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Ultracold atoms offer valuable opportunities where interparticle interactions can be controlled at will. In particular, by extinguishing the two-body interaction, one can realize unique systems governed by the three-body interaction, which…

Quantum Gases · Physics 2018-01-31 Yuta Sekino , Yusuke Nishida

When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…

Spectral Theory · Mathematics 2009-11-11 Amaury Mouchet

Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy…

Mathematical Physics · Physics 2009-10-05 Horng-Tzer Yau , Jun Yin

It is shown that at least one particle is bound in the $N$-particle semi-relativistic Pauli-Fierz model with negative potential $V(\bx)$. It is assumed that the particles have no spin and obey the Bose or Boltzmann statistics, and the one…

Mathematical Physics · Physics 2013-03-26 Itaru Sasaki

We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…

Mathematical Physics · Physics 2015-05-18 Natalie Gilka

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They…

Nuclear Theory · Physics 2009-11-07 D. Van Neck , Y. Dewulf , M. Waroquier

This Letter provides the solution to a yet unsolved basic problem of Solid State Physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50 year old…

Superconductivity · Physics 2011-11-28 Michel Crouzeix , Monique Combescot

The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic…

High Energy Physics - Phenomenology · Physics 2008-11-26 Wolfgang Lucha , Franz F. Schöberl

We show the convergence of the solutions to the massive nonlinear Klein-Gordon equation toward solutions to a relativistic Euler with potential type system in the semi-classical limit. In particular, the momentum and the density of…

Analysis of PDEs · Mathematics 2026-02-24 Tony Salvi

We consider systems of $N$ bosons in $\mathbb{R}^3$, trapped by an external potential. The interaction is repulsive and has a scattering length of the order $N^{-1}$ (Gross-Pitaevskii regime). We determine the ground state energy and the…

Mathematical Physics · Physics 2021-12-28 Christian Brennecke , Benjamin Schlein , Severin Schraven

By considering the Higgs mechanism in the framework of a parity-preserving Planar Quantum Electrodynamics, one shows that an attractive electron-electron interaction may come out. The e-e interaction potential emerges as the…

High Energy Physics - Theory · Physics 2012-08-27 H. Belich , O. M. Del Cima , M. M. Ferreira, , J. A. Helayel-Neto

The exact $q\bar{q}$ Bethe-Salpeter bound state amplitude is investigated in the space of relative energy $E$ for fixed value of relative position. By means of approximate analysis it is shown to possess singularities in $E$ whenever one of…

High Energy Physics - Theory · Physics 2015-06-19 Tomasz Radozycki

We derive the ground-state energy of $N$ composite bosons made of fermion pairs using the recently developed composite boson many-body formalism. We concentrate on the $N$-pair energy linear in density. We show that the scattering relevant…

Strongly Correlated Electrons · Physics 2015-06-15 Shiue-Yuan Shiau , Yia-Chung Chang , Monique Combescot

A sixth order quadrupole boson Hamiltonian is treated through a time dependent variational principle approach choosing as trial function a coherent state with respect to zeroth $b^{\dagger}_0$ and second $b^{\dagger}_2+b^{\dagger}_{-2}$…

Nuclear Theory · Physics 2009-11-11 F. D. Aaron , A. A. Raduta

We study two-body correlations for $N$ identical bosons by use of the hyperspherical adiabatic expansion method. We use the zero-range interaction and derive a transcendental equation determining the key ingredient of the hyperradial…

Other Condensed Matter · Physics 2015-06-24 T. Sogo , O. Sørensen , A. S. Jensen , D. V. Fedorov

The effective separable meson-baryon potentials are constructed to match the equivalent chiral amplitudes up to the second order in external meson momenta. We fit the model parameters (low energy constants) to the threshold and low energy…

Nuclear Theory · Physics 2010-10-07 A. Cieply , J. Smejkal

We consider a gas of bosons interacting through a three-body hard-core potential in the thermodynamic limit. We derive an upper bound on the ground state energy of the system at the leading order using a Jastrow factor. Our result matches…

Mathematical Physics · Physics 2024-06-14 Lukas Junge , François Louis Antoine Visconti

The last unsolved problem about the many-polaron system, in the Pekar-Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exactly 1 (the 'neutral case'). We prove that the ground state…

Mathematical Physics · Physics 2015-06-22 Rafael D. Benguria , Rupert L. Frank , Elliott H. Lieb

We consider systems of parabolic linear equations, subject to Neumann boundary conditions on bounded domains in $\mathbb{R}^d$, that are coupled by a matrix-valued potential $V$, and investigate under which conditions each solution to such…

Analysis of PDEs · Mathematics 2023-07-06 Alexander Dobrick , Jochen Glück

We consider the dynamics of N bosons in one dimension. We assume that the pair interaction is attractive and given by N^{\beta -1}V(N^{\beta}\cdot) where \int V\leqslant 0. We develop new techniques in treating the N-body Hamiltonian so…

Analysis of PDEs · Mathematics 2016-04-21 Xuwen Chen , Justin Holmer