相关论文: Exact Green's Function of the reversible diffusion…
Many physics problems have $J(x)=L(x)E(x)+h(x)$, source $h(x)$, fields $E$,$J$ satisfying differential constraints, symbolized by $E\in\cal E$,$J\in\cal J$ where $\cal E$,$\cal J$ are orthogonal spaces. If $L(x)$ takes values in certain…
The main problem in theoretical analysis of structures with strong confinement is the fact that standard mathematical tools: differential equations and Fourier's transformations are no longer applicable. In this paper we have demonstrated…
We investigate the full pair-distribution function of a homogeneous suspension of spherical active Brownian particles interacting by a Weeks-Chandler-Andersen potential in two spatial dimensions. The full pair-distribution function depends…
The total energy and electron addition and removal spectra can in principle be obtained exactly from the one-body Green's function. In practice, the Green's function is obtained from an approximate self-energy. In the framework of many-body…
Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice $\Z^d$ with random coefficients. It has previously been shown that if the random environment is translational invariant, then the averaged…
Spin distribution in the diffraction pattern of two-dimensional electron gas by a split gate and a quantum point contact is computed in the presence of the spin-orbit coupling. After diffracted, the component of spin perpendicular to the…
Jeffery's equation with diffusion is widely used to predict the motion of concentrated fiber suspensions in flows with low Reynold's numbers. Unfortunately, the evaluation of the fiber orientation distribution can require excessive…
A finite-time fluctuation theorem for the diffusion-influenced surface reaction A <=> B is investigated for spherical and Janus catalytic particles. The finite-time rates and thermodynamic force are analytically calculated by solving…
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact…
We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a third species $\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary…
A first principles approach, based on the real space multiple scattering Green's function method, is presented for spin- and angle-resolved resonant photoemission from magnetic surfaces. It is applied to the Fe(010) valence band…
We show that exact time dependent single particle Green function in the Imambekov-Glazman theory of nonlinear Luttinger liquids can be written, for any value of the Luttinger parameter, in terms of a particular solution of the Painlev\'e IV…
A simple exact-exchange density-functional method for a quasi-two-dimensional electron gas with variable density is presented. An analytical expression for the exact-exchange potential with only one occupied subband is provided, without…
We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.
We show that the exact solution of the Schr\"odinger equation for two electrons confined to two distinct concentric rings or spheres can be found in closed form for particular sets of the ring or sphere radii. In the case of two concentric…
In this work we study differential problems in which the reflection operator and the Hilbert transform are involved. We reduce these problems to ODEs in order to solve them. Also, we describe a general method for obtaining the Green's…
This paper provides a theoretical framework of deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and chemical reaction. Very general forms of the…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
The study of wave propagation and scattering in time-dependent materials is a rapidly growing field of research. Whereas for 1D applications there is a simple relation between the wave equations for space-dependent and time-dependent…
An analytical general analysis of the electromagnetic Dyadic Green's Function for two-dimensional sheet (or a very thin film) is presented, with an emphasis on on the case of graphene. A modified steepest descent treatment of the fields…