMFT+Σ approximation. We consider the wide region of attractive potentials U from the weak coupling region, where superconductivity is described by BCS model, to the strong coupling region, where the superconducting transition is related with Bose–Einstein condensation (ВЕС) of compact Cooper pairs formed at temperatures essentially larger than the temperature of superconducting transition, and a wide range of disorder—from weak to strong, where the system is in the vicinity of Anderson transition. In the case of semielliptic bare density of states, disorder’s influence upon the coefficients A and В of the square and the fourth power of the order parameter is universal for any value of electron correlation and is related only to the general disorder widening of the bare band (generalized Anderson theorem). Such universality is absent for the gradient term expansion coefficient C. In the usual theory of “dirty” superconductors, the С coefficient drops with the growth of disorder. In the limit of strong disorder in BCS limit, the coefficient С is very sensitive to the effects of Anderson localization, which lead to its further drop with disorder growth up to the region of the Anderson insulator. In the region of BCS–ВЕС crossover and in ВЕС limit, the coefficient С and all related physical properties are weakly dependent on disorder. In particular, this leads to relatively weak disorder dependence of both penetration depth and coherence lengths, as well as of related slope of the upper critical magnetic field at superconducting transition, in the region of very strong coupling.     

Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model

The localization properties of eigenfunctions for two interacting particles in theone-dimensional Anderson model are studied for system sizes up to N = 5000 sitescorresponding to a Hilbert space of dimension ≈10⁷ using the Green function Arnoldi method. Theeigenfunction structure is illustrated in position, momentum and energy representation,the latter corresponding to an expansion in non-interacting product eigenfunctions.Different types of localization lengths are computed for parameter ranges in system size,disorder and interaction strengths inaccessible until now. We confirm that one-parameterscaling theory can be successfully applied provided that the condition of N being significantlylarger than the one-particle localization length L₁ is verified.The enhancement effect of the two-particle localization length L₂ behaving asL₂ ~ L₂¹ is clearly confirmed for a certain quite large intervalof optimal interactions strengths. Further new results for the interaction dependence in avery large interval, an energy value outside the band center, and different interactionranges are obtained.     

Statistical theory of nuclear reactions and the Gaussian orthogonal ensemble

Using methods developed in field theory and statistical mechanics, especially in the context of the Anderson model as generalised by Wegner, a novel approach to the statistical theory of nuclear reactions is developed. A finite set of N bound states, coupled to each other by an ensemble of Gaussian orthogonal matrices, is considered and coupled to a set of channels via fixed coupling matrix elements. The ensemble average and the variance of the elements of the nuclear scattering matrix are evaluated, using the method of a generating function combined with the replica trick, followed by the Hubbard-Stratonovitch transformation and a modified loop expansion. In the limit N → ∞, it is shown quite generally that, aside from a trivial dependence on average S-matrix elements, the variance depends only on the transmission coefficients, and that the correlation width of a pair of S-matrix elements is given by a universal function of the transmission coefficients. A modified loop expansion yields an asymptotic series valid for strong absorption. The terms in this series are partly novel, and partly coincide with results obtained earlier in the framework of a model which did not take account of the GOE eigenvalue fluctuations. This suggests that average cross sections are mainly sensitive to the stiffness of the GOE spectrum. Fluctuation properties are also derived, and the link to Ericson fluctuation theory is established.     

Quantum waveguide theory of a fractal structure

The electronic transport properties of fractal quantum waveguide networks in the presence of a magnetic field are studied. A Generalized Eigen-function Method (GEM) is used to calculate the transmission and reflection coefficients of the studied systems unto the fourth generation Sierpinski fractal network with node number N=123$N=123$. The relationship among the transmission coefficient T, magnetic flux Φ and wave vector k is investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux Φ are observed and discussed, and compared with the results of the tight-binding model.     

Photon localization in amorphous photonic crystal

The photon localization in disordered two-dimensional photonic crystal is studied theoretically. It is found that the mean transmission coefficient in the photonic band decreases exponentially as the disorder degree increases, reflecting the occurrence of Anderson localization. The strength of photon localization can be controlled by tuning the disorder degree in the photonic crystal. We think the variation regular of the transmission coefficient in our disordered system is equivalent to that of the scaling theory of localization. PACS 42.70.Qs; 41.20.Jb; 42.25.Dd     

Optical and physical properties of different composition of InxSe1−x thin films

Thin film binary alloys of In_xSe_1−x (0.05?x?0.30) have been prepared by the thermal evaporation technique. The optical transmission and reflection spectrum of these films were measured in the range 300-1100 nm. Both refractive index, n and extinction coefficient k have been determined from transmission and reflection measurements in terms of Murmann's equations. The dispersion of the refractive index is discussed in terms of the single-oscillator Wemple-DiDomenico model. The width of band tail is determined and the optical absorption edge is described using the ‘non-direct transition’ model proposed by Tauc. Finally, the relationship between the optical gap and chemical composition in In_xSe_1−x amorphous system is discussed in terms of the average heat of atomization H_s and average coordination number N_c. The results of these calculations can be used rationalize the observed optical properties of these materials. Finally, the chemical bond approach has been also applied to interpret the decrease of the glass optical gap with increasing In content.     

Transmission spectrum of a dielectric binary multilayered structure with diluted disorder

In this work we investigate the transmission properties of a binary multilayered structure with diluted disorder. This system consists of two interpenetrating sub-sequences. One of them is composed by layers of refractive index n_a and thickness d_a, inserted into the odd positions of a stack. The second sub-sequence consists of randomly distributed layers of type A and B, distributed with probability 1 ? p and p, respectively and inserted into the even sites of the stack. The layer thicknesses were taken to satisfy the Bragg condition n_ad_a = n_bd_b. Using a transfer matrix method, we compute the transmission spectrum, the frequency averaged transmission as a function of the system size and the reduced Lyapunov coefficient for different values of the defect concentration p. For 0 < p < 1 the system depicts a wide band-gap due to the Anderson localization of the electromagnetic modes promoted by the underlying disorder. However, the diluted character of the disorder implies in the absence of the quarter-wavelength resonant mode within the band-gap that usually appears in random binary structures. This particular feature suggests that binary dielectric structures with diluted disorder shall perform better as a wide band-gap filter than uncorrelated disordered multilayer structures.     

Anomalies in Conductance and Localization Length of Disordered Ladders

We discuss the conditions under which an anomaly occurs in conductance and localization length of Anderson model on a lattice. Using the ladder Hamiltonian and analytical calculation of average conductance we find the set of resonance conditions which complements the π-coupling rule for anomalies. We identify those anomalies that might vanish due to the symmetry of the lattice or the distribution of the disorder. In terms of the dispersion relation it is known from strictly one-dimensional model that the lowest order (i.e., the most strong) anomalies satisfy the equation E(k)=E(3k). We show that the anomalies of the generalized model studied here are also the solutions of the same equation with modified dispersion relation.     

Exotic electron states and tunable magneto-transport in a fractal Aharonov–Bohm interferometer

A Sierpinski gasket fractal network model is studied in respect of its electronic spectrum and magneto-transport when each ‘arm’ of the gasket is replaced by a diamond shaped Aharonov–Bohm interferometer, threaded by a uniform magnetic flux. Within the framework of a tight binding model for non-interacting, spinless electrons and a real space renormalization group method we unravel a class of extended and localized electronic states. In particular, we demonstrate the existence of extreme localization of electronic states at a special finite set of energy eigenvalues, and an infinite set of energy eigenvalues where the localization gets ‘delayed’ in space (staggered localization). These eigenstates exhibit a multitude of localization areas. The two terminal transmission coefficient and its dependence on the magnetic flux threading each basic Aharonov–Bohm interferometer is studied in details. Sharp switch on–switch off effects that can be tuned by controlling the flux from outside, are discussed. Our results are analytically exact.     

Condensation of a chain polymer molecule

A new expression for the expansion coefficient of a flexible chain polymer molecule can be given in such a way that its first term corresponds to the case with only a hard-sphere repulsion and the other terms represent the effects of attraction between the segments. For low and high temperatures, more convenient expressions are used to find a possible condensation into a liquid-like condensed state from a gas-like state. It is found that in the condensed state, the square average end-to-end distance varies as N^?, where N is the number of segments and the exponent ? is around 0.6 in contrast to 1.2 for the high temperature case.     

Loose,Flat Knots in Collapsed Polymers

We consider single ring polymers which are confined on a plane but maintain a fixed three-dimensional knotted topology. The equilibrium statistics of such systems is studied on the basis of a model on square lattice in which the configurations are represented by N-step polygons with a number of self-intersections restricted to the minimum compatible with the topology. This allows to define the size, s, of the flat knots and to study their localization properties. Due to the presence of both excluded volume and attractive interactions, the model undergoes a theta transition. Accurate Monte Carlo results show that, while in the high temperature swollen regime both prime and composite knot components are localized (〈s〉 _N ～N ^t , with t=0), in the low temperature, compact phase they are fully delocalized (t=1). Right at the theta transition weak localization prevails (t=0.44±0.02). Part of the results can be interpreted by taking into account a dominance of figure eight shapes for the coarse grained knotted polymer configurations, and by applying the scaling theory of polymer networks of fixed topology. In particular t=3/7 can be conjectured as an exact exponent characterizing the weak knot localization at the theta point.     

Field dependence of hole mobility in TPD-doped polystyrene

Field and temperature dependence of hole mobility in N,N^′-diphenyl-N,N^′-bis(3-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine (TPD) doped in polystyrene (PS) is studied using the transient photoconductivity technique. We observe both the positive and negative field dependence of mobility with increasing field and temperature. The field and temperature at which negative field dependence begins is low compared with earlier reports on similar systems (with 20 wt% dopant concentration). Results are discussed on the basis of the Gaussian disorder model (GDM), which predicts that the interplay of both the energetic and positional disorder of dopant molecules in the sample decides the slope of the logμ versus E^1/2 plot. The observed mobility dependence is rationalized on the basis of low energetic disorder in the sample. The reason for low energetic disorder is purely due to the film morphology of the sample. Even for a dopant concentration of 20 wt%, we observe clustering and chaining of TPD molecules, which may provide low energetic and positional disorder.     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

Compositional dependence of the optical properties of amorphous semiconducting glass Ge10AsxSe(90−x) thin films

Optical properties of ternary chalcognide amorphous Ge₁₀As_xSe_(90−x) (with 10?x?25 at%) thin films prepared by thermal evaporation have been measured in visible and near-infrared spectral region. The straightforward analysis proposed by Swanepoel has been successfully employed, and it has allowed us to determine the average thickness , and the refractive index, n, of the films, with high accuracy. The refractive index, n and the average thickness has been determined from the upper and lower envelopes of the transmission spectra measured at normal incidence, in the spectral range 400-2500 nm. The absorption coefficient α, and therefore extinction coefficient k, have been determined from the transmission spectra in the strong-absorption region. The dispersion of the refractive index is discussed in terms of the single oscillator Wemple-DiDomenico model, and the optical absorption edge is described using the ‘nondirect transition’ model proposed by Tauc. Likewise, the optical energy gap is derived from Tauc's extrapolation. The relationship between the optical gap and chemical composition in Ge₁₀As_xSe_(90−x) amorphous system is discussed in terms of the average heat of atomization H_s and average coordination number N_c. Finally, the chemical bond approach has been also applied successfully to interpret the decrease of the glass optical gap with increasing As content.     

Field theory of the random flux model

The random flux model (defined here as a model of lattice fermions hopping under the influence of maximally random link disorder) is analysed field theoretically. It is shown that the long range physics of the model is described by the supersymmetric version of a field theory that has been derived earlier in connection with lattice fermions subject to weak random hopping. More precisely, the field theory relevant for the behaviour of n-point correlation functions is of non-linear σ model type, where the group GL(n|n) is the global invariant manifold. It is argued that the model universally describes the long range physics of random phase fermions and provides further evidence in favour of the existence of delocalised states in the middle of the band in two dimensions. The same formalism is applied to the study of non-Abelian generalisations of the random flux model, i.e. N-component fermions whose hopping is mediated by random U(N) matrices. We discuss some physical applications of these models and argue that, for sufficiently large N, the existence of long range correlations in the band centre (equivalent to metallic behaviour in the Abelian case) can be safely deduced from the RG analysis of the model.     

Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping

In the previous work, it was shown that, in supersymmetric (matrix) discretized quantum mechanics, inclusion of an external field twisting the boundary condition of fermions enables us to discuss spontaneous breaking of supersymmetry (SUSY) in the path-integral formalism in a well-defined way. In the present work, we continue investigating the same systems from the points of view of localization and Nicolai mapping. The localization is studied by changing of integration variables in the path integral, which is applicable whether or not SUSY is explicitly broken. We examine in detail how the integrand of the partition function with respect to the integral over the auxiliary field behaves as the auxiliary field vanishes, which clarifies a mechanism of the localization. In SUSY matrix models, we obtain a matrix-model generalization of the localization formula. In terms of eigenvalues of matrix variables, we observe that eigenvalues' dynamics is governed by balance of attractive force from the localization and repulsive force from the Vandermonde determinant. The approach of the Nicolai mapping works even in the presence of the external field. It enables us to compute the partition function of SUSY matrix models for finite N (N is the rank of matrices) with arbitrary superpotential at least in the leading nontrivial order of an expansion with respect to the small external field. We confirm the restoration of SUSY in the large-N limit of a SUSY matrix model with a double-well scalar potential observed in the previous work.     

Random pseudofractal networks with competition

In this paper, we present a simple rule which assigns fitness to each edge to generate random pseudofractal networks (RPNs). This RPN model is both scale-free and small-world. We obtain the theoretical results that the power-law exponent is γ=2+1/(1+α) for the tunable parameter α>-1, and that the degree distribution is of an exponential form for others. Analytical results also show that an RPN has a large clustering coefficient and can process hierarchical structure as C(k)∼k^-1 that is in accordance with many real networks. And we prove that the mean distance L(N) scales slower logarithmically with network size N. In particular, we explain the effect of nodes with degree 2 on the clustering coefficient. These results agree with numerical simulations very well.