Related papers: Born-Oppenheimer Approximation for a Simple Renorm…
One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how…
We identify a general criterion for detecting entanglement of pure bipartite quantum states describing a system of two identical particles. Such a criterion is based both on the consideration of the Slater-Schmidt number of the fermionic…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
In this paper we are concerned with existence of positive solutions for a Schr\"odinger-Maxwell system with singular or strongly-singular terms. We overcome the difficulty given by the singular terms through an approximation scheme and…
We present a simple algorithm to switch between $N$-body time integrators in a reversible way. We apply it to planetary systems undergoing arbitrarily close encounters and highly eccentric orbits, but the potential applications are broader.…
We use Wilsons weak coupling ``momentum'' shell renormalization group method to show that two-particle interaction terms commonly neglected in bosonization of one-dimensional correlated electron systems with open boundaries are indeed…
To describe the interactions in magnetically soft particle systems either numerical full-field methods or dipole models are used. Whereas the former are computationally challenging, simple dipole interactions are largely underestimating the…
The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which…
The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is reinvestigated within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we…
For a bi-partite quantum system defined in a finite dimensional Hilbert space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement operator, which is then shown to…
The motion of a system of particles under electromagnetic interaction is considered. Under the assumption that the force acting on an electric charge is given by the sum of the electromagnetic fields produced by any other charged particles…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
This article describes a normal form algorithm for the Brieskorn lattice of an isolated hypersurface singularity. It is the basis of efficient algorithms to compute the Bernstein-Sato polynomial, the complex monodromy, and Hodge-theoretic…
We consider systems of interacting bosons confined to one-dimensional harmonic traps. In the limit of perturbatively weak two-body interactions the system exhibits several universal states that are exact solutions for a large class of…
We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
We study a heavy-heavy-light three-body system confined to one space dimension. Both binding energies and corresponding wave functions are obtained for (i) the zero-range, and (ii) two finite-range attractive heavy-light interaction…
Prior to recombination photons, electrons, and atomic nuclei rapidly scattered and behaved, almost, like a single tightly-coupled photon-baryon plasma. We investigate here the accuracy of the tight-coupling approximation commonly used to…
The exact solution of the Schr\"odinger equation for the one-dimensional system of interacting particles with the linear dispersion law in an arbitrary external field is found. The solution is reduced to two groups of particles moving with…
In this paper we discuss a master equation applied to the two level system of an atom and derive an exact solution to it in an abstract manner. We also present a problem and a conjecture based on the three level system. Our results may give…