arXiv subjects

David Mukamel

Publications and source records attributed to David Mukamel.

At least 19 recordsLinked to original sources

arXiv2025

Ensemble Inequivalence in Long-Range Quantum Spin Systems

Ensemble inequivalence occurs when a systems thermodynamic properties vary depending on the statistical ensemble used to describe it. This phenomenon is known to happen in systems with long-range interactions and has been observed in many classical systems. In this study, we provide a detailed analysis of a long-range quantum ferromagnet spin model that exhibits ensemble inequivalence. At zero temperature ($T = 0$), the microcanonical phase diagram matches that of the canonical ensemble. However, the two ensembles yield different phase diagrams at finite temperatures. This behavior contrasts with the conventional understanding in statistical mechanics of systems with short-range interactions, where thermodynamic properties are expected to align across different ensembles in the thermodynamic limit. We discuss the implications of these findings for synthetic quantum long-range platforms, such as atomic, molecular, and optical (AMO) systems.

cond-mat.stat-mech↗

arXiv2024

Full counting statistics of 1d short-range Riesz gases in confinement

We investigate the full counting statistics (FCS) of a harmonically confined 1d short-range Riesz gas consisting of $N$ particles in equilibrium at finite temperature. The particles interact with each other through a repulsive power-law interaction with an exponent $k>1$ which includes the Calogero-Moser model for $k=2$. We examine the probability distribution of the number of particles in a finite domain $[-W, W]$ called number distribution, denoted by $\mathcal{N}(W, N)$. We analyze the probability distribution of $\mathcal{N}(W, N)$ and show that it exhibits a large deviation form for large $N$ characterised by a speed $N^{\frac{3k+2}{k+2}}$ and by a large deviation function of the fraction $c = \mathcal{N}(W, N)/N$ of the particles inside the domain and $W$. We show that the density profiles that create the large deviations display interesting shape transitions as one varies $c$ and $W$. This is manifested by a third-order phase transition exhibited by the large deviation function that has discontinuous third derivatives. Monte-Carlo (MC) simulations show good agreement with our analytical expressions for the corresponding density profiles. We find that the typical fluctuations of $\mathcal{N}(W, N)$, obtained from our field theoretic calculations are Gaussian distributed with a variance that scales as $N^{\nu_k}$, with $\nu_k = (2-k)/(2+k)$. We also present some numerical findings on the mean and the variance. Furthermore, we adapt our formalism to study the index distribution (where the domain is semi-infinite $(-\infty, W])$, linear statistics (the variance), thermodynamic pressure and bulk modulus.

cond-mat.stat-mech↗

arXiv2024

Ensemble inequivalence in long-range quantum systems

Ensemble inequivalence, i.e. the possibility of observing different thermodynamic properties depending on the statistical ensemble which describes the system, is one of the hallmarks of long-range physics, which has been demonstrated in numerous classical systems. Here, an example of ensemble inequivalence of a long-range quantum ferromagnet is presented. While the $T=0$ microcanonical quantum phase-diagram coincides with that of the canonical ensemble, the phase-diagrams of the two ensembles are different at finite temperature. This is in contrast with the common lore of statistical mechanics of systems with short-range interactions where thermodynamic properties are bound to coincide for macroscopic systems described by different ensembles. The consequences of these findings in the context of atomic, molecular and optical (AMO) setups are delineated.

cond-mat.stat-mech↗

arXiv2023

Metastability of Discrete-Symmetry Flocks

We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of the ordered phase nucleate and grow. We characterize analytically this self-similar growth and demonstrate that droplets spread ballistically in all directions. Our results imply that, in the thermodynamic limit, discrete-symmetry flocks -- and, by extension, continuous-symmetry flocks with rotational anisotropy -- are metastable in all dimensions.

cond-mat.soft↗

arXiv2023

Mixed Order Phase Transitions

Mixed order phase transitions are transitions which have common features with both first order and second order transitions. I review some results obtained in the context of one of the prototypical models of mixed order transitions, the one-dimensional Ising model with long-range coupling that decays as truncated inverse square distance between spins. The correspondence between this model and the Poland Scheraga model of DNA denaturation, a subject to which Michael Fisher made substantial contribution, is then outlined.

cond-mat.stat-mech↗

arXiv2021

Edge fluctuations and third-order phase transition in harmonically confined long-range systems

We study the distribution of the position of the rightmost particle $x_{\max}$ in a $N$-particle Riesz gas in one dimension confined in a harmonic trap. The particles interact via long-range repulsive potential, of the form $r^{-k}$ with $-2 -2$. We also find that these large deviation functions describe a pulled to pushed type phase transition as observed in Dyson's log-gas ($k\to 0$) and $1d$ one component plasma ($k=-1$). Remarkably, we find that the phase transition remains $3^{\rm rd}$ order for the entire regime. Our results demonstrate the striking universality of the $3^{\rm rd}$ order transition even in models that fall outside the paradigm of Coulomb systems and the random matrix theory. We numerically verify our analytical expressions of the large deviation functions via Monte Carlo simulation using an importance sampling algorithm.

cond-mat.stat-mech↗

arXiv2021

Long-range influence of a pump on a critical fluid

A pump coupled to a conserved density generates long-range modulations, resulting from the non-equilibrium nature of the dynamics. We study how these modulations are modified at the critical point where the system exhibits intrinsic long-range correlations. To do so, we consider a pump in a diffusive fluid, which is known to generate a density profile in the form of an electric dipole potential and a current in the form of a dipolar field above the critical point. We demonstrate that while the current retains its form at the critical point, the density profile changes drastically. At criticality, in $d<4$ dimensions, the deviation of the density from the average is given by ${\rm sgn}(\cos(\theta))|\cos({\theta})/r^{(d-1)}|^{1/\delta}$ at large distance $r$ from the pump and angle $\theta$ with respect to the pump's orientation. At short distances, there is a crossover to a $\cos({\theta})/r^{d-3+\eta}$ profile. Here $\delta$ and $\eta$ are Ising critical exponents. The effect of the local pump on the domain wall structure below the critical point is also considered.

cond-mat.stat-mech↗

arXiv2021

Harmonically confined long-ranged interacting gas in the presence of a hard wall

In this paper, we compute exactly the average density of a harmonically confined Riesz gas of $N$ particles for large $N$ in the presence of a hard wall. In this Riesz gas, the particles repel each other via a pairwise interaction that behaves as $|x_i - x_j|^{-k}$ for $k>-2$, with $x_i$ denoting the position of the $i^{\rm th}$ particle. This density can be classified into three different regimes of $k$. For $k \geq 1$, where the interactions are effectively short-ranged, the appropriately scaled density has a finite support over $[-l_k(w),w]$ where $w$ is the scaled position of the wall. While the density vanishes at the left edge of the support, it approaches a nonzero constant at the right edge $w$. For $-1<k<1$, where the interactions are weakly long-ranged, we find that the scaled density is again supported over $[-l_k(w),w]$. While it still vanishes at the left edge of the support, it diverges at the right edge $w$ algebraically with an exponent $(k-1)/2$. For $-2<k< -1$, the interactions are strongly long-ranged that leads to a rather exotic density profile with an extended bulk part and a delta-peak at the wall, separated by a hole in between. Exactly at $k=-1$ the hole disappears. For $-2<k< -1$, we find an interesting first-order phase transition when the scaled position of the wall decreases through a critical value $w=w^*(k)$. For $w<w^*(k)$, the density is a pure delta-peak located at the wall. The amplitude of the delta-peak plays the role of an order parameter which jumps to the value $1$ as $w$ is decreased through $w^*(k)$. Our analytical results are in very good agreement with our Monte-Carlo simulations.

cond-mat.stat-mech↗

arXiv2020

Attraction and condensation of driven tracers in a narrow channel

Emergent bath-mediated attraction and condensation arise when multiple particles are simultaneously driven through an equilibrated bath under geometric constraints. While such scenarios are observed in a variety of non-equilibrium phenomena, with an abundance of experimental and numerical evidence, little quantitative understanding of how these interactions arise is currently available. Here we approach the problem by studying the behavior of two driven "tracer" particles, propagating through a bath in a 1D lattice with excluded-volume interactions. We analytically explore the mechanism responsible for the tracers' emergent interactions and compute the resulting effective attractive potential. This mechanism is then numerically shown to extend to a realistic model of hard driven Brownian discs confined to a narrow 2D channel.

cond-mat.stat-mech↗

arXiv2020

Driven tracer dynamics in a one dimensional quiescent bath

The dynamics of a driven tracer in a quiescent bath subject to geometric confinement effectively models a broad range of phenomena. We explore this dynamics in a 1D lattice model where geometric confinement is tuned by varying particle overtaking rates. Previous studies of the model's stationary properties on a ring of $L$ sites have revealed a phase in which the bath density profile extends over an $\sim \mathcal{O}(L)$ distance from the tracer and the tracer's velocity vanishes as $\sim 1/L$. Here, we study the model's dynamics in this phase as $L\rightarrow \infty$ and for long times. We show that the bath density profile evolves on a $\sim \sqrt{t}$ time-scale and, correspondingly, that the tracer's velocity decays as $\sim 1/\sqrt{t}$. Unlike the well-studied non-driven tracer, whose dynamics becomes diffusive whenever overtaking is allowed, we here find that driving the tracer preserves its hallmark sub-diffusive single-file dynamics, even in the presence of overtaking.

cond-mat.stat-mech↗

arXiv2019

Phase transition in a 1d driven tracer model

The effect of particle overtaking on transport in a narrow channel is studied using a 1d model of a driven tracer in a quiescent bath. In contrast with the well-studied non-driven case, where the tracer's long-time dynamics changes from sub-diffusive to diffusive whenever overtaking is allowed, the driven tracer is shown to exhibit a phase transition at a finite overtaking rate. The transition separates a phase in which the stationary bath density profile, as seen in the tracer's frame, is extended, as in the non-overtaking case, to a phase with a localized bath density profile. In the extended phase the tracer velocity vanishes in the thermodynamic limit while it remains finite in the localized phase. The phase diagram of the model, as well as the tracer velocity and the bath density profile in both phases, are studied, demonstrating their distinct features.

cond-mat.stat-mech↗

arXiv2019

Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth order critical point

The canonical phase diagram of the Blume-Emery-Griffiths (BEG) model with infinite-range interactions is known to exhibit a fourth order critical point at some negative value of the bi-quadratic interaction $K<0$. Here we study the microcanonical phase diagram of this model for $K<0$, extending previous studies which were restricted to positive $K$. A fourth order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth order critical point is studied in detail revealing some distinct features from the canonical counterpart.

cond-mat.stat-mech↗

arXiv2019

Harmonically confined particles with long-range repulsive interactions

We study an interacting system of $N$ classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law $\propto \sum_{\substack{i\neq j}}^N|x_i-x_j|^{-k}$ (with $k>-2$) of their mutual distance. This is a generalization of the well known cases of the one component plasma ($k=-1$), Dyson's log-gas ($k\to 0^+$), and the Calogero-Moser model ($k=2$). Due to the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all $k>-2$. We compute exactly the average density profile for large $N$ for all $k>-2$ and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on $k$ with distinct behavior for $-2 1$ and $k=1$.

cond-mat.stat-mech↗

arXiv2019

Fluctuation-dominated phase ordering at a mixed order transition

Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.

cond-mat.stat-mech↗

arXiv2018

Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas

A recently developed non-linear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model. We show that in this model the energy current scales anomalously with system size $L$ as $\sim L^{-2/3}$ in the leading order with a diffusive correction of order $\sim L^{-1}$. The crossover length $\ell_{c}$ from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.

cond-mat.stat-mech↗

arXiv2016

Exact extreme value statistics at mixed order transitions

We study extreme value statistics (EVS) for spatially extended models exhibiting mixed order phase transitions (MOT). These are phase transitions which exhibit features common to both first order (discontinuity of the order parameter) and second order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising (TIDSI) model which is a prototypical model exhibiting MOT, and study analytically the extreme value statistics of the domain lengths. The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size $L$. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length $l_{\max}$ converges, in the large $L$ limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of $l_{\max}$ are governed by novel distributions which we compute exactly. Our main analytical results are verified by numerical simulations.

cond-mat.stat-mech↗

arXiv2015

Interface localization in the 2D Ising model with a driven line

We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional biased Kawasaki dynamics in the central ring. Based on the exact solution of the two-dimensional Ising model, we are able to compute the phase diagram of the driven model within a special limit of fast drive and slow spin flips in the central ring. The model is found to exhibit two phases where the interface is pinned to the central ring: one in which it fluctuates symmetrically around the central ring and another where it fluctuates asymmetrically. In addition, we find a phase where the interface is centered in the bulk of the system, either below or above the central ring of the cylinder. In the latter case, the symmetry breaking is `stronger' than that found in equilibrium when considering a repulsive potential on the central ring. This equilibrium model is analyzed here by using a restricted solid-on-solid model.

cond-mat.stat-mech↗

arXiv2015

Condensation transition and drifting condensates in the accelerated exclusion process

Recently, it was shown that spatial correlations may have a drastic effect on the dynamics of real-space condensates in driven mass-transport systems: in models with a spatially correlated steady state, the condensate is quite generically found to drift with a non-vanishing velocity. Here we examine the condensate dynamics in the accelerate exclusion process (AEP), where spatial correlations are present. This model is a "facilitated" generalization of the totally asymmetric simple exclusion process (TASEP) where each hopping particle may trigger another hopping event. Within a mean-field approach that captures some of the effects of correlations, we calculate the phase diagram of the AEP, analyze the nature of the condensation transition, and show that the condensate drifts, albeit with a velocity that vanishes in the thermodynamic limit. Numerical simulations are consistent with the mean-field phase diagram.

cond-mat.stat-mech↗