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A new approach utilising the concept of ionic charge theory has been used to explain the inherent properties such as lattice thermal conductivity and bulk modulus of 3,5 and 2,6 semiconductors. The lattice thermal conductivity of these…
Geometrical methods are extensively applied to thermodynamics including stochastic thermodynamics. In the case of slow-driving linear response regime, a geometrical framework, known as thermodynamic geometry, is established. The key of this…
We address the question of existence of nonconstant stable stationary solution to the heat equation on a class of convex domains subject to nonlinear boundary flux involving a positive parameter. Such solutions which were known to exist in…
We consider convection in an internally heated layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled by a fixed heat flux. Using solely analytical methods, we…
We discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is…
We consider heat transport through systems with broken time-reversal symmetry. We apply strong magnetic fields to weakly charged particle systems, where the dynamics are dominated by the Lorentz force and spring forces. The standard…
This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the…
Within the emerging field of quantum thermodynamics the issues of heat transfer and heat rectification are basic ingredients for the understanding and design of heat engines or refrigerators at nanoscales. Here, a consistent and versatile…
This paper proves the local well posedness of differential equations in metric spaces under assumptions that allow to comprise several different applications. We consider below a system of balance laws with a dissipative non local source,…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
Consider the linear stochastic biharmonic heat equation on a $d$-dimensional torus ($d=1,2,3$), driven by a space-time white noise and with periodic boundary conditions: \begin{equation} \label{0} \left(\frac{\partial}{\partial…
The expressions for average densities of currents and charges induced by a weak electromagnetic field in spatially inhomogeneous systems are obtained. The case of finite temperatures is considered. It is shown that average values are…
To explore the nature of the metallic state near the transition to a Mott insulator we investigate the t-J model with random exchange interaction in d=infinity dimensions. A numerically exact solution is obtained by an extension of the…
The theory of the insulating state discriminates between insulators and metals by means of a localization tensor, which is finite in insulators and divergent in metals. In absence of time-reversal symmetry, this same tensor acquires an…
In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by F\"uhrer& Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven. In the present…
Collisional reservoirs are becoming a major tool for modelling open quantum systems. In their simplest implementation, an external agent switches on, for a given time, the interaction between the system and a specimen from the reservoir.…
We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an associated parameter-dependent elliptic PDE. The quality of the…
We study the polarization response to the temperature gradient in insulators, known as the thermopolarization effect. We show that this response can be understood through the free energy response function to an electric field gradient,…
The solution of Boltzmann equation for plasma in magnetic field, with arbitrarily degenerate electrons and non-degenerate nuclei, is obtained by Chapman-Enskog method. Functions, generalizing Sonin polynomials are used for obtaining an…
The thermal Hall conductivity $\kappa_{xy}$ and Hall conductivity $\sigma_{xy}$ in CeCoIn$_5$ are used to determine the Lorenz number ${\cal L}_H$ at low temperature $T$. This enables the separation of the observed thermal conductivity into…