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Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation…
We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the…
The problem of a spatially correlated noise affecting a complex system is studied in this paper. We present a comprehensive analysis of a 2D model polymer chain, driven by the spatially correlated Gaussian noise, for which we have varied…
This work is devoted to the study of relaxation--dissipation processes in systems described by Quantum Field Theory. In the first part, I focus on the phi^4 scalar quantum field theory in finite volume in the large N limit. I find that the…
We study the extremal process associated with the Discrete Gaussian Free Field on the square lattice and elucidate how the conformal symmetries manifest themselves in the scaling limit. Specifically, we prove that the joint process of…
We consider stochastic heat equations with fractional Laplacian on $\mathbb{R}^d$. Here, the driving noise is generalized Gaussian which is white in time but spatially homogenous and the spatial covariance is given by the Riesz kernels. We…
Mean-field systems provide a natural framework in which collective effects persist as the number of degrees of freedom N increases, raising fundamental questions about the emergence of integrability and the nature of chaos in large but…
We study the large scale behaviour of a population consisting of two types which evolve in dimension d = 1, 2 according to a spatial Lambda- Fleming-Viot process subject to random time-independent selection. If one of the two types is rare…
After a rapid increase in temperature across the deconfinement temperature $% T_{d}$, pure gauge theories exhibit unstable long wavelength fluctuations in the approach to equilibrium. This phenomenon is analogous to spinodal decomposition…
We propose a new Cahn-Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive…
We investigate the finite-size origin of the emission linewidth of a spatially-extended, one-dimensional non-equilibrium condensate. We show that the well-known Schawlow-Townes scaling of laser theory, possibly including the Henry…
We present an alternative derivation of the dynamical density functional theory for the one body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation elucidates further…
Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations…
The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their…
Molecular dynamics simulations were employed to investigate the phase separation process of a two-dimensional active Brownian dumbbell model. We evaluated the time dependence of the typical size of the dense component using the scaling…
A statistical theory of two-dimensional Laplacian growths is formulated from first-principles. First the area enclosed by the growing surface is mapped conformally to the interior of the unit circle, generating a set of dynamically evolving…
This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting system leads to complex patterns involving a separation into…
Universal features in the scalings of Shannon-R\'enyi entropies of many-body groundstates are studied for interacting spin-$\frac{1}{2}$ systems across (2+1) dimensional $O(3)$ critical points, using quantum Monte Carlo simulations on…
The gravitational evolution of scale free initial spectra $P(k)\propto k^n$ in an Einstein-de Sitter universe is widely believed to be self-similar for $-3<n<4$. However, for $-3<n<-1$ the existence of self-similar scaling has not been…
We study transport in a one-dimensional boundary-driven Anderson insulator (the XX spin chain with onsite disorder) with randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a…