Related papers: Homotopy perturbation method: when infinity equals…
It is shown that for the hopping regime, the thermopowers in both finite two-terminal and three-terminal systems are governed by the edges of the samples. This is due to the fact that the energy transfer between a transport electron and a…
In this proceedings we present a state-of-the-art method of calculating thermodynamic potential at finite temperature and finite chemical potential, using Hard Thermal Loop perturbation theory (HTLpt) up to next-to-next-leading-order…
We explain the essence of perturbation problems. The key to understanding is the structure of chain homotopy equivalence -- the standard one must be replaced by a finer notion which we call a strong chain homotopy equivalence. We prove an…
We calculate the zero-temperature gap and quasiparticle weight of the half-filled Hubbard model with a random dispersion relation. After extrapolation to the thermodynamic limit, we obtain reliable bounds on these quantities for the Hubbard…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H-Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum…
We discuss the interchangeability of the thermodynamic limit \beta \to \infty and the infinite limit of the Trotter number n \to \infty when Trotter formula e^{H_{0}+V} =\lim_{n \to \infty} (e^{H_{0}/n} e^{V/n}) is used to calculate…
We derive rigorous quantum mechanical bounds for the heat current through a nanojunction connecting two thermal baths at different temperatures. Based on exact sum rules, these bounds compliment the well-known quantum of thermal conductance…
We prove the Gallavotti-Cohen fluctuation theorem for a model of heat conduction through a chain of anharmonic oscillators coupled to two Hamiltonian reservoirs at different temperatures.
We prove holomorphic anomaly equations for $\mathbb{C}^5/\mathbb{Z}_5$.
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
We consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we derive solution representations as the limit of solutions of…
We prove R\'enyi entropic inequalities in a holographic setup based on the recent proposal for the holographic formula of R\'enyi entropies when the bulk is stable against any perturbation. Regarding the R\'enyi parameter as an inverse…
We study the existence of solutions for Darcy's problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The studied model allows thermal diffusion and viscosity…
Convection-diffusion of heat transfer is one of the important phenomena in fluid flow and industrial problems. The involved parameters, boundary conditions, and material properties are greatly affecting the same. As such, the uncertainness…
We present a fluctuation relation for heat dissipation in a nonequilibrium system. A nonequilibrium work is known to obey the fluctuation theorem in any time interval $t$. A heat, which differs from a work by an energy change, is shown to…
In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of…
Recently we developed a diagonal homotopy method to compute a numerical representation of all positive dimensional components in the intersection of two irreducible algebraic sets. In this paper, we rewrite this diagonal homotopy in…
A method for solving zero-finding problems is developed by tracking homotopy paths, which define connecting channels between an auxiliary problem and the objective problem. Current algorithms' success highly relies on empirical knowledge,…
Computing solutions to partial differential equations using the fast Fourier transform can lead to unwanted oscillatory behavior. Due to the periodic nature of the discrete Fourier transform, waves that leave the computational domain on one…