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Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a…

Statistical Mechanics · Physics 2023-01-18 Alessandro Campa , Lapo Casetti , Pierfrancesco Di Cintio , Ivan Latella , J. Miguel Rubi , Stefano Ruffo

We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and non-interacting spin wave approximations. It is based on an exact mapping of the constrained model to…

Quantum Gases · Physics 2010-08-24 S. Diehl , M. Baranov , A. J. Daley , P. Zoller

Even simplified models of quantum many-body systems can be difficult to analyse. However, taking inspiration from the foundations of physics, one may wonder whether there are practical advantages to constructing alternative beyond-quantum…

Quantum Physics · Physics 2026-05-01 Sahar Atallah , Peter Carrekmor , Michael Garn , Yukuan Tao , Shashank Virmani

Some properties of the periodic solution of the three-body problem where three particles of equal mass follow the same trajectory are discussed. This trajectory has the shape of a figure-8. The three particles have a constant separation in…

General Mathematics · Mathematics 2017-07-21 F. L. Janssens

We present a non-variational, kinetic energy operator approach to the solution of quantum three-body problem with Coulomb interactions, based on the utilization of symmetries intrinsic to the kinetic energy operator, i.e., the three-body…

Computational Physics · Physics 2015-06-26 Xuguang Chi , Wuyi Hsiang , Ping Sheng

The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…

Mathematical Physics · Physics 2007-05-23 A. V. Shchepetilov , I. E. Stepanova

The problem of three particles interacting through harmonic forces is discussed within the Newtonian formalism. By means of a didactic approach, an exact analytical solution is found, and ways to extend it to the N-body case are pointed…

Classical Physics · Physics 2007-05-23 Elysandra Figueredo , Antonio S. de Castro

We consider the problem of $n$ points with positive masses interacting pairwise with forces inversely proportional to the distance between them. In particular, it is the classical gravitational, Coulomb or photo-gravitational $n$-body…

Chaotic Dynamics · Physics 2025-04-25 Maria Przybylska , Andrzej J. Maciejewski

The dominantly orbital state method allows a semiclassical description of quantum systems. At the origin, it was developed for two-body relativistic systems. Here, the method is extended to treat two-body Hamiltonians and systems with three…

Quantum Physics · Physics 2013-06-07 Claude Semay , Fabien Buisseret

A higher-order dispersive equation is introduced as a candidate for the governing equation of a field theory. A new class of solutions of the three-dimensional field equation are considered, which are not localized functions in the sense of…

Pattern Formation and Solitons · Physics 2016-06-15 C. I. Christov

An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…

Mathematical Physics · Physics 2007-05-23 Abu Bakr Mehmood , S. Umer Abbas , Ghulam Shabbir

Within an adiabatic approximation to the three-body Coulomb system, we study the strength of the leading order conformaly invariant attractive dipole interaction produced when a slow charged particle $q_3$ (with mass $m_3$) is captured by…

Atomic Physics · Physics 2015-05-14 A. Delfino , T. Frederico , Lauro Tomio

We report analytic solutions of a recently discovered quasi-exactly solvable model consisting of two electrons, interacting {\em via} a Coulomb potential, but restricted to remain on the surface of a $\mathcal{D}$-dimensional sphere.…

Other Condensed Matter · Physics 2011-01-14 Pierre-François Loos , Peter M. W. Gill

We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the…

Quantum Gases · Physics 2026-02-24 Tran Duong Anh-Tai , Miguel A. García-March , Thomas Busch , Thomás Fogarty

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…

Exactly Solvable and Integrable Systems · Physics 2008-11-26 D. Gomez-Ullate , A. Gonzalez-Lopez , M. A. Rodriguez

We consider bound states of asymmetric three-body systems confined to two dimensions. In the universal regime, two energy ratios and two mass ratios provide complete knowledge of the three-body energy measured in units of one two-body…

Quantum Gases · Physics 2012-02-06 F. F. Bellotti , T. Frederico , M. T. Yamashita , D. V. Fedorov , A. S. Jensen , N. T. Zinner

We quantize the 1-dimensional 3-body problem with harmonic and inverse square pair potential by separating the Schr\"odinger equation following the classic work of Calogero, but allowing all possible self-adjoint boundary conditions for the…

Mathematical Physics · Physics 2009-11-10 L. Feher , I. Tsutsui , T. Fulop

We examine a system of three-bosons confined to two dimensions in the presence of a perpendicular magnetic field within the framework of the adiabatic hyperspherical method. For the case of zero-range, regularized pseudo-potential…

Atomic Physics · Physics 2016-01-20 Seth T. Rittenhouse , Andrew Wray , B. L. Johnson

Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…

Astrophysics · Physics 2007-05-23 Douglas C. Heggie

We study the existence of normalized ground states for the 3D dipolar Bose-Einstein condensate equation with attractive three-body interactions: \begin{align}\label{1} -\Delta u+\beta u+\lambda_1|u|^2 u+\lambda_2…

Analysis of PDEs · Mathematics 2022-02-22 Yongming Luo , Athanasios Stylianou