Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models

Using numerical diagonalization we study the crossover among different random matrix ensembles (Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE) and Gaussian symplectic ensemble (GSE)) realized in two different microscopic models. The specific diagnostic tool used to study the crossovers is the level spacing distribution. The first model is a one-dimensional lattice model of interacting hard-core bosons (or equivalently spin 1/2 objects) and the other a higher dimensional model of non-interacting particles with disorder and spin-orbit coupling. We find that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We also find that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. We also conjecture that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system.

Influence of finite size effect on magnetic and magnetotransport properties of La0.5Sr0.5CoO3 thin films

We present a comprehensive study of the thickness dependent structural, magnetic and magnetotransport properties of oriented La0.5Sr0.5CoO3 thin films grown on LaAlO3 by Pulsed Laser Deposition. We observe that these films undergo a reduction in Curie temperature (T-c) with a decrease in film thickness, and it is found to be primarily caused by the finite size effect since the finite scaling law [T-c(infinity) T-c(t)/T-c(infinity) = (c/t)lambda holds good over the studied thickness range. We rule out the contribution from the strain induced suppression of Curie temperature with decreasing film thickness since all the films exhibit a constant out of plane tensile strain (0.5%) irrespective of their varying thickness. However, we observe that the coercivity of the films is an order of magnitude higher than that of the bulk due to the tensile strain. In addition, we also observe an increase in the magneto resistance peak and a decrease in coercivity and electrical resistivity with an increase in film thickness. (C) 2010 Elsevier Ltd. All rights reserved.

Experimental evidence for interplay of dynamic heterogeneity and finite-size effect in glassy polymers

Despite two decades of extensive research, direct experimental evidence of a dynamical length scale determining the glass transition of confined polymers has yet to emerge. Using a recently established experimental technique of interface micro-rheology we provide evidence of finite-size effect truncating the growth of a quantity proportional to a dynamical length scale in confined glassy polymers, on cooling towards the glass transition temperature. We show how the interplay of variation of polymer film thickness and this temperature-dependent growing dynamical length scale determines the glass transition temperature, which in our case of 2-3nm thick films, is reduced significantly as compared to their bulk values.

Self-organized criticality in dynamics without branching

We demonstrate the phenomenon of self-organized criticality (SOC) in a simple random walk model described by a random walk of a myopic ant, i.e., a walker who can see only nearest neighbors. The ant acts on the underlying lattice aiming at uniform digging, i.e., reduction of the height profile of the surface but is unaffected by the underlying lattice. In one, two, and three dimensions we have explored this model and have obtained power laws in the time intervals between consecutive events of "digging." Being a simple random walk, the power laws in space translate to power laws in time. We also study the finite size scaling of asymptotic scale invariant process as well as dynamic scaling in this system. This model differs qualitatively from the cascade models of SOC.

Growing length and time scales in glass-forming liquids

The glass transition, whereby liquids transform into amorphous solids at low temperatures, is a subject of intense research despite decades of investigation. Explaining the enormous increase in relaxation times of a liquid upon supercooling is essential for understanding the glass transition. Although many theories, such as the Adam-Gibbs theory, have sought to relate growing relaxation times to length scales associated with spatial correlations in liquid structure or motion of molecules, the role of length scales in glassy dynamics is not well established. Recent studies of spatially correlated rearrangements of molecules leading to structural relaxation, termed ``spatially heterogeneous dynamics,'' provide fresh impetus in this direction. A powerful approach to extract length scales in critical phenomena is finite-size scaling, wherein a system is studied for sizes traversing the length scales of interest. We perform finite-size scaling for a realistic glass-former, using computer simulations, to evaluate the length scale associated with spatially heterogeneous dynamics, which grows as temperature decreases. However, relaxation times that also grow with decreasing temperature do not exhibit standard finite-size scaling with this length. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode-coupling theory. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions.

Analysis of Dynamic Heterogeneity in a Glass Former from the Spatial Correlations of Mobility

The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.

Triangular Ising antiferromagnet in a staggered field

We study the equilibrium properties of the nearest-neighbor Ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states. Using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice, we classify the ground states into sectors specified by the number of "strings." We show that the effect of the staggered field is to generate long-range interactions between strings. In the limiting case of the antiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three different dynamics. We find that in all the three cases, equilibration times for low-field values increase rapidly with system size at low temperatures. Due to this difficulty in equilibrating sufficiently large systems at low temperatures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of st phase transition for finite values of J. A surprising feature in the system is the fact that unlike usual glassy systems; a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.

Short-Time Beta Relaxation in Glass-Forming Liquids Is Cooperative in Nature

Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. Using molecular dynamics simulations for three model glass-forming liquids, we show that the short-time beta relaxation is cooperative in nature. Using finite-size scaling analysis, we extract a growing length scale associated with beta relaxation from the observed dependence of the beta relaxation time on the system size. We find, in qualitative agreement with the prediction of the inhomogeneous mode coupling theory, that the temperature dependence of this length scale is the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time alpha-relaxation regime.

Application of lateral photovoltage towards contactless light beam induced current measurements and its dependence on the finite beam size

The nature of the signal due to light beam induced current (LBIC) at the remote contacts is verified as a lateral photovoltage for non-uniformly illuminated planar p-n junction devices; simulation and experimental results are presented. The limitations imposed by the ohmic contacts are successfully overcome by the introduction of capacitively coupled remote contacts, which yield similar results without any significant loss in the estimated material and device parameters. It is observed that the LBIC measurements introduce artefacts such as shift in peak position with increasing laser power. Simulation of LBIC signal as a function of characteristic length L-c of photo-generated carriers and for different beam diameters has resulted in the observed peak shifts, thus attributed to the finite size of the beam. Further, the idea of capacitively coupled contacts has been extended to contactless measurements using pressure contacts with an oxidized aluminium electrodes. This technique avoids the contagious sample processing steps, which may introduce unintentional defects and contaminants into the material and devices under observation. Thus, we present here, the remote contact LBIC as a practically non-destructive tool in the evaluation of device parameters and welcome its use during fabrication steps. (C) 2014 AIP Publishing LLC.

Modeling Finite Buffer Effects on TCP Traffic over an IEEE 802.11 Infrastructure WLAN

The network scenario is that of an infrastructure IEEE 802.11 WLAN with a single AP with which several stations (STAs) are associated. The AP has a finite size buffer for storing packets. In this scenario, we consider TCP controlled upload and download file transfers between the STAs and a server on the wireline LAN (e.g., 100 Mbps Ethernet) to which the AP is connected. In such a situation, it is known (see, for example, (3), [9]) that because of packet loss due to finite buffers at the Ap, upload file transfers obtain larger throughputs than download transfers. We provide an analytical model for estimating the upload and download throughputs as a function of the buffer size at the AP. We provide models for the undelayed and delayed ACK cases for a TCP that performs loss recovery only by timeout, and also for TCP Reno.

Modeling finite buffer effects on TCP traffic over an IEEE 802.11 infrastructure WLAN

The network scenario is that of an infrastructure IEEE 802.11 WLAN with a single AP with which several stations (STAs) are associated. The AP has a finite size buffer for storing packets. In this scenario, we consider TCP-controlled upload and download file transfers between the STAs and a server on the wireline LAN (e.g., 100 Mbps Ethernet) to which the AP is connected. In such a situation, it is well known that because of packet losses due to finite buffers at the AP, upload file transfers obtain larger throughputs than download transfers. We provide an analytical model for estimating the upload and download throughputs as a function of the buffer size at the AP. We provide models for the undelayed and delayed ACK cases for a TCP that performs loss recovery only by timeout, and also for TCP Reno. The models are validated incomparison with NS2 simulations.

Fidelity susceptibility of one-dimensional models with twisted boundary conditions

Recently it has been shown that the fidelity of the ground state of a quantum many-body system can be used todetect its quantum critical points (QCPs). If g denotes the parameter in the Hamiltonian with respect to which the fidelity is computed, we find that for one-dimensional models with large but finite size, the fidelity susceptibility chi(F) can detect a QCP provided that the correlation length exponent satisfies nu < 2. We then show that chi(F) can be used to locate a QCP even if nu >= 2 if we introduce boundary conditions labeled by a twist angle N theta, where N is the system size. If the QCP lies at g = 0, we find that if N is kept constant, chi(F) has a scaling form given by chi(F) similar to theta(-2/nu) f (g/theta(1/nu)) if theta << 2 pi/N. We illustrate this both in a tight-binding model of fermions with a spatially varying chemical potential with amplitude h and period 2q in which nu = q, and in a XY spin-1/2 chain in which nu = 2. Finally we show that when q is very large, the model has two additional QCPs at h = +/- 2 which cannot be detected by studying the energy spectrum but are clearly detected by chi(F). The peak value and width of chi(F) seem to scale as nontrivial powers of q at these QCPs. We argue that these QCPs mark a transition between extended and localized states at the Fermi energy. DOI: 10.1103/PhysRevB.86.245424

Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation

We undertake a systematic, direct numerical simulation of the twodimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. Firstly, there are transients that depend on the initial conditions. In the second regime, powerlaw scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other.

Universality in the fast orientational relaxation near isotropic-nematic transition

Detailed molecular dynamics simulations of Lennard-Jones ellipsoids have been carried out to investigate the emergence of criticality in the single-particle orientational relaxation near the isotropic-nematic (IN) phase transition. The simulations show a sudden appearance of a power-law behavior in the decay of the second-rank orientational relaxation as the IN transition is approached. The simulated value of the power-law exponent is 0.56, which is larger than the mean-field value (0.5) but less than the observed value (0.63) and may be due to the finite size of the simulated system. The decay of the first-rank orientational time correlation function, on the other hand, is nearly exponential but its decay becomes very slow near the isotropic-nematic transition, The zero-frequency rotational friction, calculated from the simulated angular Velocity correlation function, shows a marked increase near the IN transition.

Electron-electron interactions in polyacetylene

Experimental evidence for strong electron-electron interactions in polyacetylene is presented. These include (i) observation of a dipole forbidden state below the optical gap, (ii) observation of negative spin densities at sites at which noninteracting models predict zero spin density (iii) vanishing optical gap, in the infinite chain limit, in the closely related symmetrical linear cyanine dyes. To correctly explain these features it is necessary to solve correlated model Hamiltonians. Using diagrammatic valence bond method model exact solutions of correlated models of finite-size systems can be obtained and various physical properties of the low-lying states can be computed. These properties, when extrapolated to the infinite chain limit explain many of the experimental features observed in polyacetylene.