arXiv subjects

Soheli Mukherjee

Publications and source records attributed to Soheli Mukherjee.

8 recordsLinked to original sources

arXiv2025

Nonequilibrium steady state of Brownian motion in an intermittent potential

We calculate the steady state distribution $P_{\text{SSD}}(\boldsymbol{X})$ of the position of a Brownian particle under an intermittent confining potential that switches on and off with a constant rate $γ$. We assume the external potential $U(\boldsymbol{x})$ to be smooth and have a unique global minimum at $\boldsymbol{x} = \boldsymbol{x}_0$, and in dimension $d>1$ we additionally assume that $U(\boldsymbol{x})$ is central. We focus on the rapid-switching limit $γ\to \infty$. Typical fluctuations follow a Boltzmann distribution $P_{\text{SSD}}(\boldsymbol{X}) \sim e^{- U_{\text{eff}}(\boldsymbol{X}) / D}$, with an effective potential $U_{\text{eff}}(\boldsymbol{X}) = U(\boldsymbol{X})/2$, where $D$ is the diffusion coefficient. However, we also calculate the tails of $P_{\text{SSD}}(\boldsymbol{X})$ which behave very differently. In the far tails $|\boldsymbol{X}| \to \infty$, a universal behavior $P_{\text{SSD}}\left(\boldsymbol{X}\right)\sim e^{-\sqrt{γ/D} \, \left|\boldsymbol{X}-\boldsymbol{x}_{0}\right|}$ emerges, that is independent of the trapping potential. The mean first-passage time to reach position $\boldsymbol{X}$ is given, in the leading order, by $\sim 1/P_{\text{SSD}}(\boldsymbol{X})$. This coincides with the Arrhenius law (for the effective potential $U_{\text{eff}}$) for $\boldsymbol{X} \simeq \boldsymbol{x}_0$, but deviates from it elsewhere. We give explicit results for the harmonic potential. Finally, we extend our results to periodic one-dimensional systems. Here we find that in the limit of $γ\to \infty$ and $D \to 0$, the logarithm of $P_{\text{SSD}}(X)$ exhibits a singularity which we interpret as a first-order dynamical phase transition (DPT). This DPT occurs in absence of any external drift. We also calculate the nonzero probability current in the steady state that is a result of the nonequilibrium nature of the system.

cond-mat.stat-mech↗

arXiv2024

Large deviations in statistics of the local time and occupation time for a run and tumble particle

We investigate the statistics of the local time $\mathcal{T} = \int_0^T δ(x(t)) dt$ that a run and tumble particle (RTP) $x(t)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the number of times the RTP crosses the origin, we find that the local time distribution $P(\mathcal{T})$ satisfies the large deviation principle $P(\mathcal{T}) \sim \, e^{-T \, I(\mathcal{T} / T)} $ in the large observation time limit $T \to \infty$. Remarkably, we find that in presence of drift the rate function $I(ρ)$ is nonanalytic: We interpret its singularity as dynamical phase transitions of first order. We then extend these results by studying the statistics of the amount of time $\mathcal{R}$ that the RTP spends inside a finite interval (i.e., the occupation time), with qualitatively similar results. In particular, this yields the long-time decay rate of the probability $P(\mathcal{R} = T)$ that the particle does not exit the interval up to time $T$. We find that the conditional endpoint distribution exhibits an interesting change of behavior from unimodal to bimodal as a function of the size of the interval. To study the occupation time statistics, we extend the Donsker-Varadhan large-deviation formalism to the case of RTPs, for general dynamical observables and possibly in the presence of an external potential.

cond-mat.stat-mech↗

arXiv2024

Large deviations in statistics of the convex hull of passive and active particles: A theoretical study

We investigate analytically the distribution tails of the area A and perimeter L of a convex hull for different types of planar random walks. For N noninteracting Brownian motions of duration T we find that the large-L and A tails behave as $\mathcal{P}\left(L\right)\sim e^{-b_{N}L^{2}/DT}$ and $\mathcal{P}\left(A\right)\sim e^{-c_{N}A/DT}$, while the small-$L$ and $A$ tails behave as $\mathcal{P}\left(L\right)\sim e^{-d_{N}DT/L^{2}}$ and $\mathcal{P}\left(A\right)\sim e^{-e_{N}DT/A}$, where $D$ is the diffusion coefficient. We calculated all of the coefficients ($b_N, c_N, d_N, e_N$) exactly. Strikingly, we find that $b_N$ and $c_N$ are independent of N, for $N\geq 3$ and $N \geq 4$, respectively. We find that the large-L (A) tails are dominated by a single, most probable realization that attains the desired L (A). The left tails are dominated by the survival probability of the particles inside a circle of appropriate size. For active particles and at long times, we find that large-L and A tails are given by $\mathcal{P}\left(L\right)\sim e^{-TΨ_{N}^{\text{per}}\left(L/T\right)}$ and $\mathcal{P}\left(A\right)\sim e^{-TΨ_{N}^{\text{area}}\left(\sqrt{A}/T\right)}$ respectively. We calculate the large deviation functions $Ψ_N$ exactly and find that they exhibit multiple singularities. We interpret these as dynamical phase transitions of first order. We extended several of these results to dimensions $d>2$. Our analytic predictions display excellent agreement with existing results that were obtained from extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2023

Dynamical phase transition in the occupation fraction statistics for non-crossing Brownian particles

We consider a system of $N$ non-crossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we find that, for any general $N \geq 2$, the system undergoes $N-1$ dynamical phase transitions of second order. The $N-1$ transitions are the boundaries of $N$ phases that correspond to different numbers of particles which are in the vicinity of the interval throughout the dynamics. We achieve this by mapping the problem to that of finding the ground-state energy for $N$ noninteracting spinless fermions in a square-well potential. The phases correspond to different numbers of single-body bound states for the quantum problem. We also study the process conditioned on a given occupation fraction and the large-$N$ limiting behavior.

cond-mat.stat-mech↗

arXiv2023

Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets

Critical end points and tricritical points are multicritical points that separate lines of continuous transitions from lines of first order transitions in the phase diagram of many systems. In models like the spin-1 disordered Blume-Capel model and the repulsive Blume-Emery-Griffiths model, the tricritical point splits into a critical end point and a bicritical end point with an increase in disorder and repulsive coupling strength respectively. In order to make a distinction between these two multicritical points, we investigate and contrast the behaviour of the first order phase boundary and the co-existence diameter around them.

cond-mat.stat-mech↗

arXiv2022

Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields

We study the effect of different symmetric random field distributions: trimodal and Gaussian on the phase diagram of the infinite range Blume-Capel model. For the trimodal random field, the model has a very rich phase diagram. We find three new ordered phases, multicritical points like tricritical point (TCP), bicritical end point (BEP), critical end point (CEP) along with some multi-phase coexistence points. We also find re-entrance at low temperatures for some values of the parameters. On the other hand for the Gaussian distribution the phase diagram consists of a continuous line of transition followed by a first order transition line, meeting at a TCP. The TCP vanishes for higher strength of the random field. In contrast to the trimodal case, in Gaussian case no new phase emerges.

cond-mat.stat-mech↗

arXiv2021

Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph

For the repulsive Blume-Emery-Griffiths model the phase diagram in the space of three fields, temperature (T), crystal field ($Δ$), and magnetic field (H), is computed on a complete graph, in the canonical and microcanonical ensembles. For weak strength of the biquadratic interaction (K), there exists a tricritical point in the phase diagram where three critical lines meet. As K decreases below a threshold value(which is ensemble dependent), new multicritical points like the critical end point and bicritical end point arise in the (T,$Δ$) plane. For K>-1, we observe that the two critical lines in the H plane and the multicritical points are different in the two ensembles. At K=-1, the two critical lines in the H plane disappear and as K decreases further, there is no phase transition in the H plane. Exactly at K=-1 the two ensembles become equivalent. Beyond that for all K<-1, there are no multicritical points and there is no ensemble inequivalence in the phase diagram. We also study the transition lines in the H plane for positive K i.e. for attractive biquadratic interaction. We find that the transition lines in the H plane are not monotonic in temperature for large positive K.

cond-mat.stat-mech↗

arXiv2020

Emergence of a bicritical end point in the random crystal field Blume-Capel model

We obtain the phase diagram for the Blume-Capel model with bimodal distribution for random crystal fields, in the space of three fields: temperature, crystal field and magnetic field. We find that three critical lines meet at a tricritical point, but only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first order surface in the H=0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.

cond-mat.stat-mech↗