Related papers: Trapping neutral fermions with kink-like potential…
We discuss excited Bose-condensed states and find the criterion of dynamical stability of a kink-wise state, i.e., a standing matter wave with one nodal plane perpendicular to the axis of a cylindrical trap. The dynamical stability requires…
We compute a nonperturbative effective potential between two static fermions in light-front Yukawa theory as a Hamiltonian eigenvalue problem. Fermion pair production is suppressed, to make possible an exact analytic solution in the form of…
Twisted kinks in the massless NJL$_2$ model interpolate between two distinct vacua on the chiral circle. If one approaches the chiral limit from finite bare fermion masses $m_0$, the vacuum is unique and twist cannot exist. This issue is…
In this paper, we study the following Kirchhoff type problem:% $$ \left\{\aligned&-\bigg(\alpha\int_{\bbr^3}|\nabla u|^2dx+1\bigg)\Delta u+(\lambda a(x)+a_0)u=|u|^{p-2}u&\text{ in }\bbr^3,\\%…
This manuscript is the first of a series of two papers that study the problem of elasticity and stability of the collision of two kinks with low speed $v$ for the nonlinear wave equation known as the $\phi^{6}$ model in dimension $1+1$. In…
We study an integrable quantum field theory of a single stable particle with an infinite number of resonance states. The exact $S$--matrix of the model is expressed in terms of Jacobian elliptic functions which encode the resonance poles…
A Luttinger Liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a…
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…
Two-dimensional scalar field theories with spontaneous symmetry breaking subject to the action of Jackiw-Teitelboim gravity are studied. Solutions for the $\phi^4$ and sine-Gordon self-gravitating kinks are presented, both for general…
An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy…
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…
We explore a new variational principle for studying one-dimensional quantum systems in a trapping potential. We focus on the Fermi polaron problem, where a single distinguishable impurity interacts through a contact potential with a…
We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework,…
We investigate the semiclassical regularity of thermal equilibria in the presence of a harmonic potential at low temperature; that is, we obtain the asymptotic behavior of the Schatten norms of commutators of the one-body operators…
This paper investigates a particular type of wormhole. The wormhole solutions studied are obtained by sewing together two static, spherically symmetric, charged black-hole metrics at their horizons. The charged wormholes are in a background…
We describe the asymptotic behavior of small energy solutions of an NLS with a trapping potential. In particular we generalize work of Soffer and Weinstein, and of Tsai et. al. The novelty is that we allow generic spectra associated to the…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…
We derive norm bounds that imply the convergence of perturbation theory in fermionic quantum field theory if the propagator is summable and has a finite Gram constant. These bounds are sufficient for an application in renormalization group…
We rigorously solve the time-independent Schr\"odinger equation for the Rosen-Morse type potential. By using the Nikiforov-Uvarov method, we obtain, in a systematic way, the complete solution of such equation, which includes the so-called…