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arXiv2013

Field theory of disordered systems -- Avalanches of an elastic interface in a random medium

In this thesis I discuss analytical approaches to disordered systems using field theory. Disordered systems are characterized by a random energy landscape due to heterogeneities, which remains fixed on the time scales of the phenomena considered. I focus specifically on elastic interfaces in random media, such as pinned domain walls in ferromagnets containing defects, fluid contact lines on rough surfaces, etc. The goal is to understand static properties (e.g. the roughness) of such systems, and their dynamics in response to an external force. The interface moves in avalanches, triggered at random points in time, separated by long periods of quiescence. For magnetic domain walls, this phenomenon is known as Barkhausen noise. I first study the model of a particle in a Brownian random force landscape, applicable to high-dimensional interfaces. Its exact solution for a monotonous, but time-varying driving force is obtained. This allows computing the joint distribution of avalanche sizes and durations, and their spatial and temporal shape. I then generalize these results to a short-range correlated disorder. Using the functional renormalization group, I compute the universal distributions of avalanche sizes, durations, and their average shape as a function of time. The corrections with respect to the Brownian model become important in sufficiently low dimension (e.g. for a crack front in the fracture of a solid). I then discuss connections to the rough phase of Kardar-Parisi-Zhang nonlinear surface growth, and an application to the variable-range hopping model of electric conductance in a disordered insulator.

cond-mat.dis-nn↗
arXiv2013

Hot spots spontaneously emerging in thin film photovoltaics

We present data exhibiting hot spots spontaneously emerging in forward biased thin film photovoltaics based on a-Si:H technology. These spots evolve over time shrinking in their diameter and increasing temperature up to approximately 300 $^o$C above that of the surrounding area. Our numerical approach explores a system of many identical diodes in parallel connected through the resistive electrode and through thermal connectors, a model which couples electric and thermal processes. The modeling results show that hot spots emerge collapsing from a rather large area of nonuniform temperature, then collapse to local entities. Finally, we present a simplified analytical treatment establishing relations between the hot spot parameters.

cond-mat.dis-nn↗
arXiv2013

The ground state structure of electron's ensemble on one-dimension disordered lattice

The ground state of interacting particles on a disordered one-dimensional host-lattice is studied by a direct numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal, replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.

cond-mat.dis-nn↗
arXiv2014

Statistical Physics of Pure Barkhausen Noise

We discuss a model metallic glass in which Barkhausen Noise can be studied in exquisite detail, free of thermal effects and of the rate of ramping of the magnetic field. The mechanism of the jumps in magnetic moment that cause the Barkhausen Noise can be fully understood as consecutive instabilities where an eigenvalue of the Hessian matrix hits zero, leading to a magnetization jump $Δm$ which is simultaneous with a stress and energy changes $Δσ$ and $ΔU$ respectively. Contrary to common belief we find no "movements of magnetic domain boundaries" across pinning sites, no fractal domains, no self-organized criticality and no exact scaling behaviour. We present a careful numerical analysis of the statistical properties of the phenomenon, and show that with every care taken this analysis is tricky, and easily misleading. Without a guiding theory it is almost impossible to get the right answer for the statistics of Barkhausen Noise. We therefore present an analytic theory, showing that the probability distribution function (pdf) of Barkhausen Noise is not a power law times an exponential cutoff.

cond-mat.stat-mech↗
arXiv2014

Soft modes in jammed hard spheres (I): Mean field theory of the isostatic transition

In this paper we consider different models for soft modes in jammed hard spheres. We show how one can construct mean field models that can be solved analytically. The analytic solution of these models displays an excess of low energy soft modes that become more and more localized by decreasing the energy. A simple solution of these models is found in the infinite dimensional limit.

cond-mat.soft↗
arXiv2014

Dynamical Heterogeneity in the Glassy State

We compare dynamical heterogeneities in equilibrated supercooled liquids and in the nonequilibrium glassy state within the framework of the random first order transition theory. Fluctuating mobility generation and transport in the glass are treated by numerically solving stochastic continuum equations for mobility and fictive temperature fields that arise from an extended mode coupling theory containing activated events. Fluctuating spatiotemporal structures in aging and rejuvenating glasses lead to dynamical heterogeneity in glasses with characteristics distinct from those found in the equilibrium supercooled liquid. The non-Gaussian distribution of activation free energies, the stretching exponent $β$, and the growth of characteristic lengths are studied along with the four-point correlation function. Asymmetric thermodynamic responses upon heating and cooling are predicted to be the results of the heterogeneity and the out-of-equilibrium behavior of glasses below $T_g$. Numerical results agree with experimental calorimetry. We numerically confirm the prediction of Lubchenko and Wolynes in the glass that the dynamical heterogeneity can lead to noticeably bimodal distributions of local fictive temperatures which explains in a unified way recent experimental observations that have been interpreted as coming from two distinct equilibration mechanisms in glasses.

cond-mat.stat-mech↗
arXiv2014

Numerical Detection of the Ergodicity Breaking in a Lattice Glass Model

We directly detect the ergodicity breaking in a lattice glass model by a numerical simulation. The obtained results nicely agree with those by the cavity method that the model on a regular random graph exhibits a dynamical transition with the ergodicity breaking at an occupation density. The present method invented for a numerical detection of the ergodicity breaking is applicable to glassy systems in finite dimensions.

cond-mat.dis-nn↗
arXiv2014

Quantum Cybernetics and Complex Quantum Systems Science - A Quantum Connectionist Exploration

Quantum cybernetics and its connections to complex quantum systems science is addressed from the perspective of complex quantum computing systems. In this way, the notion of an autonomous quantum computing system is introduced in regards to quantum artificial intelligence, and applied to quantum artificial neural networks, considered as autonomous quantum computing systems, which leads to a quantum connectionist framework within quantum cybernetics for complex quantum computing systems. Several examples of quantum feedforward neural networks are addressed in regards to Boolean functions' computation, multilayer quantum computation dynamics, entanglement and quantum complementarity. The examples provide a framework for a reflection on the role of quantum artificial neural networks as a general framework for addressing complex quantum systems that perform network-based quantum computation, possible consequences are drawn regarding quantum technologies, as well as fundamental research in complex quantum systems science and quantum biology.

cs.NE↗
arXiv2014

Generalized Random Energy Model at Complex Temperatures

Motivated by the Lee--Yang approach to phase transitions, we study the partition function of the Generalized Random Energy Model (GREM) at complex inverse temperature $β$. We compute the limiting log-partition function and describe the fluctuations of the partition function. For the GREM with $d$ levels, in total, there are $\frac 12 (d+1)(d+2)$ phases, each of which can symbolically be encoded as $G^{d_1}F^{d_2}E^{d_3}$ with $d_1,d_2,d_3\in\mathbb{N}_0$ such that $d_1+d_2+d_3=d$. In phase $G^{d_1}F^{d_2}E^{d_3}$, the first $d_1$ levels (counting from the root of the GREM tree) are in the glassy phase (G), the next $d_2$ levels are dominated by fluctuations (F), and the last $d_3$ levels are dominated by the expectation (E). Only the phases of the form $G^{d_1}E^{d_3}$ intersect the real $β$ axis. We describe the limiting distribution of the zeros of the partition function in the complex $β$ plane (= Fisher zeros). It turns out that the complex zeros densely touch the positive real axis at $d$ points at which the GREM is known to undergo phase transitions. Our results confirm rigorously and considerably extend the replica-method predictions from the physics literature.

math.PR↗
arXiv2014

Comment on "Metal-Insulator Transition in an Aperiodic Ladder Network: An Exact Result"

Sil, Maiti, and Chakrabarti (SMC) (Phys. Rev. Lett. 101, 076803 (2008), arXiv:0801.2670) introduce an aperiodic two-leg ladder network composed of atomic sites with on-site potentials distributed according to a quasiperiodic Aubry-Andre potential. SMC claim the existence of multiple mobility edges, i.e. metal-insulator transitions at multiple values of the Fermi energy. SMC use numerical calculations of the conductance and den- sity of states, and an analytical result in a limiting case. In the following, we restate in the real space the change of basis done by SMC. This change of basis reduces their model to two decoupled chains, each with its own Aubry- Andre potential. Each of the chains has its own critical point, where all states change from metallic to insulat- ing, without any notion of a mobility edge. Since the two chains are not interacting, their spectra may overlap such that localized states (from one chain) and delocal- ized states (from the other chain) coexist at the same en- ergy. Consequently, the analysis of the density of states and the conductance alone is misleading, and that is due to the choice of the symmetric quasiperiodic potential. We briefly outline the possibility to obtain true mobility edges.

cond-mat.dis-nn↗
arXiv2014

Measuring the transmission matrix for microwave radiation propagating through random waveguides: fundamentals and applications

This thesis describes the measurement and analysis of the transmission matrix (TM) for microwave radiation propagating through multichannel random waveguides in the crossover to Anderson localization. Eigenvalues of the transmission matrix and the associated eigenchannels are obtained via a singular value decomposition of the TM. The sum of the transmission eigenvalues yields the transmittance $\it T$, which is the classical analog of the dimensionless conductance $\textsl g$. The dimensionless conductance $\textsl g$ is the electronic conductance in units of the quantum conductance, $G/(e^2/h)$.

cond-mat.dis-nn↗
arXiv2014

Wavelike fracture pattern in metallic glasses: a Kelvin-Helmholtz flow instability

We report a wavelike fracture pattern in a Zr-based bulk metallic glass that has been deformed under quasi-static uniaxial tensions at temperatures between room temperature (300 K) and liquid nitrogen temperature (77 K). We attribute this wavelike pattern to a Kelvin-Helmholtz flow instability that occurred at certain interfaces between local cracking/softening regions. The instability criterion for the pattern formation is achieved via a hydrodynamic perturbation analysis, and furthermore an instability map is built which demonstrates that the shear velocity difference on both sides of the interface is the main destabilizing factor. Finally, the characteristic instability time (the inverse of the instability growth rate) is explored by seeking the dispersion relation in the dominant (fastest) instability mode. The results increase the understanding of the flow and fracture of metallic glasses as well as the nature of their liquid structures.

cond-mat.dis-nn↗
arXiv2014

Fixation in cyclically competing species on a directed graph with quenched disorder

A simple model of cyclically competing species on a directed graph with quenched disorder is proposed as an extension of the rock-paper-scissors model. By assuming that the effects of loops in a directed random graph can be ignored in the thermodynamic limit, it is proved for any finite disorder that the system fixates to a frozen configuration when the species number $s$ is larger than the spatial connectivity $c$, and otherwise stays active. Nontrivial lower and upper bounds for the persistence probability of a site never changing its state are also analytically computed. The obtained bounds and numerical simulations support the existence of a phase transition as a function of disorder for $1<c_l(s)\le c <s$, with a $s$-dependent threshold of the connectivity $c_l(s)$.

cond-mat.stat-mech↗
arXiv2014

Three Dimensional Edwards-Anderson Spin Glass Model in an External Field

We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field. We employ an indicator composed of a ratio of susceptibilities at finite wavenumbers, which was recently proposed to avoid the difficulties of a zero momentum quantity, for capturing the spin glass phase transition. Unfortunately, this new indicator is fairly noisy, so a large pool of samples at low temperature and small external field are needed to generate results with sufficiently small statistical error for analysis. We thus implement the Monte Carlo method using graphics processing units to drastically speedup the simulation. We confirm previous findings that conventional indicators for the spin glass transition, including the Binder ratio and the correlation length do not show any indication of a transition for rather low temperatures. However, the ratio of spin glass susceptibilities do show crossing behavior, albeit a systematic analysis is beyond the reach of the present data. This calls for a more thorough study of the three-dimension Edwards-Anderson model in an external field.

cond-mat.stat-mech↗
arXiv2014

Comment to "Critical Exponents of the Superfluid-Bose Glass Transition in Three-Dimensions" by Z. Yao et al., arXiv:1402.5417v1

In this comment we address the preprint Z. Yao et al. (arXiv:1402.5417v1) concerning the conditions upon which the correct critical temperature exponent $ϕ$ can be observed (experimentally or numerically) close to the superfluid-Bose glass quantum phase transition in three dimensions. Yao et al. announce to have resolved the contradiction between the predictions of Fisher et al. [Phys. Rev. B 40, 546 (1989)] that $ϕ= νz \geq 2$ (where $ν$ and $z$ are critical exponents at the quantum phase transition) and recent experiments and simulations, showing an exponent $ϕ\sim 1.1$. Yao et al's resolution hinges on claiming that the $ϕ\sim 1.1$ observations, which were conducted by varying the chemical potential, were not made to sufficiently close to the critical point to observe universal behavior. Here we critically examine their criteria for observing universal behavior. We show that past simulations were in fact conducted closer to the quantum critical point than the new results of Yao et al.; and that Yao et al.'s own results for varying chemical potential are consistent with previous results showing $ϕ\sim 1.1$, and do not show a clear crossover to a different $ϕ$ value.

cond-mat.dis-nn↗
arXiv2014

Thermal conductivity of molecular crystals with self-organizing disorder

The thermal conductivity of some orientational glasses of protonated C2H5OH and deuterated C2D5OD ethanol, cyclic substances (cyclohexanol C6H11OH, cyanocyclohexane C6H11CN, cyclohexene C6H10), and freon 112 (CFCl2)2 have been analyzed in the temperature interval 2-130 K. The investigated substances demonstrate new effects concerned with the physics of disordered systems. Universal temperature dependences of the thermal conductivity of molecular orientational glasses have been revealed. At low temperatures, the thermal conductivity exhibits a universal behavior that can be described by the soft potential model. At relatively high temperatures, the thermal conductivity has a smeared maximum and than decreases with increase in the temperature, which occurs typically in crystalline structures.

cond-mat.dis-nn↗