Amir A, Paulose J, Nelson DR. Theory of interacting dislocations on cylinders. Phys Rev E Stat Nonlin Soft Matter Phys. 2013;87 (4) :042314.Abstract
We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The interaction energy and forces between dislocations are solved analytically, and analyzed asymptotically. The results of continuum elastic theory agree well with numerical simulations on finite lattices even for relatively small systems. Isolated dislocations on a cylinder act like grain boundaries. With colloidal crystals in mind, we show that saddle points are created by a Peach-Koehler force on the dislocations in the circumferential direction, causing dislocation pairs to unbind. The thermal nucleation rate of dislocation unbinding is calculated, for an arbitrary mobility tensor and external stress, including the case of a twist-induced Peach-Koehler force along the cylinder axis. Surprisingly rich phenomena arise for dislocations on cylinders, despite their vanishing Gaussian curvature.
Nelson DR, Amir A. Defects on cylinders: superfluid helium films and bacterial cell walls. Lectures given by D. R. Nelson at the Les Houches School on ”Soft Interfaces,” July 2-27. 2012;arxiv:1303.5896.
Amir A, Oreg Y, Imry Y. On relaxations and aging of various glasses. Proc Natl Acad Sci U S A. 2012;109 (6) :1850-5.Abstract
Slow relaxation occurs in many physical and biological systems. "Creep" is an example from everyday life. When stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: The relaxation is slow, in many cases logarithmic, and can still be observed after many hours. The form of the relaxation also depends on the duration of the stretching, the "waiting time." This ubiquitous phenomenon is called aging, and is abundant both in natural and technological applications. Here, we suggest a general mechanism for slow relaxations and aging, which predicts logarithmic relaxations, and a particular aging dependence on the waiting time. We demonstrate the generality of the approach by comparing our predictions to experimental data on a diverse range of physical phenomena, from conductance in granular metals to disordered insulators and dirty semiconductors, to the low temperature dielectric properties of glasses.
Amir A, Nelson DR. Dislocation-mediated growth of bacterial cell walls. Proc Natl Acad Sci U S A. 2012;109 (25) :9833-8.Abstract
Recent experiments have illuminated a remarkable growth mechanism of rod-shaped bacteria: proteins associated with cell wall extension move at constant velocity in circles oriented approximately along the cell circumference [Garner EC, et al., (2011) Science 333:222-225], [Domínguez-Escobar J, et al. (2011) Science 333:225-228], [van Teeffelen S, et al. (2011) PNAS 108:15822-15827]. We view these as dislocations in the partially ordered peptidoglycan structure, activated by glycan strand extension machinery, and study theoretically the dynamics of these interacting defects on the surface of a cylinder. Generation and motion of these interacting defects lead to surprising effects arising from the cylindrical geometry, with important implications for growth. We also discuss how long range elastic interactions and turgor pressure affect the dynamics of the fraction of actively moving dislocations in the bacterial cell wall.
Amir A, Oreg Y, Imry Y. Electron glass dynamics. Annu. Rev. Condens. Matter Phys. 2011;2 (235-62).Abstract

Examples of glasses are abundant, yet it remains one of the phases of matter whose understanding is very elusive. In recent years, remarkable experiments have been performed on the dynamical aspects of glasses. Electron glasses offer a particularly good example of the trademarks of glassy behavior, such as aging and slow relaxations. In this work we review the experimental literature on electron glasses, as well as the local mean-field theoretical framework put forward in recent years to understand some of these results. We also present novel theoretical results explaining the periodic aging experiment.

Amir A, Borini S, Oreg Y, Imry Y. Huge (but finite) time scales in slow relaxations: beyond simple aging. Phys Rev Lett. 2011;107 (18) :186407.Abstract
Experiments performed in the last years demonstrated slow relaxations and aging in the conductance of a large variety of materials. Here, we present experimental and theoretical results for conductance relaxation and aging for the case-study example of porous silicon. The relaxations are experimentally observed even at room temperature over time scales of hours, and when a strong electric field is applied for a time tw, the ensuing relaxation depends on tw. We derive a theoretical curve and show that all experimental data collapse onto it with a single time scale as a fitting parameter. This time scale is found to be of the order of thousands of seconds at room temperature. The generic theory suggested is not fine-tuned to porous silicon, and thus we believe the results should be universal, and the presented method should be applicable for many other systems manifesting memory and other glassy effects.
Amir A, Oreg Y, Imry Y. Localization, anomalous diffusion, and slow relaxations: a random distance matrix approach. Phys Rev Lett. 2010;105 (7) :070601.Abstract
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum), for low densities, and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results.
Imry Y, Amir A. The localization transition at finite temperatures: electric and thermal transport. In: Abrahams E 50 Years of Anderson Localization. Singapore: World Scientific ; 2010. Publisher's VersionAbstract

The Anderson localization transition is considered at finite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients. An interesting critical behavior of the latter is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using the conductivity and thermopower measurements, is outlined.

Amir A, Oreg Y, Imry Y. 1/f noise and slow relaxations in glasses. TIDS conference. 2009;18 (12) :836.Abstract

Recently we have shown that slow relaxations in the electron glass system can be understood in terms of the spectrum of a matrix describing the relaxation of the system close to a metastable state. The model focused on the electron glass system, but its generality was demonstrated on various other examples. Here, we study the noise spectrum in the same framework. We obtain a remarkable relation between the spectrum of relaxation rates λ described by the distribution function P(λ)1/λ and the 1/f noise in the fluctuating occupancies of the localized electronic sites. This noise can be observed using local capacitance measurements. We confirm our analytic results using numerics, and also show how the Onsager symmetry is fulfilled in the system.

Amir A, Lahini Y, Perets HB. Classical diffusion of a quantum particle in a noisy environment. Phys Rev E Stat Nonlin Soft Matter Phys. 2009;79 (5 Pt 1) :050105.Abstract
We study the spreading of a quantum-mechanical wave packet in a tight-binding model with a noisy potential and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite correlation time of the noisy environment and treat the system by utilizing the separation of fast (dephasing) and slow (diffusion) processes. We show that classical diffusive behavior emerges at long times and we calculate analytically the dependence of the classical diffusion coefficient on the noise magnitude and correlation time. This method provides a general solution to this problem for arbitrary conditions of the noisy environment. The calculation can be done in any dimension, but we demonstrate it in one dimension for clarity of representation. The results are relevant to a large variety of physical systems, from electronic transport in solid-state physics to light transmission in optical devices, diffusion of excitons, and quantum computation.
Amir A, Oreg Y, Imry Y. Slow relaxations and aging in the electron glass. Phys Rev Lett. 2009;103 (12) :126403.Abstract
Glassy systems are ubiquitous in nature. They are characterized by slow relaxations to equilibrium without a typical time scale, aging, and memory effects. Understanding this has been a long-standing problem in physics. We study the aging of the electron glass, a system showing remarkable slow relaxations of the conductance. We find that the appropriate broad distribution of relaxation rates leads to a universal relaxation of the form log(1 + t_{w}/t) for the common aging protocol, where t_{w} is the length of time the perturbation driving the system out of equilibrium was on, and t the time of measurement. These results agree well with several experiments performed on different glassy systems, and examining different physical observables, for times ranging from seconds to several hours. The suggested theoretical framework appears to offer a paradigm for aging in a broad class of glassy materials.
Amir A, Oreg Y, Imry Y. Variable range hopping in the Coulomb glass. Physical Review B. 2009;80 (245214).Abstract

We use a local mean-field (Hartree-like) approach to study the conductance of a strongly localized electron system in two dimensions. We find a crossover between a regime where Coulomb interactions modify the conductance significantly to a regime where they are negligible. We show that under rather general conditions the conduction obeys a scaling relation which we verify using numerical simulations. The use of a local mean-field approach gives a clear physical picture, and removes the ambiguity of the use of single-particle tunneling density of states (DOS) in the calculation of the conductance. Furthermore, the theory contains interaction-induced correlations between the on site energy of the localized states and distances, as well as finite temperature corrections of the DOS.

Amir A, Oreg Y, Imry Y. Decays in quantum hierarchical models. Physical Review A. 2008;77 (050101(R).Abstract

We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudocontinuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudocontinuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random, several cases are identified. For a pseudocontinuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For intermediate bandwidth one finds mesoscopic fluctuations in the probability with amplitude inversely proportional to the square root of the volume of the pseudocontinuum space. They last for a long time compared to the nonrandom case.

Amir A, Oreg Y, Imry Y. Mean-field model for electron-glass dynamics. Physical Review B. 2008;77 (165207).Abstract

We study a microscopic mean-field model for the dynamics of the electron glass near a local equilibrium state. Phonon-induced tunneling processes are responsible for generating transitions between localized electronic sites, which eventually lead to the thermalization of the system. We find that the decay of an excited state to a locally stable state is far from being exponential in time and does not have a characteristic time scale. Working in a mean-field approximation, we write rate equations for the average occupation numbers ni and describe the return to the locally stable state by using the eigenvalues of a rate matrix A describing the linearized time evolution of the occupation numbers. By analyzing the probability distribution P(λ) of the eigenvalues of A, we find that, under certain physically reasonable assumptions, it takes the form P(λ)1/λ, leading naturally to a logarithmic decay in time. While our derivation of the matrix A is specific for the chosen model, we expect that other glassy systems, with different microscopic characteristics, will be described by random rate matrices belonging to the same universality class of A. Namely, the rate matrix has elements with a very broad distribution, as in the case of exponentials of a variable with nearly uniform distribution.