Talks

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.

In this talk I will discuss the potential of future high-resolution CMB observations to probe structure on sub-galactic scales. In particular, I will discuss how a CMB-HD experiment can measure lensing over the range 0.005 h/Mpc < k < 55 h/Mpc, spanning four orders of magnitude, with a total lensing signal-to-noise ratio from the temperature, polarization, and lensing power spectra greater than 1900. These lensing measurements would allow CMB-HD to distinguish between cold dark matter (CDM) and non-CDM models that can resolve apparent small-scale tensions with CDM. In addition, CMB-HD can distinguish between baryonic feedback effects and non-CDM models due to the different way each impacts the lensing signal. The kinetic Sunyaev-Zel’dovich power spectrum measured by CMB-HD further constrains non-CDM models that deviate from CDM. In sum, future CMB experiments will not only measure traditional cosmological parameters with unprecedented precision, but will also simultaneously constrain baryonic physics and dark matter properties that impact sub-galactic scales.

Consider a thermodynamic system that shows a phase transition between an ordered and a disordered phase. The question we ask is: in the parameter regime in which the system exhibits a disordered phase, can we induce order by manoeuvring the system (i) either by forcefully establishing order in a small subset of the total number of degrees of freedom,(ii) or, by shuffling the inherent properties of the individual system constituents among themselves ? Within the ambit of the Kuramoto model, a paradigmatic nonlinear dynamical many-body system, we discuss both analytical and experimental results on how schemes (i)
and (ii) lead to a rich dynamics and, most remarkably, establishing of macroscopic order even in parameter regimes in which the bare dynamics does not support any such ordering.

I will review the work done with my collaborators on intruders in single-file systems. In such systems, particles are on a one-dimensional line and cannot pass one another. This confinement induces an anomalous dynamics for any given tagged particle (subdiffusion or sub-ballistic motion). Focusing on lattice models (SEP), I will explain how to uncover the underlying structure behind this anomalous dynamics using two methods that we developed. At equilibrium we were able to solve for non-stationary density-displacement corrélations. And for out-of-equilibrium problems at high density, we show that everything is encoded in the random walk of a single vacancy.

A model for opinion formation is proposed where an individual's opinion is influenced by interactions with a group of agents. The model introduces a novel bias mechanism that favours one opinion. Several results are reported including the evidence of a critical slowing down as the bias vanishes.

I will present a few recent exact results about macroscopic fluctuations (large deviations) in non-equilibrium states. These include fluctuations in the non-equilibrium stationary state of systems coupled with unequal reservoirs, in the non-stationary state evolving towards equilibrium, and in active matter. Most of these results are based on fluctuating hydrodynamic descriptions. I will conclude by presenting an approach for this macroscopic description, starting from microscopic dynamics.

I will discuss the motion of a slow distinguishable particle (an impurity) in one-dimensional quantum liquids within a microscopic theory. The impurity experiences the friction force due to scattering off thermally excited quasiparticles. I will present detailed analysis of an arbitrarily strong impurity coupling constant in a wide range of temperatures and uncover new regimes of the impurity dynamics.

We shall discuss properties of quantum scars in a Rydberg ladder with staggered detuning. We shall demonstrate that they are qualitatively different from their counterparts in the well-known Rydberg chain and lead to long-time ETH violating imbalance in absence of disorder.