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On the basis of analytic solutions of Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential the equations for the bound one-active electron states are discussed. It is vary…
Being able to effectively locate saddle (and other fixed) points in dynamical systems holds tremendous implications in a number of applications in engineering and science, among which the study of rare events in molecular simulations stands…
We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting…
In the context of four-fermion and gauge interactions, the Schwinger-Dyson equation for the fermion self-energy function is studied with the Wilson fermion on a lattice. We find that the critical line obtained by Bardeen, Leung and Love is…
Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…
The description of fission remains a challenge for nuclear microscopic theories. The time-dependent Hartree-Fock approach with BCS pairing is applied to study the last stage of the fission process. A good agreement is found for the one-body…
At very high energies, weak coupling, non-perturbative methods can be used to study classical gluon production in nuclear collisions. One observes in numerical simulations that after an initial ``formation'' time, the produced partons are…
The modified Dirac-Pauli equations, which are introduced by means of ${\gamma_5}$-mass factorization of the ordinary Klein-Gordon operator, are considered. We also take into account the interaction of fermions with the intensive homogenous…
The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with $\delta$-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering…
We discuss the possible existence of new long-range forces mediated by spin-1 or spin-0 particles. By adding their effects to those of gravity, they could lead to apparent violations of the Equivalence Principle. While the vector part in…
A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…
We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a…
Saddle points play important roles as the transition states of activated process in gradient system driven by energy functional. However, for the same energy functional, the saddle points, as well as other stationary points, are different…
We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism…
The authors of Ref. \cite{1-2}, investigated cosmic evolution in an external interacting model of scalar tensor gravity namely Brans Dicke chameleon scenario. The procedure of this work contains novelties but, it shall be observed from this…
We apply a full-polaron master equation and a weak-coupling non-Markovian master equation to describe the steady-state time-averaged properties of a driven two-level system, an electron coherently tunneling between double quantum dots…
Context: The strong electric fields associated with magnetic reconnection in solar flares are a plausible mechanism to accelerate populations of high energy, non-thermal particles. One such reconnection scenario occurs at a 3D magnetic null…
In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an…
A comprehensive analysis of the exact unitary dynamics of two-component mass-imbalanced fermions in a one-dimensional double-well potential is accomplished by considering the total number of particles maximum up to six. The simultaneous…
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…