Related papers: Quantitative low-temperature spectral asymptotics …
We study the correlation functions of quantum spin $1/2$ ladders at finite temperature, under a magnetic field, in the gapless phase at various relevant temperatures $T\neq 0$, momentum $q$ and frequencies $\omega$. We compute those…
We consider a model of heat conduction which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptotic behavior of the invariant measure. We show that, in this…
The temperature dependence of most solid-state properties is dominated by lattice vibrations, but metals display notable purely electronic effects at low temperature, such as the linear specific heat and the linear entropy, that were…
We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
We address diffusion processes in a bounded domain, while focusing on somewhat unexplored affinities between the presence of absorbing and/or inaccessible boundaries. For the Brownian motion (L\'{e}vy-stable cases are briefly mentioned)…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of…
We consider an explicitly solvable model (formulated in the Riemannian geometry terms) for a stationary wave process in a specific thin domain with the Dirichlet boundary conditions on the boundary of the domain. The transition from the…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval…
Bound-bound transitions can occur when localized atomic orbitals are thermally depleted, allowing excitations that would otherwise be forbidden at zero temperature. We predict signatures of bound-bound transitions in x-ray Thomson…
Accurately evaluating finite-temperature properties of quantum many-body systems remains a central challenge. Many existing quantum approaches typically require thermal-state preparation at each target temperature, making low-temperature…
We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two…
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…
We theoretically study Langevin systems with a tilted periodic potential. It has been known that the ratio $\Theta$ of the diffusion constant to the differential mobility is not equal to the temperature of the environment (multiplied by the…
We study a frequency-dependent damping model of hyper-diffusion within the generalized Langevin equation. The model allows for the colored noise defined by its spectral density, assumed to be proportional to $\omega^{\delta-1}$ at low…
The problem of characterizing low-temperature spin dynamics in antiferromagnetic spin chains has so far remained elusive. We reinvestigate it by focusing on isotropic antiferromagnetic chains whose low-energy effective field theory is…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
We obtained estimates for first eigenvalues of the Dirichlet boundary value problem for elliptic operators in divergence form (i.e. for the principal frequency of non-homogeneous membranes) in bounded domains $\Omega \subset \mathbb C$…