Publications

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Characteristic features of an active polar filament pushing a load

Prabhakar Maurya, Shalabh Kumar Anand, Sunil Pratap Singh

SciPost Phys. 18, 189 (2025) · published 16 June 2025 | · pdf

We present the structural and dynamical behavior of an active polar filament that is pushing a load using overdamped Langevin dynamics simulations. By varying the bending rigidity and the connectivity between the filament and the load, we smoothly transition the boundary condition of the filament from pivoted to clamped. In the clamped state, the load remains strongly aligned with the filament, whereas in the pivoted state, the load is free to rotate at its attachment point. Under the pivoted boundary condition, the active polar filament buckles and exhibits various fascinating dynamical phases, including snake-like motion, rotational motion, and helical conformations. However, under the clamped boundary condition, the helical phase disappears, and the filament attains either an extended or a bent conformation. The transition from the extended state to the helical phase is characterized using a global helical order parameter in the parameter space of active force and a physical quantity associated with the boundary condition. We have obtained various power laws relating the curvature radius of the helical phase, effective diffusivity, and rotational motion of the monomers to the active force. Furthermore, we demonstrate that the filament’s effective diffusivity in the helical phase exhibits a non-monotonic dependence on the active force: it initially increases linearly but decreases sharply at high active force strengths.
Sustaining a temperature difference

Matteo Polettini, Alberto Garilli

SciPost Phys. 9, 030 (2020) · published 2 September 2020 | · pdf

We derive an expression for the minimal rate of entropy that sustains two reservoirs at different temperatures $T_0$ and $T_\ell$. The law displays an intuitive $\ell^{-1}$ dependency on the relative distance and a characterisic $\log^2 (T_\ell/T_0)$ dependency on the boundary temperatures. First we give a back-of-envelope argument based on the Fourier Law (FL) of conduction, showing that the least-dissipation profile is exponential. Then we revisit a model of a chain of oscillators, each coupled to a heat reservoir. In the limit of large damping we reobtain the exponential and squared-log behaviors, providing a self-consistent derivation of the FL. For small damping "equipartition frustration" leads to a well-known balistic behaviour, whose incompatibility with the FL posed a long-time challenge.
On the breakdown of dimensional reduction and supersymmetry in random-field models

Gilles Tarjus, Matthieu Tissier, Ivan Balog

SciPost Phys. 19, 001 (2025) · published 1 July 2025 | · pdf

We discuss the breakdown of the Parisi-Sourlas supersymmetry (SUSY) and of the dimensional-reduction (DR) property in the random field Ising and O($N$) models as a function of space dimension $d$ and/or number of components $N$. The functional renormalization group (FRG) predicts that this takes place below a critical line $d_\mathrm{DR}(N)$. We revisit the perturbative FRG results for the RFO($N$)M in $d=4+\epsilon$ and carry out a more comprehensive investigation of the nonperturbative FRG approximation for the RFIM. In light of this FRG description, we discuss the perturbative results in $\epsilon=6-d$ recently derived for the RFIM by Kaviraj, Rychkov, and Trevisani. We stress in particular that the disappearance of the SUSY/DR fixed point below $d_\mathrm{DR}$ arises as a consequence of the nonlinearity of the FRG equations and cannot be found via the perturbative expansion in $\epsilon=6-d$ (nor in $1/N$). We also provide an error bar on the value of the critical dimension $d_\mathrm{DR}$ for the RFIM, which we find around $5.11±0.09$, by studying several successive orders of the nonperturbative FRG approximation scheme.
Collective dynamics of densely confined active polar disks with self- and mutual alignment

Weizhen Tang, Yating Zheng, Amir Shee, Guozheng Lin, Zhangang Han, Pawel Romanczuk, Cristián Huepe

SciPost Phys. 19, 012 (2025) · published 8 July 2025 | · pdf

We study the emerging collective states in a simple mechanical model of a dense group of self-propelled polar disks with off-centered rotation, confined within a circular arena. Each disk presents self-alignment towards the sum of contact forces acting on it, resulting from disk-substrate interactions, while also displaying mutual alignment with neighbors due to having its center of rotation located a distance $R$ behind its centroid, so that central contact forces can also introduce torques. The effect of both alignment mechanisms produces a variety of collective states that combine high-frequency localized circular oscillations with low-frequency milling around the center of the arena, in fluid or solid regimes. We consider cases with small/large $R$ values, isotropic/anisotropic disk-substrate damping, smooth/rough arena boundaries, different densities, and multiple systems sizes, showing that the emergent collective states that we identify are robust, generic, and potentially observable in real-world natural or artificial systems.
Gaussian approximation of dynamic cavity equations for linearly-coupled stochastic dynamics

Mattia Tarabolo, Luca Dall'Asta

SciPost Phys. 19, 019 (2025) · published 17 July 2025 | · pdf

Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and approximation techniques required to analyze these complex systems are still under development, posing significant technical challenges and resulting in a reliance on numerical simulations. We introduce a novel computational framework for investigating the dynamics of sparse disordered systems with continuous degrees of freedom. Starting with a graphical model representation of the dynamic partition function for a system of linearly-coupled stochastic differential equations, we use dynamic cavity equations on locally tree-like factor graphs to approximate the stochastic measure. Here, cavity marginals are identified with local functionals of single-site trajectories. Our primary approximation involves a second-order truncation of a small-coupling expansion, leading to a Gaussian form for the cavity marginals. For linear dynamics with additive noise, this method yields a closed set of causal integro-differential equations for cavity versions of one-time and two-time averages. These equations provide an exact dynamical description within the local tree-like approximation, retrieving classical results for the spectral density of sparse random matrices. Global constraints, non-linear forces, and state-dependent noise terms can be addressed using a self-consistent perturbative closure technique. The resulting equations resemble those of dynamical mean-field theory in the mode-coupling approximation used for fully-connected models. However, due to their cavity formulation, the present method can also be applied to ensembles of sparse random graphs and employed as a message-passing algorithm on specific graph instances.
Integrable fishnet circuits and Brownian solitons

Žiga Krajnik, Enej Ilievski, Tomaž Prosen, Benjamin J. A. Héry, Vincent Pasquier

SciPost Phys. 19, 027 (2025) · published 21 July 2025 | · pdf

We introduce classical many-body dynamics on a one-dimensional lattice comprising local two-body maps arranged on discrete space-time mesh that serve as discretizations of Hamiltonian dynamics with arbitrarily time-varying coupling constants. Time evolution is generated by passing an auxiliary degree of freedom along the lattice, resulting in a 'fishnet' circuit structure. We construct integrable circuits consisting of Yang-Baxter maps and demonstrate their general properties, using the Toda and anisotropic Landau-Lifschitz models as examples. Upon stochastically rescaling time, the dynamics is dominated by fluctuations and we observe solitons undergoing Brownian motion.
Nonequilibrium steady-state dynamics of Markov processes on graphs

Stefano Crotti, Thomas Barthel, Alfredo Braunstein

SciPost Phys. 19, 045 (2025) · published 18 August 2025 | · pdf

We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite matrix products. For homogeneous ensembles on regular graphs, the distribution is parametrized by a single $d× d× r^2$ tensor, where $r$ is the number of states per variable, and $d$ is the matrix-product bond dimension. While the method becomes exact in the large-$d$ limit, it typically provides highly accurate results even for small bond dimensions $d$. The $d^2r^2$ parameters are determined by solving a fixed point equation, for which we provide an efficient belief-propagation procedure. We apply this approach to a variety of models, including Ising-Glauber dynamics with symmetric and asymmetric couplings, as well as the SIS model. Even for small $d$, the results are compatible with Monte Carlo estimates and accurately reproduce known exact solutions. The method provides access to precise temporal correlations, which, in some regimes, would be virtually impossible to estimate by sampling.
Numerical aspects of large deviations

Alexander K. Hartmann

SciPost Phys. Lect. Notes 100 (2025) · published 30 September 2025 | · pdf

An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli process is used throughout the text. Next, Markov chain Monte Carlo (MCMC) simulations are introduced. In particular, the Metropolis-Hastings algorithm is explained. As first implementation of MCMC, sampling of the plain Bernoulli model is shown. Next, an exponential bias is used for the same model, which allows one to obtain the tails of the distribution of a measurable quantity. This approach is generalized to MCMC simulations, where the states are vectors of $U(0,1)$ random entries. This allows one to use the exponential or any other bias to access the large-deviation properties of rather arbitrary random processes. Finally, some recent research applications to study more complex models are discussed.
Lifted TASEP: Long-time dynamics, generalizations, and continuum limit

Fabian H. L. Essler, Jeanne Gipouloux, Werner Krauth

SciPost Phys. Core 8, 063 (2025) · published 2 October 2025 | · pdf

We investigate the lifted TASEP and its generalization, the GL-TASEP. We analyze the spectral properties of the transition matrix of the lifted TASEP using its Bethe ansatz solution, and use them to determine the scaling of the relaxation time (the inverse spectral gap) with particle number. The observed scaling with particle number was previously found to disagree with Monte Carlo simulations of the equilibrium autocorrelation times of the structure factor and of other large-scale density correlators for a particular value of the pullback $\alpha_{\rm crit}$. We explain this discrepancy. We then construct the continuum limit of the lifted TASEP, which remains integrable, and connect it to the event-chain Monte Carlo algorithm. The critical pullback $\alpha_{\rm crit}$ then equals the system pressure. We generalize the lifted TASEP to a large class of nearest-neighbour interactions, which lead to stationary states characterized by non-trivial Boltzmann distributions. By tuning the pullback parameter in the GL-TASEP to a particular value we can again achieve a polynomial speedup in the time required to converge to the steady state. We comment on the possible integrability of the GL-TASEP.
Boundary layers, transport and universal distribution in boundary driven active systems

Pritha Dolai, Arghya Das

SciPost Phys. 19, 088 (2025) · published 8 October 2025 | · pdf

We discuss analytical results for a run-and-tumble particle (RTP) in one dimension in presence of boundary reservoirs. It exhibits "kinetic boundary layers", nonmonotonous distribution, current without density gradient, diffusion facilitated current reversal and optimisation on tuning dynamical parameters, and a new transport effect in the steady state. The spatial and internal degrees of freedom together possess a symmetry, using which we find the eigenspectrum for large systems. The eigenvalues are arranged in two bands which can mix in certain conditions resulting in a crossover in the relaxation. The late time distribution for large systems is obtained analytically; it retains a strong and often dominant "active" contribution in the bulk rendering an effective passive-like description inadequate. A nontrivial "Milne length" also emerges in the dynamics. Finally, a novel universality is proposed in the absorbing boundary problem for dynamics with short-range colored noise. Active processes driven by active reservoirs may thus provide a common physical ground for diverse and new nonequilibrium phenomena.

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