Indo-French workshop on Classical and quantum dynamics in out of equilibrium systems

Recent experiments have implemented resetting by means of a time-varying external trap whereby trap stiffnesses are changed from an initial to a final value in finite-time. Such setups have also been studied in the context of Landauer's erasure principle. We analyse the thermodynamic costs of such a setup in steady state.

he emergence of surprising collective behaviors in systems driven out of equilibrium by local energy injection at the particle level remains a central theme in the study of active matter. Recently, chaotic flows reminiscent of turbulence have garnered significant attention due to their appearance in diverse biological and physical active matter systems. In this talk, I will demonstrate how even the simplest model of active particles -— self-propelled point particles -— can exhibit mesoscale flows, characterized by streams and vortices, when very persistent active forces compete with crowding at high densities.

In the second part, I will introduce a minimal model of non-reciprocal interactions inspired by human crowds, which generates collective flows strikingly similar to those of the self-propelled particles. Interestingly, as the system approaches the equilibrium limit by reducing non-reciprocity, it undergoes an absorbing phase transition characterized by an infinite number of absorbing states and critical exponents consistent with the conserved directed percolation universality class.

Of special interest in aggregation processes is the occurrence of extremely large clusters, or condensates, which hold a finite fraction of the mass. We find that condensates coexist with a power law distribution in the Takayasu model of aggregation with input, even though the mass is not conserved. While approaching steady state, mini-condensates form on a growing length scale. There is a single mobile condensate in steady state, and its movement leads to a dynamic re-organization of the landscape on a macroscopic scale, along with an emergent power law which differs from the usual Takayasu power. In an open system, the exit of the condensate from the edges leads to intermittent fluctuations of the total mass in steady state, quantified through a divergence of the scaled kurtosis.

[1] A. Das and M. Barma, Indian J. Phys., Special issue on Nonequilibrium Statistical Physics (2024)
https://link.springer.com/article/10.1007/s12648-023-03030-1
[2] R. Negi, R. Pereira and M. Barma, arXiv:2407.09827 , to appear, Phys. Rev. E (2024)

Consider two systems initially at different temperatures that are then quenched to the same final low temperature. The Mpemba effect is a counterintuitive phenomenon where the initially hotter system reaches equilibrium faster than the colder one. While initially observed in the freezing of water, the Mpemba effect is not limited to this scenario and can be explored in the relaxation dynamics of various systems, including those far from equilibrium, such as granular systems. In this presentation, I will provide a general overview of the Mpemba effect, and then focus on the effect in trapped colloidal particles, both active and inactive. Additionally, I will address the challenges in defining the Mpemba effect and explore potential underlying mechanisms.    

We show that heterogeneity in self-propulsion speed leads to the emergence of effective short-range repulsion among active particles coupled via strong attractive potentials. Taking the example of two harmonically coupled active Brownian particles, we analytically compute the stationary distribution of the distance between them in the strong coupling regime, i.e., where the coupling strength is much larger than the rotational diffusivity of the particles. The effective repulsion in this regime is manifest in the emergence of a minimum distance between the
particles, proportional to the difference in their self-propulsion speeds. Physically, this distance of the closest approach is associated to the orientations of the particles being parallel to each other. We show that the physical scenario remains qualitatively similar for any long-range coupling potential, which is attractive everywhere. Moreover, we show that, for a collection of N particles interacting via pairwise attractive potentials, a short-range repulsion emerges for each pair of particles with different self-propulsion speeds. Finally, we show that our results are robust and hold irrespective of the specific active dynamics of the particles.

Release of synaptic vesicles carrying neurotransmitters (also called “quantal content”), form the basis of electrochemical signal transmissions across all synapses. For 70 years, it has been known experimentally that the statistical distribution of each such individual release is a Binomial. Yet the size of the reservoir from which these vesicles get released, fluctuates. Hence the question of the actual distribution of quantal content averaged over these fluctuations, remained open. The problem is difficult due to history dependence -- we make progress by focusing on the steady state. Our work reveals that for fixed frequency electrical input stimulation, the statistically averaged distribution is still a Binomial — for this case, we compare our theory to experimental data from MNTB-LSO synapses of juvenile mice. On the other hand, for random input stimulations the averaged distribution is generically non-Binomial. Often under physiological conditions presynaptic input signals are random. So the exact results in our paper will hopefully help in analyzing experimental distributions in such cases, and make estimates of the model parameters associated with the concerned neuron.

We study a quantum spin chain where the dissipation is induced by the coupling of the density to local baths à la Caldeira and Leggett. In our perspective the bath acts as an annealed disorder with slow dynamics and can induce ordering in the system. At sufficiently strong coupling and zero temperature, it leads in fact to a phase transition between a Luttinger liquid phase and a spin density wave. The nature of the dissipative phase depends on the properties of both the system and the bath and in the incommensurate case it occurs in absence of the opening of a gap but it is due to fractional excitations. We also show, by computing the DC conductivity, that the system is insulating in the presence of a subohmic bath. We interpret this phenomenon as localization induced by the bath.

Many-body localization is a fascinating phenomenon observed in strongly disordered interacting quantum systems. In this talk, I will describe some of our recent works focusing on quantum coherence and single particle excitations across the MBL transition. I will discuss exact relations between various norms of coherence and measure of localization for any generic quantum system and discuss it for a standard model of MBL. Interestingly, though coherence of the full system vanishes in the MBL phase, subsystem coherence increases as the disorder strength increases which can have strong application potential in superconducting qubit arrays and other quantum devices where controlling coherence is a big challenge. On a completely different note, I will discuss single-particle excitations across the MBL transition in systems with random and quasiperiodic potentials and demonstrate that they belong to two different universality classes.

We study the exact fluctuating hydrodynamics of the scaled Light-Heavy model (sLH), in which two species of particles (light and heavy) interact with a fluctuating surface. This model is similar in definition to the unscaled Light-Heavy model (uLH), except it uses rates scaled with the system size. The consequence, it turns out, is a phase diagram that differs from that of the unscaled model. We derive the fluctuating hydrodynamics for this model using an action formalism involving the construction of path integrals for the probability of different states that give the complete macroscopic picture starting from the microscopic one. This is then used to obtain a form for the two-point static correlation between fluctuations in density fields in the homogeneous phase in the steady state. We find that these theoretical results match well with microscopic simulations away from the critical line.

In the hydrodynamic theory, the non-equilibrium dynamics of a many-body system is approximated, at large scales of space and time, by irreversible relaxation to local entropy maximisation. This results in a convective equation corrected by viscous or diffusive terms in a gradient expansion, such as the Navier-Stokes equations. Diffusive terms are evaluated using the Kubo formula, and possibly arising from an emergent noise due to discarded microscopic degrees of freedom. In one dimension of space, diffusive scaling is often broken as noise leads to super-diffusion. But in linearly degenerate hydrodynamics, such as that of integrable models, diffusive behaviors are observed, and it has long be thought that the standard diffusive picture remains valid. In this letter, we show that in such systems, the Navier-Stokes equation breaks down beyond linear response. We demonstrate that diffusive-order corrections do not take the form of a gradient expansion. Instead, they are completely determined by ballistic transport of initial-state fluctuations, and obtained from the non-local two-point correlations recently predicted by the ballistic macroscopic fluctuation theory (BMFT); the resulting hydrodynamic equations are reversible. To do so, we establish a regularised fluctuation theory, putting on a firm basis the recent idea that ballistic transport of initial-state fluctuations determines fluctuations and correlations beyond the Euler scale. This extends the idea of ``diffusion from convection'' previously developed to explain the Kubo formula in integrable systems, to generic non-equilibrium settings.