Related papers: The Critical 2d Stochastic Heat Flow

The purpose of this article is threefold. First, we introduce a new type of boundary condition for the multiplicative-noise stochastic heat equation on the half space. This is essentially a Dirichlet boundary condition but with a nontrivial…

We consider the energy super critical nonlinear Schr\"odinger equation $$i\pa_tu+\Delta u+u|u|^{p-1}=0$$ in large dimensions $d\geq 11$ with spherically symmetric data. For all $p>p(d)$ large enough, in particular in the super critical…

This paper concerns a long-range random walk in random environment in dimension $1+1$, where the environmental disorder is independent in space but has long-range correlations in time. We prove that two types of rescaled partition functions…

Two-dimensional (2D) turbulence, despite being an idealization of real flows, is of fundamental interest as a model of the spontaneous emergence of order from chaotic flows. The emergence of order often displays critical behavior, whose…

Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order…

We propose a scaling description of phase separation of polymer solutions. The scaling incorporates three universal limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the "ideal-gas" limit for…

Finite-size scaling is investigated in detail around the critical point in the heavy-quark region of nonzero temperature QCD. Numerical simulations are performed with large spatial volumes up to the aspect ratio $N_s/N_t=12$ at a fixed…

In stars and planets natural processes heat convective flows in the bulk of a convective region rather than at hard boundaries. By characterizing how convective dynamics are determined by the strength of an internal heating source we can…

We have used a toy model to study the behaviour of confined binary systems in 2$D$ and compare it with previously known result in 3$D$. In the case of 2$D$, in which canonical distribution exists only above a critical temperature, we…

The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the…

We consider the stochastic heat equation with multiplicative white noise: $\partial_t u =\partial_x^2u + b(u) +\sigma(u) \dot W$, both on $[0,1]$ and $\mathbf{R}$. In the case of $[0,1]$ we show that the finite Osgood criterion on $b$ is a…

For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic…

Using recent insights obtained in heavy fermion physics on the thermodynamic singularity structure associated with quantum phase transitions, we present here an experimental strategy to establish if the zero-temperature transition in the…

We consider a purely harmonic chain of oscillators which is perturbed by a stochastic noise. Under this perturbation, the system exhibits two conserved quantities: the volume and the energy. At the level of the hydrodynamic limit, under…

We consider a system of $d$ non-linear stochastic heat equations in spatial dimension $k \geq 1$, whose solution is an $\R^d$-valued random field $u= \{u(t\,,x),\, (t,x) \in \R_+ \times \R^k\}$. The $d$-dimensional driving noise is white in…

In this paper, we explore the Kibble-Zurek scaling of the conserved charge, using the stachastic diffusion dynamics. After determining the characteristic scales $\tau_{kz}$ and $l_{kz}$ and properly rescaling the traditional correlation…

This paper leads with a random polymer model in $\Z^2$ having long-range self-repulsive interactions. By comparison with a long range one-dimensional ferromagnetic Ising model we shown that the polymer models we considered here undergo a…

We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…

These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…

Consider anomalous energy spread in solid phases, i.e., $MSD= \int (x -{\langle x \rangle}_E)^2 \rho_E(x,t)dx \propto t^{\beta}$, as induced by a small initial excess energy perturbation distribution $\rho_{E}(x,t=0)$ away from equilibrium.…