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Source author record

Ariel Amir

Ariel Amir appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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cond-mat.dis-nncond-mat.stat-mechBiological Physicscond-mat.softCell Behaviorcond-mat.mtrl-sciSubcellular Processescond-mat.mes-hallPopulations and EvolutionQuantitative Methodscond-mat.str-elquant-phcond-mat.othermath-phmath.MPNeurons and Cognitionphysics.data-anphysics.flu-dynphysics.opticsphysics.pop-ph

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Published work

34 published item(s)

preprint2026arXiv

Essential Role of Extrinsic Noise in Models of E. coli Division Control

Our understanding of cell division control in bacteria still relies largely on interpreting correlations between phenomenological variables, with limited connection to the underlying molecular mechanisms. Here, we analytically solve a stochastic threshold-accumulation model in which a size-dependent divisor protein triggers division upon reaching a noisy, autocorrelated threshold, quantifying within a unified framework the combined effects of intrinsic and extrinsic noise and key mechanistic parameters such as protein reset and threshold memory. We show that incorporating these elements yields behavior far richer than the commonly assumed adder, spanning a continuum of division strategies from timer to sizer while modulating size fluctuations in a nontrivial fashion. Comparison with single-cell E. coli data shows that extrinsic noise and additional mechanistic ingredients are required to account for the observed size fluctuations. The adder emerges when threshold correlations balance protein reset, generalizing the hypothesis that full reset is necessary to maintain adder control. Our results establish a unified analytical framework linking stochastic molecular processes to emergent division laws, to be used in more complex bacterial cell-cycle models.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Conditional Probability as Found in Nature: Facilitated Diffusion

Transcription Factors (TFs) are proteins that regulate gene expression. The regulation mechanism is via the binding of a TF to a specific part of the gene associated with it, the TF's target. The target of a specific TF corresponds to a vanishingly small part of the entire DNA, where at the same time the search must end in a matter of tens of seconds at most for its biological purpose to be fulfilled - this makes the search a problem of high interest. Facilitated Diffusion is a mechanism used in nature for a robust and efficient search process. This mechanism combines 1D diffusion along the DNA and "excursions" of diffusion in 3D that help the TF to quickly arrive at distant parts of the DNA. In this paper we provide a derivation concerning this mechanism that links this search process to fundamental concepts in probability theory (conditional probability).

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Universal catastrophe time distributions of dynamically unstable polymers

Dynamic instability -- the growth, catastrophe, and shrinkage of quasi-one-dimensional filaments -- has been observed in multiple biopolymers. Scientists have long understood the catastrophic cessation of growth and subsequent depolymerization as arising from the interplay of hydrolysis and polymerization at the tip of the polymer. Here, we show that for a broad class of catastrophe models, the expected catastrophe time distribution is exponential. We show that the distribution shape is insensitive to noise, but that depletion of monomers from a finite pool can dramatically change the distribution shape by reducing the polymerization rate. We derive a form for this finite-pool catastrophe time distribution and show that finite-pool effects can be important even when the depletion of monomers does not greatly alter the polymerization rate.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Bending Instability of Rod-shaped Bacteria

A thin-walled tube, e.g., a drinking straw, manifests an instability when bent by localizing the curvature change in a small region. This instability has been extensively studied since the seminal work of Brazier nearly a century ago. However, the scenario of pressurized tubes has received much less attention. Motivated by rod-shaped bacteria such as E. coli, whose cell walls are much thinner than their radius and are subject to a substantial internal pressure, we study, theoretically, how this instability is affected by this internal pressure. In the parameter range relevant to the bacteria, we find that the internal pressure significantly postpones the onset of the instability, while the bending stiffness of the cell wall has almost no influence. This study suggests a new method to infer turgor pressure in rod-shaped bacteria from bending experiments.

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preprint2021arXiv

Temporal Evolution of Flow in Pore-Networks: From Homogenization to Instability

We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A large deviation principle linking lineage statistics to fitness in microbial populations

In exponentially proliferating populations of microbes, the population typically doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population's growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a population's growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a non-monotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

From single-cell variability to population growth

Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate are usually based on the assumption that the generation times of mother and daughter cells are uncorrelated. This assumption, however, is inconsistent with the exponential growth of cell volume in time observed for many cell types. Here we develop a more general and biologically relevant model in which cells grow exponentially and generation times are correlated in a manner which controls cell size. In addition to the fluctuating generation times, we also allow the single-cell growth rates to fluctuate and account for their correlations across the lineage tree. Surprisingly, we find that the population growth rate only depends on the distribution of single-cell growth rates and their correlations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Non-genetic variability: survival strategy or nuisance?

The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context of antibiotic treatments or exponential growth in constant environments, non-genetic variability has shown to have significant effects on population dynamics. Here, we review research that elucidates the relationship between cell-to-cell variability and population dynamics. After summarizing the relevant experimental observations, we discuss models of bet-hedging and phenotypic switching. In the context of these models, we discuss how switching between phenotypes at the single-cell level can help populations survive in uncertain environments. Next, we review more fine-grained models of phenotypic variability where the relationship between single-cell growth rates, generation times and cell sizes is explicitly considered. Variability in these traits can have significant effects on the population dynamics, even in a constant environment. We show how these effects can be highly sensitive to the underlying model assumptions. We close by discussing a number of open questions, such as how environmental and intrinsic variability interact and what the role of non-genetic variability in evolutionary dynamics is.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The effect of interactions and disorder on the relaxation of two-level systems in amorphous solids

At low temperatures the dynamical degrees of freedom in amorphous solids are tunnelling two-level systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLS-TLS interactions, we obtain a "TLS-glass", described by the random field Ising model with random $1/r^3$ interactions. In this paper we perform a self consistent mean field calculation, previously used to study the electron-glass (EG) model [A.~Amir {\it et al.}, Phys. Rev. B {\bf 77}, 165207, (2008)]. Similar to the electron-glass, we find $\frac{1}λ$ distribution of relaxation rates $λ$, leading to logarithmic slow relaxation. However, with increased interactions the EG model shows slower dynamics whereas the TLS glass model shows faster dynamics. This suggests that given system specific properties, glass dynamics can be slowed down or sped up by the interactions.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

An elementary renormalization-group approach to the Generalized Central Limit Theorem and Extreme Value Distributions

The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge under appropriate scaling to a distribution belonging to a special family known as Levy stable distributions. Similarly, the maximum of i.i.d. variables may converge to a distribution belonging to one of three universality classes (Gumbel, Weibull and Frechet). Here, we rederive these known results following a mathematically non-rigorous yet highly transparent renormalization-group-like approach that captures both of these universal results following a nearly identical procedure.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Thermal conductance of one dimensional disordered harmonic chains

We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find non-trivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that a system with strong disorder, characterized by a `heavy-tailed' probability distribution, and with large impedance mismatch between the bath and the system satisfies Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.

0 citations0 reviewsNo code linkedOpen access
preprint2017arXiv

Interrogating the Escherichia coli cell cycle by cell dimension perturbations

Bacteria tightly regulate and coordinate the various events in their cell cycles to duplicate themselves accurately and to control their cell sizes. Growth of Escherichia coli, in particular, follows a relation known as Schaechter 's growth law. This law says that the average cell volume scales exponentially with growth rate, with a scaling exponent equal to the time from initiation of a round of DNA replication to the cell division at which the corresponding sister chromosomes segregate. Here, we sought to test the robustness of the growth law to systematic perturbations in cell dimensions achieved by varying the expression levels of mreB and ftsZ. We found that decreasing the mreB level resulted in increased cell width, with little change in cell length, whereas decreasing the ftsZ level resulted in increased cell length. Furthermore, the time from replication termination to cell division increased with the perturbed dimension in both cases. Moreover, the growth law remained valid over a range of growth conditions and dimension perturbations. The growth law can be quantitatively interpreted as a consequence of a tight coupling of cell division to replication initiation. Thus, its robustness to perturbations in cell dimensions strongly supports models in which the timing of replication initiation governs that of cell division, and cell volume is the key phenomenological variable governing the timing of replication initiation. These conclusions are discussed in the context of our recently proposed adder-per-origin model, in which cells add a constant volume per origin between initiations and divide a constant time after initiation.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Non-Hermitian Localization in Biological Networks

We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions, and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes, but also with respect to 90 degree rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias dependent shape of this hole tracks the bias independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's Law" (each site is purely excitatory or inhibitory), and conclude with perturbation theory results that describe the limit of large bias g, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Single-cell analysis of growth in budding yeast and bacteria reveals a common size regulation strategy

To maintain a constant cell size, dividing cells have to coordinate cell cycle events with cell growth. This coordination has for long been supposed to rely on the existence of size thresholds determining cell cycle progression [1]. In budding yeast, size is controlled at the G1/S transition [11]. In agreement with this hypothesis, the size at birth influences the time spent in G1: smaller cells have a longer G1 period [3]. Nevertheless, even though cells born smaller have a longer G1, the compensation is imperfect and they still bud at smaller cell sizes. In bacteria, several recent studies have shown that the incremental model of size control, in which size is controlled by addition of a constant volume (in contrast to a size threshold), is able to quantitatively explain the experimental data on 4 different bacterial species [6, 5, 6, 7]. Here, we report on experimental results for the budding yeast Saccharomyces cerevisiae, finding, surprisingly, that cell size control in this organism is very well described by the incremental model, suggesting a common strategy for cell size control with bacteria. Additionally, we argue that for S. cerevisiae the volume increment is not added from birth to division, but rather between two budding events.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Stochastic modeling of cell growth with symmetric or asymmetric division

We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the "master equation" describing how the resource distribution evolves over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendix, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Surprises in numerical expressions of physical constants

In science, as in life, `surprises' can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of mathematical constants like pi or e. The inverse problem also arises, whereby the measured value of a physical constant admits a `surprisingly' simple approximation in terms of well-known mathematical constants. Can we estimate the probability for this to be a mere coincidence, rather than an inkling of some theory? We answer the question in the most naive form.

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preprint2015arXiv

An elementary derivation of first and last return times of 1D random walks

Random walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first return time distribution of a 1D random walker, which is a heavy-tailed distribution with infinite mean. Using the same method we find the last return time distribution, which follows the arcsine law. Both results have a broad range of applications in physics and other disciplines. The derivation presented here is readily accessible to physics undergraduates, and provides an elementary introduction into random walks and their intriguing properties.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Simultaneous regulation of cell size and chromosome replication in bacteria

Bacteria are able to maintain a narrow distribution of cell sizes by regulating the timing of cell divisions. In rich nutrient conditions, cells divide much faster than their chromosomes replicate. This implies that cells maintain multiple rounds of chromosome replication per cell division by regulating the timing of chromosome replications. Here, we show that both cell size and chromosome replication may be simultaneously regulated by the long-standing initiator accumulation strategy. The strategy proposes that initiators are produced in proportion to the volume increase and is accumulated at each origin of replication, and chromosome replication is initiated when a critical amount per origin has accumulated. We show that this model maps to the incremental model of size control, which was previously shown to reproduce experimentally observed correlations between various events in the cell cycle and explains the exponential dependence of cell size on the growth rate of the cell. Furthermore, we show that this model also leads to the efficient regulation of the timing of initiation and the number of origins consistent with existing experimental results.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Bending forces plastically deform growing bacterial cell walls

Cell walls define a cell shape in bacteria. They are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain their shape. In this work, we develop experimental and theoretical approaches and show that mechanical stresses regulate bacterial cell-wall growth. By applying a precisely controllable hydrodynamic force to growing rod-shaped Escherichia coli and Bacillus subtilis cells, we demonstrate that the cells can exhibit two fundamentally different modes of deformation. The cells behave like elastic rods when subjected to transient forces, but deform plastically when significant cell wall synthesis occurs while the force is applied. The deformed cells always recover their shape. The experimental results are in quantitative agreement with the predictions of the theory of dislocation-mediated growth. In particular, we find that a single dimensionless parameter, which depends on a combination of independently measured physical properties of the cell, can describe the cell's responses under various experimental conditions. These findings provide insight into how living cells robustly maintain their shape under varying physical environments.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Cell size regulation in microorganisms

Various rod-shaped bacteria such as the canonical gram negative Escherichia coli or the well-studied gram positive Bacillus subtilis divide symmetrically after they approximately double their volume. Their size at division is not constant, but is typically distributed over a narrow range. Here, we propose an analytically tractable model for cell size control, and calculate the cell size and inter-division time distributions. We suggest ways of extracting the model parameters from experimental data. Existing data for E. coli supports partial size control, and a particular explanation: a cell attempts to add a constant volume from the time of initiation of DNA replication to the next initiation event. This hypothesis explains how bacteria control their tight size distributions and accounts for the experimentally observed correlations between parents and daughters as well as the exponential dependence of size on growth rate.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Getting into shape: how do rod-like bacteria control their geometry?

Rod-like bacteria maintain their cylindrical shapes with remarkable precision during growth. However, they are also capable to adapt their shapes to external forces and constraints, for example by growing into narrow or curved confinements. Despite being one of the simplest morphologies, we are still far from a full understanding of how shape is robustly regulated, and how bacteria obtain their near-perfect cylindrical shapes with excellent precision. However, recent experimental and theoretical findings suggest that cell-wall geometry and mechanical stress play important roles in regulating cell shape in rod-like bacteria. We review our current understanding of the cell wall architecture and the growth dynamics, and discuss possible candidates for regulatory cues of shape regulation in the absence or presence of external constraints. Finally, we suggest further future experimental and theoretical directions, which may help to shed light on this fundamental problem.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Universal frequency-dependent conduction of electron glasses

Characterizing the frequency-dependent response of amorphous systems and glasses can provide important insights into their physics. Here, we study the response of an electron glass, where Coulomb interactions are important and have previously been shown to significantly modify the conductance and lead to memory effects and aging. We propose a model which allows us to take the interactions into account in a self-consistent way, and explore the frequency-dependent conduction at all frequencies. At low frequencies conduction occurs on the percolation backbone, and the model captures the variable-range-hopping behavior. At high frequencies conduction is dominated by localized clusters. Despite the difference in physical mechanisms at low and high frequency, we are able to scale all numerical data onto a single curve, using two parameters: the DC conduction and dielectric constant. The behavior follows the universal scaling that is experimentally observed for a large class of amorphous solids.

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preprint2013arXiv

Defects on cylinders: superfluid helium films and bacterial cell walls

There is a deep analogy between the physics of crystalline solids and the behavior of superfluids, dating back to pioneering work of Phillip Anderson, Paul Martin and others. The stiffness to shear deformations in a periodic crystal resembles the superfluid density that controls the behavior of supercurrents in neutral superfluids such as He^4. Dislocations in solids have a close analogy with quantized vortices in superfluids. Remarkable recent experiments on the way rod-shaped bacteria elongate their cell walls have focused attention on the dynamics and interactions of point-like dislocation defects in partially ordered cylindrical crystalline monolayers. In these lectures, we review the physics of superfluid helium films on cylinders and discuss how confinement in one direction affects vortex interactions with supercurrents. Although there are similarities with the way dislocations respond to strains on cylinders, important differences emerge, due to the vector nature of the topological charges characterizing the dislocations.

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preprint2013arXiv

Elucidating the stop bands of structurally colored systems through recursion

Interference phenomena are the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics; namely, specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer and solve it using recursion relations. We present experimental data for various beetles, whose optical structure resembles the proposed model. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursive relations. In order for these to converge, an infinitesimal amount of absorption needs to be present, reminiscent of the regularization procedures commonly used in physics calculations. Thus, using only the phenomenon of interference and the idea of recursion, we are able to elucidate the concepts of band structure and regularization in the context of experimentally observed phenomena, such as the high reflectance and the iridescent color appearance of structurally colored beetles.

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preprint2013arXiv

Emergent percolation length and localization in random elastic networks

We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency and the spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localization/delocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach we calculate the speed-of-sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density, and find good agreement of these predictions with numerical results using a recursive Green function method adapted for this problem. The connection of our results to recent experiments on amorphous solids are discussed.

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preprint2013arXiv

Theory of interacting dislocations on cylinders

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.

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preprint2012arXiv

Dislocation-mediated growth of bacterial cell walls

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 et al., Science (2011), Dominguez-Escobar et al. Science (2011), van Teeffelen et al. PNAS (2011). 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.

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preprint2011arXiv

Huge (but finite) time scales in slow relaxations: beyond simple aging

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 timescales of hours, and when a strong electric field is applied for a time $t_w$, the ensuing relaxation depends on $t_w$. We derive a theoretical curve and show that all experimental data collapse onto it with a single timescale as a fitting parameter. This timescale 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.

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preprint2011arXiv

On relaxations and aging of various glasses

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 iscalled 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.

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preprint2010arXiv

Localization, anomalous diffusion and slow relaxations: a random distance matrix approach

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) and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results.

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preprint2010arXiv

The localization transition at finite temperatures: electric and thermal transport

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.

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preprint2009arXiv

1/f noise and slow relaxations in glasses

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 $P(λ) \sim 1/λ$ 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.

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preprint2009arXiv

Classical Diffusion of a quantum particle in a noisy environment

We study the spreading of a quantum-mechanical wavepacket in a one-dimensional 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 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.

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preprint2009arXiv

Variable range hopping in the Coulomb glass

We use a 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 Hartree self-consistent 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.

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