arXiv subjects

Eric I. Corwin

Publications and source records attributed to Eric I. Corwin.

At least 19 recordsLinked to original sources

arXiv2025

Universal Fluctuations in the Tail Probability for d=2 Random Walks in Space-Time Random Environments

Many diffusive systems involve correlated random walkers due to a shared environment. Such systems can be modeled as random walks in random environments (RWRE). These models differ from classical diffusion in the behavior of the extremes -- the walkers that move the fastest or farthest. In spatial dimension $d=1$ RWRE models have been well studied numerically and analytically and exhibit universal behavior in the Kardar-Parisi-Zhang universality class. Here, we study discrete lattice RWRE models in $d=2$. We find that the tail probability exhibits a different universal scaling form, which is nevertheless characterized by the same coefficient, $\lambda_\mathrm{ext}$, as in the $d=1$ case. We observe a critical scaling regime for fluctuations in the tail probability at positions that scale linearly in time.

cond-mat.stat-mech↗

arXiv2025

Numerically Discovered Inherent States are Always Protocol Dependent in Jammed Packings

The energy landscape for soft sphere packings exists in a high-dimensional space and plays host to an astronomical number of local minima in a hierarchical and ultrametric arrangement. Each point in the landscape is a configuration that can be unambiguously mapped to its inherent state, defined as the local minimum that the configuration will flow to under perfectly overdamped continuous dynamics. Typically, discrete in time dynamics are used to computationally find local minima, but it is not known whether these algorithms are capable of reliably finding inherent states. Here, we use steepest descent dynamics to find the distribution of the largest time step, $\delta_\textrm{best}$, which finds the inherent state. We find that for systems of $N$ particles, $\delta_\textrm{best}$ is approximately proportional to $N^{-3}$, and weakly dependent on d and $\varphi$. We argue that the proportionality is due to saddle points in the energy landscape. Our results suggest that it is impossible, in practice, to reliably find inherent states for systems of about 64 particles or more.

cond-mat.soft↗

arXiv2025

Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring

We provide explicit formulas to diagonalize the Hamiltonian for the Heisenberg-Ising XXZ spin-1/2 chain on a discrete ring. Two distinguished bases for the Hilbert space include the basis labeled by the coordinates of the particle configurations and the basis obtained from the eigenvectors of the Hamiltonian. We diagonalize the Hamiltonian by providing an explicit transformation between these two distinguished bases. The transformation from the coordinate basis to the eigenbasis is given by the well-known coordinate Bethe Ansatz. Our contribution is the transformation from the eigenbasis to the coordinate basis, which we call the inverse coordinate Bethe Ansatz transformation/formula. We prove that the inverse coordinate Bethe Ansatz transformation is indeed the inverse of the transformation obtained from the Bethe Ansatz for the case of N = 2 particles and a ring of odd length L with a small nonzero anisotropy term $\Delta < (L-1)/(2L)$ and $\Delta$ outside some exceptional finite set. The case of N > 2 particles and a ring of odd length L is numerically confirmed for different arbitrary choices of parameters and is left as a conjecture. Additionally, assuming that the conjecture is true, we derive an exact formula for the one-point function of the system through special identities for the Izergin-Korepin determinant. Moreover, if the conjecture is true, this implies that the Bethe Ansatz is complete.

math-ph↗

arXiv2025

Measurements of extreme first passage times in photon transport

Photon transport through turbid media has typically been modeled through diffusion or telegraph equations. These models describe behavior of the average, or typical, photon with remarkable accuracy, however, we show here that they fail to capture the Extreme First Passage Times (EFPTs) of photon transport. By sending ultra-fast bursts of photons through a scattering medium and timing the arrival of the first passage photon, we measure the distribution of these EFPTs of photons in a random environment. Our measured EFPTs differ from those predicted by both the diffusion approximation and telegraph equation. Instead, we observe the EFPT as the time expected for light to travel through an index-averaged medium. These results reveal flaws in both models and invite a re-examining of their underlying assumptions.

physics.optics↗

arXiv2023

Anomalous Fluctuations of Extremes in Many-Particle Diffusion

In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of Einstein's treatment of single-particle diffusion, has each particle taking independent homogeneous random walks. This, however, neglects the fact that all particles diffuse in a common and often inhomogeneous environment that can affect their motion. A more sophisticated model treats this common environment as a space-time random biasing field which influences each particle's independent motion. While the bulk (or typical particle) behavior of these two models has been found to match to high degree, recent theoretical work of Barraquand, Corwin and Le Doussal on a one-dimensional exactly solvable version of this random environment model suggests that the extreme behavior is quite different between the two models. We transform these asymptotic (in system size and time) results into physically applicable predictions. Using high precision numerical simulations we reconcile different asymptotic phases in a manner that matches numerics down to realistic system sizes, amenable to experimental confirmation. We characterize the behavior of extreme diffusion in the random environment model by the presence of a new phase with anomalous fluctuations related to the Kardar-Parisi-Zhang universality class and equation.

cond-mat.stat-mech↗

arXiv2023

First Passage Time for Many Particle Diffusion in Space-Time Random Environments

The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently. We consider two models for many particle diffusion -- one treats each particle as independent simple random walkers while the other treats them as coupled to a common space-time random forcing field that biases particles nearby in space and time in similar ways. The first passage time of a single diffusing particle under both of these models show the same statistics and scaling behavior. However, for many particle diffusions, the first passage time among all particles (the `extreme first passage time') is very different between the two models, effected in the latter case by the randomness of the common forcing field. We develop an asymptotic (in the number of particles and location where first passage is being probed) theoretical framework to separate out the impact of the random environment with that of sampling trajectories within it. We identify a new power-law describing the impact to the extreme first passage time variance of the environment. Through numerical simulations we verify that the predictions from this asymptotic theory hold even for systems with widely varying numbers of particles, all the way down to 100 particles. This shows that measurements of the extreme first passage time for many-particle diffusions provide an indirect measurement of the underlying environment in which the diffusion is occurring.

cond-mat.stat-mech↗

arXiv2022

The Jamming Transition and the Marginally Stable Solid

We review the physics of jamming from the theoretical, experimental and numerical perspectives. We summarize the mean-field theory of jamming and the marginally stable solid phase, with particular emphasis on the connection with the Replica Symmetry Breaking theory of glasses. We report validations of the mean-field theory of jamming from experimental and numerical studies of critical behaviors near the transition. In particular, we describe the physics of jamming of frictionless, spherical particles, as well as more recent work on jamming of frictionless, non-spherical particles and frictional, nearly spherical particles. We also present current efforts in expanding the mean-field theory to systems that more closely resemble externally driven granular media, cell aggregates, and active colloidal suspensions.

cond-mat.soft↗

arXiv2022

Emergence of zero modes in disordered solids under periodic tiling

In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the particles' images move together. An infinitely repeated structure, on the other hand, does not necessarily have this constraint. As a consequence, a jammed packing (or a rigid elastic network) under periodic boundary conditions may have a corresponding infinitely repeated lattice representation that is not rigid or indeed may not even be at a local energy minimum. In this manuscript, we prove this claim and discuss ways in which periodic boundary conditions succeed to capture the physics of repeated structures and where they fall short.

cond-mat.soft↗

arXiv2022

Hyperuniform Jammed Sphere Packings Have Anomalous Material Properties

A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is disordered hyperuniformity: the presence of hyperuniform scaling without long-range configurational order. Jammed granular packings have been proposed as an example of disordered hyperuniformity, but recent numerical investigation has revealed that many jammed systems instead exhibit a complex set of distinct behaviors at long, emergent length scales. We use the Voronoi tesselation as a tool to define a set of rescaling transformations that can impose hyperuniformity on an arbitrary weighted point process, and show that these transformations can be used in simulations to iteratively generate hyperuniform, mechanically stable packings of athermal soft spheres. These hyperuniform jammed packings display atypical mechanical properties, particularly in the low-frequency phononic excitations, which exhibit an isolated band of highly collective modes and a band-gap around zero frequency.

cond-mat.soft↗

arXiv2021

Free-then-freeze: transient learning degrees of freedom for introducing function in materials

The introduction of transient learning degrees of freedom into a system can lead to novel material design and training protocols that guide a system into a desired metastable state. In this approach, some degrees of freedom, which were not initially included in the system dynamics, are first introduced and subsequently removed from the energy minimization process once the desired state is reached. Using this conceptual framework, we create stable jammed packings that exist in exceptionally deep energy minima marked by the absence of low-frequency quasilocalized modes; this added stability persists in the thermodynamic limit. The inclusion of particle radii as transient degrees of freedom leads to deeper and much more stable minima than does the inclusion of particle stiffnesses. This is because particle radii couple to the jamming transition whereas stiffnesses do not. Thus different choices for the added degrees of freedom can lead to very different training outcomes.

cond-mat.soft↗

arXiv2021

Marginal Stability Enables Memory Training in Jammed Solids

Memory encoding by cyclic shear is a reliable process to store information in jammed solids, yet its underlying mechanism and its connection to the amorphous structure are not fully understood. When a jammed sphere packing is repeatedly sheared with cycles of the same strain amplitude, it optimizes its mechanical response to the cyclic driving and stores a memory of it. We study memory by cyclic shear training as a function of the underlying stability of the amorphous structure in marginally stable and highly stable packings, the latter produced by minimizing the potential energy using both positional and radial degrees of freedom. We find that jammed solids need to be marginally stable in order to store a memory by cyclic shear. In particular, highly stable packings store memories only after overcoming brittle yielding and the cyclic shear training takes place in the shear band, a region which we show to be marginally stable.

cond-mat.soft↗

arXiv2021

Predicting Defects in Soft Sphere Packings Near Jamming Using The Force Network Ensemble

Amorphous systems of soft particles above jamming have more contacts than are needed to achieve mechanical equilibrium. The force network of a granular system with a fixed contact network is thus underdetermined, and can be characterized as a random instantiation within the space of the force network ensemble. In this work, we show that by examining the boundaries of this space of allowed force networks, defect contacts which are not necessary for stability of the system can be uniquely identified. We further show that in the near jamming limit, this identification is nearly always correct and the defect contacts are broken under decompression of the system.

cond-mat.soft↗

arXiv2021

A direct link between active matter and sheared granular systems

The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their critical behavior should be equivalent in infinite dimensions, up to a rescaling factor that depends on the correlation length of the applied field. We test these predictions in 2d using a new numerical protocol, termed `athermal quasi-static random displacement', and find that these mean-field predictions are surprisingly accurate in low dimensions. We identify a general class of perturbations that smoothly interpolate between the uncorrelated localized forces that occur in the high-persistence limit of dense active matter, and system-spanning correlated displacements that occur under applied shear. These results suggest a universal framework for predicting flow, deformation, and failure in active and sheared disordered materials.

cond-mat.soft↗

arXiv2021

Long-Range Anomalous Decay of the Correlation in Jammed Packings

We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role they play in the configuration of jammed packings, we analyze the propagation through the system of the weak forces and of the variation of the coordination number with respect to the isostaticity condition $ΔZ$. We show that these correlations can be successfully probed by introducing a correlation function weighted on the density-density fluctuations. The results of this analysis can be further improved by introducing a representation of the system based on the contact points between particles. In particular, we find evidence that the weak forces and the $ΔZ$ fluctuations support the hypothesis of randomly jammed packings of spherical particles being hyperuniform by exhibiting an anomalous long-range decay. Moreover, we find that the large-scale structure of the density-density correlation exhibits a complex behavior due to the superimposition of two exponentially damped oscillating signals propagating with linearly depending frequencies.

cond-mat.soft↗

arXiv2021

Finite size effects in the microscopic critical properties of jammed configurations: A comprehensive study of the effects of different types of disorder

Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is that small interparticle forces ($f$) and gaps ($h$) are distributed according to nontrivial power laws. A recently developed mean-field (MF) theory predicts the characteristic exponents of these distributions in the limit of very high spatial dimension, $d\rightarrow\infty$ and, remarkably, their values seemingly agree with numerical estimates in physically relevant dimensions, $d=2$ and $3$. These exponents are further connected through a pair of inequalities derived from stability conditions, and both theoretical predictions and previous numerical investigations suggest that these inequalities are saturated. Systems at the jamming point are thus only marginally stable. Despite the key physical role played by these exponents, their systematic evaluation has yet to be attempted. Here, we carefully test their value by analyzing the finite-size scaling of the distributions of $f$ and $h$ for various particle-based models for jamming. Both dimension and the direction of approach to the jamming point are also considered. We show that, in all models, finite-size effects are much more pronounced in the distribution of $h$ than in that of $f$. We thus conclude that gaps are correlated over considerably longer scales than forces. Additionally, remarkable agreement with MF predictions is obtained in all but one model, namely near-crystalline packings. Our results thus help to better delineate the domain of the jamming universality class. We furthermore uncover a secondary linear regime in the distribution tails of both $f$ and $h$. This surprisingly robust feature is understood to follow from the (near) isostaticity of our configurations.

cond-mat.dis-nn↗

arXiv2021

Mean-Field Predictions of Scaling Prefactors Match Low-Dimensional Jammed Packings

No known analytic framework precisely explains all the phenomena observed in jamming. The replica theory for glass and jamming is a mean field theory which attempts to do so by working in the limit of infinite dimensions, such that correlations between neighbors are negligible. As such, results from this mean field theory are not guaranteed to be observed in finite dimensions. However, many results in mean field for jamming have been shown to be exact or nearly exact in low dimensions. This suggests that the infinite dimensional limit is not necessary to obtain these results. In this paper, we perform precision measurements of jamming scaling relationships between pressure, excess packing fraction, and number of excess contacts from dimensions 2-10 in order to extract the prefactors to these scalings. While these prefactors should be highly sensitive to finite dimensional corrections, we find the mean field predictions for these prefactors to be exact in low dimensions. Thus the mean field approximation is not necessary for deriving these prefactors. We present an exact, first principles derivation for one, leaving the other as an open question.

cond-mat.soft↗

arXiv2021

Interplay between percolation and glassiness in the random Lorentz gas

The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media. It also models the dynamics of a tracer in a glassy system. These two perspectives, however, are fundamentally inconsistent. Arrest in the former is related to percolation, and hence continuous, while glass-like arrest is discontinuous. In order to clarify the interplay between percolation and glassiness in the RLG, we consider its exact solution in the infinite-dimensional $d\rightarrow\infty$ limit, as well as numerics in $d=2\ldots 20$. We find that the mean field solutions of the RLG and glasses fall in the same universality class, and that instantonic corrections related to rare cage escapes destroy the glass transition in finite dimensions. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of hopping in structural glasses.

cond-mat.stat-mech↗

arXiv2019

Vibrational properties of hard and soft spheres are unified at jamming

The unconventional thermal properties of jammed amorphous solids are directly related to their density of vibrational states. While the vibrational spectrum of jammed soft sphere solids has been fully described, the vibrational spectrum of hard spheres, a model for colloidal glasses, is still unknown due to the difficulty of treating the non-analytic interaction potential. We bypass this difficulty using the recently described effective interaction potential for the free energy of thermal hard spheres. By minimizing this effective free energy we mimic a quench and produce typical configurations of low temperature colloidal glasses. We measure the resulting vibrational spectrum and characterize its evolution towards the jamming point where configurations of hard and soft spheres are trivially unified. For densities approaching jamming from below, we observe low frequency modes which agree with those found in numerical simulations of jammed soft spheres. Our measurements of the vibrational structure demonstrate that the jamming universality extends away from jamming: hard sphere thermal systems below jamming exhibit the same vibrational spectra as thermal and athermal soft sphere systems above the transition.

cond-mat.soft↗