Related papers: Approximate, analytic solutions of the Bethe equat…
We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical…
In our recent paper we gave an efficient algorithm to calculate "small" solutions of relative Thue equations (where "small" means an upper bound of type $10^{500}$ for the sizes of solutions). Here we apply this algorithm to calculating…
We give the exact solution of orbit dependent nuclear pairing problem between two non-degenerate energy levels using the Bethe ansatz technique. Our solution reduces to previously solved cases in the appropriate limits including…
Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic,…
Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expensive to compute. In this paper, we derive analytic…
The structure of the equation of state $\omega$ could be very complicate in nature while a few linear models have been successful in cosmological predictions. Linear models are treated as leading approximation of a complete Taylor series in…
We consider a general problem of inelastic collision of particles interacting with power-law potentials. Using quantum defect theory we derive an analytical formula for the energy-dependent complex scattering length, valid for arbitrary…
The charge reduction effect, produced by the nonlinear Debye screening of high-Z charges occuring in strongly-coupled plasmas, is investigated. An analytic asymptotic expression is obtained for the charge reduction factor which determines…
We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones…
We compute the Bethe equations of generalized Hubbard models, and study their thermodynamical limit. We argue how they can be connected to the ones found in the context of AdS/CFT correspondence, in particular with the so-called dressing…
We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sciences. The approximating particle system is a nonlocal…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
We discuss the dynamics of a charged nonrelativistic particle in electromagnetic field of a rotating magnetized celestial body. The equations of motion of the particle are obtained and some particular solutions are found. Effective…
A parameter method is introduced in order to estimate the relationship among the various variables of a system in equilibrium, where the potential energy functions are incompletely known or the quantum mechanical calculations very…
The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an…
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various…
Analytical forces have been derived in the Lagrangian framework for several random phase approximation (RPA) correlated total energy methods based on the range separated hybrid (RSH) approach, which combines a short-range density functional…
A simple procedure is presented to study the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically,…
The effective mass approximation is widely used across models of carrier transport, optical response, and excitons in semiconductors and insulators, but its validity hinges on the assumption that the band dispersion $E_n(\mathbf{k})$ at the…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…