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Related papers: The three-body problem in dimension one: From shor…

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We present a new three dimensional many-body Hamiltonian with three-body and five-body interactions. We obtain the exact ground state as well as some excited states of this Hamiltonian for arbitrary number of particles. These exact…

Condensed Matter · Physics 2008-02-03 Pijush K. Ghosh

We briefly summarize the most relevant steps in the search of rigorous results about the properties of quantum systems made of three bosons interacting with zero-range forces. We also describe recent attempts to solve the unboundedness…

Mathematical Physics · Physics 2020-01-29 Rodolfo Figari , Alessandro Teta

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

Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…

Quantum Physics · Physics 2014-05-28 N. L. Harshman

We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large…

Strongly Correlated Electrons · Physics 2020-01-22 Arbel Haim , Richard Kueng , Gil Refael

We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…

Quantum Physics · Physics 2020-04-17 B. Silvestre-Brac , R. Bonnaz , C. Semay , F. Brau

For N impenetrable particles in one dimension where only the nearest and next-to-nearest neighbours interact, we obtain the complete spectrum both on a line and on a circle. Further, we establish a mapping between these N-body problems and…

Condensed Matter · Physics 2009-10-31 Sudhir R. Jain , Avinash Khare

We study the three-body problem in one dimension for both zero and finite range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all…

Quantum Physics · Physics 2009-11-13 N. P. Mehta , B. D. Esry , C. H. Greene

A simple class of unitary renormalization group transformations that force hamiltonians towards a band-diagonal form produce few-body interactions in which low- and high-energy states are decoupled, which can greatly simplify many-body…

Nuclear Theory · Physics 2008-11-26 S. K. Bogner , R. J. Furnstahl , R. J. Perry

We have investigated S-wave bound states composed of three identical bosons interacting via regulated delta function potentials in non-relativistic quantum mechanics. For low-energy systems, these short-range potentials serve as an…

Nuclear Theory · Physics 2007-05-23 R. F. Mohr

The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…

Quantum Gases · Physics 2011-10-04 F. F. Bellotti , T. Frederico , M. T. Yamashita , D. V. Fedorov , A. S. Jensen , N. T. Zinner

We study the self-adjoint Hamiltonian that models the quantum dynamics of a one-dimensional (1D) three-body system consisting of a light particle interacting with two heavy ones through a zero-range force. For an attractive interaction we…

Mathematical Physics · Physics 2026-05-20 Claudio Cacciapuoti , Andrea Posilicano , Hamidreza Saberbaghi

We study by quantum Monte Carlo simulations the low-temperature phase diagram of dipolar bosons confined to one dimension, with dipole moments aligned along the direction of particle motion. A hard core repulsive potential of varying range…

Statistical Mechanics · Physics 2020-02-12 Youssef Kora , Massimo Boninsegni

Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…

Quantum Physics · Physics 2011-04-12 Marco Frasca

In this paper we find the families of relative equilibria for the three body problem in the plane, when the interaction between the bodies is given by a quasi-homogeneous potential, which is the sum of two homogeneous functions. The number…

Dynamical Systems · Mathematics 2014-05-16 John A. Arredondo

Macro properties of cold atomic gases are driven by few-body correlations, even if the gas has thousands of particles. Quantum systems composed of two and three particles with attractive zero\=/range pairwise interactions are considered for…

Quantum Gases · Physics 2014-11-12 F. F. Bellotti

A brief excursion into the three-body problem in quantum mechanics is presented for graduate students or researchers in nuclear physics. Starting from single-particle coordinates, the three-body Schr\"{o}dinger equation is systematically…

Nuclear Theory · Physics 2026-02-17 Emile Meoto

In this paper we explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction…

Quantum Gases · Physics 2019-12-11 Jeff Maki , Carlos R. Ordóñez

We propose a new method to construct a four parameter family of quantum-mechanical point interactions in one dimension, which is known as all possible self-adjoint extensions of the symmetric operator $T=-\Delta \lceil C^{\infty}_{0}({\bf…

Quantum Physics · Physics 2007-05-23 T. Shigehara , H. Mizoguchi , T. Mishima , Taksu Cheon

We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishing suitable correpondences we…

Disordered Systems and Neural Networks · Physics 2009-10-30 Klaus Frahm , Axel Mueller-Groeling , Jean-Louis Pichard