Related papers: Single Particle Battery Model via universal transf…
Batteries are pivotal components in overcoming some of today's greatest technological challenges. Yet to date there is no self-consistent atomistic description of a complete battery. We take first steps toward modeling of a battery as a…
Particle physics has evolved a coherent model that characterizes forces and particles at the most elementary level. This Standard Model, built from many theoretical and experimental studies, is in excellent accord with almost all current…
It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling…
The standard continuum model of a lithium-ion battery, the Doyle-Fuller-Newman (DFN) model, is computationally expensive to solve. Typically simpler models, such as the single particle model (SPM), are used to provide insight for control…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…
A rigorous theory of diffraction scattering from extended objects is proposed. The present theory is based on a multiple asymptotic expansion of an integral equation for the exact wave function in terms of the large parameters of the…
Most of the textbooks explaining electric conductivity in the context of quantum mechanics provide either incomplete or semi-classical explanations that are not connected with the elementary concepts of quantum mechanics. We illustrate the…
We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one dimensional Bose gas and XXZ Heisenberg spin chain.
Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier.…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General…
Using a quantum electrodynamic framework, we calculate the off-resonant scattering of a broad-band X-ray pulse from a sample initially prepared in an arbitrary superposition of electronic states. The signal consists of single-particle…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion intercalation reactions. Using the recently developed Cahn-Hilliard reaction (CHR) theory, we investigate a simple…
All-solid-state batteries are seen as promising candidates to replace conventional batteries with liquid electrolytes in many applications. However, they are not yet feasible for many relevant applications. One particular question of…
The theory for electron transport in simple liquids developed by Cohen and Lekner is extended to simple liquid mixtures. The focus is on developing benchmark models for binary mixtures of hard-spheres, using the Percus-Yevick model to…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
We develop a new approach to electron transport in mesoscopic systems by using a particular single-particle basis. Although this basis generates redundant many-particle amplitudes, it greatly simplifies the treatment. By using our method…
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases,…
Standard X-ray crystallography methods use free-atom models to calculate mean unit cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a…