Related papers: Invariant Gibbs dynamics for the dynamical sine-Go…
We extend D. Burguet's construction of SRB measures for the non invertible scenario obtaining hyperbolic invariant measures with absolutely continuous disintegrations on stable manifolds for a certain class of endomorphisms on the two…
We study Gibbs measures on the $d$-dimensional torus with $L^2$-(super)critical focusing interaction potentials. We establish a precise divergence rate of the partition function as we remove regularization, where the optimal constant is…
We investigate gauge invariance against phase space shifting in nonequilibrium systems, as represented by time-dependent many-body Hamiltonians that drive an initial ensemble out of thermal equilibrium. The theory gives rise to gauge…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
It is proposed that asymptotically nonfree gauge theories are consistently interpreted as theories of composite gauge bosons. It is argued that when hidden local symmetry is introduced, masslessness and coupling universality of dynamically…
We study single-site stochastic and deterministic transforma- tions of one-dimensional Gibbs measures in the uniqueness regime with infinite-range interactions. We prove conservation of Gibbsianness and give quantitative estimates on the…
We present accurate simulations of the dynamical bar-mode instability in full General Relativity focussing on two aspects which have not been investigated in detail in the past. Namely, on the persistence of the bar deformation once the…
In this paper, we study the long-time dynamics and stability properties of the sine-Gordon equation $$f_{tt}-f_{xx}+\sin f=0.$$ Firstly, we use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics…
We propose and investigate the modified Born$-$Infeld-type gravity model with the function $F(R) = [1-(1-\beta R/\sigma)^\sigma]/\beta$. At different values of the dimensionless parameter $\sigma$ the action is converted into some models…
We consider the one dimensional cubic nonlinear Schr{\"o}dinger equation with trapping potential behaving like |x| s (s > 1) at infinity. We construct Gibbs measures associated to the equation and prove that the Cauchy problem is globally…
We propose a noncommutative (NC) version for a global O(2) scalar field theory, whose damping feature is introduced into the scalar field theory through the NC parameter. In this context, we investigate how noncommutative drives spontaneous…
Our monograph presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Our work unifies and extends a long list of results by many authors. We make it a point to avoid any…
When training a machine learning model with observational data, it is often encountered that some values are systemically missing. Learning from the incomplete data in which the missingness depends on some covariates may lead to biased…
We formulate a strong-disorder renormalization-group (SDRG) approach to study the beta function of the tight-binding model in one dimension with both diagonal and off-diagonal disorder for states at the band center. We show that the SDRG…
In this article, a numerical simulation of two dimensional nonlinear sine-Gordon equation with Neumann boundary condition is obtained by using a composite scheme referred to as a modified cubic B spline differential quadrature method. The…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
We develop a stochastic analysis of the sine-Gordon Euclidean quantum field $(\cos (\beta \varphi))_2$ on the full space up to the second threshold, i.e. for $\beta^2 < 6 \pi$. The basis of our method is a forward-backward stochastic…
In this paper we construct an invariant probability measure concentrated on $H^2(K)\times H^1(K)$ for a general cubic Klein-Gordon equation (including the case of the wave equation). Here $K$ represents both the $3$-dimensional torus or a…
For SFTs, any equilibrium measure is Gibbs, as long a $f$ has $d$-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobru{\v{s}}in states that for strongly-irreducible subshifts, shift-invariant…
For $0<\beta<6\pi$, we prove that the distribution of the centred maximum of the $\epsilon$-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as $\epsilon \to 0$. Our…