We present a family of many-body models which are exactly solvable analytically. The models are an extended n-body interaction Lipkin-Meshkov-Glick model which considers spin-flip terms which are associated with the interaction of an external classical field which coherently manipulates the state of the system in order to, for example, process quantum information. The models also describe a two-mode Bose-Einstein condensate with a Josephson-type interaction which includes n-particle elastic and inelastic collisions. One of the models corresponds to the canonical two-mode Bose-Einstein Hamitonian plus a term which we argue must be considered in the description of the two-mode condensate. Intriguingly, this extra term allows for an exact and analytical solution of the two-particle collision two-mode BEC problem. Our results open up an arena to study many-body system properties analytically.We present a family of many-body models which are exactly solvable analytically. The models are an extended n-body interaction Lipkin-Meshkov-Glick model which considers spin-flip terms which are associated with the interaction of an external classical field which coherently manipulates the state of the system in order to, for example, process quantum information. The models also describe a two-mode Bose-Einstein condensate with a Josephson-type interaction which includes n-particle elastic and inelastic collisions. One of the models corresponds to the canonical two-mode Bose-Einstein Hamitonian plus a term which we argue must be considered in the description of the two-mode condensate. Intriguingly, this extra term allows for an exact and analytical solution of the two-particle collision two-mode BEC problem. Our results open up an arena to study many-body system properties analytically.

arXiv:quant-ph/0607191Journal of Physics A Mathematical and TheoreticalJun 19, 20078 citations

Partial solvability induced by dark states in a box trap with decentered two-body interaction

Hossein Abedi, Nathan L. Harshman, Peter Schmelcher

We consider a generalization of the two-body contact interaction for nonrelativistic particles confined to a one-dimensional box, in which the interaction is decentered, i.e., the particles interact only when they are separated by a distance c. In contrast to the harmonically trapped system, this model is nonintegrable. Despite this, we demonstrate that the system exhibits partial solvability due to the presence of dark states, i.e., bosonic or fermionic states unaffected by the interaction. These states form exactly solvable subspaces embedded within an interacting spectrum. We characterize the stationary properties of the system, identify the conditions for the appearance of dark states, and show how they structure the spectrum and delineate interacting and noninteracting sectors.We consider a generalization of the two-body contact interaction for nonrelativistic particles confined to a one-dimensional box, in which the interaction is decentered, i.e., the particles interact only when they are separated by a distance c. In contrast to the harmonically trapped system, this model is nonintegrable. Despite this, we demonstrate that the system exhibits partial solvability due to the presence of dark states, i.e., bosonic or fermionic states unaffected by the interaction. These states form exactly solvable subspaces embedded within an interacting spectrum. We characterize the stationary properties of the system, identify the conditions for the appearance of dark states, and show how they structure the spectrum and delineate interacting and noninteracting sectors.

quant-pharXiv:2604.23507Journal of Physics A Mathematical and TheoreticalApr 28, 20260 citations

ASPECTS OF EXACTLY SOLVABLE PARTICLE SYSTEMS

van Diejen, Jan

Jan 1, 20050 citations

Spectral functions in an exactly solvable self-boundA-body system

Dimitri Van Neck, S. Rombouts, S. Verdonck

We consider an exactly solvable Hamiltonian for bosons in one-dimension interacting through zero-range attractive forces, and construct a complete basis of its A-particle eigenstates. The structure of the single-particle spectral function in the removal domain is investigated, by taking the overlap of the A-particle ground state with the various excited states of the $(A\ensuremath{-}1)$ system. In particular we study the contribution to the spectral function of the different break-up channels in the $A\ensuremath{-}1$ continuum, and compare the results to general statements available in the literature. It is shown that the asymptotic behavior in coordinate space does not agree with conventional assumptions. The relation to recent $(e,{e}^{'}p)$ experiments at large values of missing energy and momentum is pointed out.We consider an exactly solvable Hamiltonian for bosons in one-dimension interacting through zero-range attractive forces, and construct a complete basis of its A-particle eigenstates. The structure of the single-particle spectral function in the removal domain is investigated, by taking the overlap of the A-particle ground state with the various excited states of the $(A\ensuremath{-}1)$ system. In particular we study the contribution to the spectral function of the different break-up channels in the $A\ensuremath{-}1$ continuum, and compare the results to general statements available in the literature. It is shown that the asymptotic behavior in coordinate space does not agree with conventional assumptions. The relation to recent $(e,{e}^{'}p)$ experiments at large values of missing energy and momentum is pointed out.

Physical Review CNov 29, 20052 citations

Single-particle propagator in the many-body system

WORLD SCIENTIFIC eBooksMay 1, 20080 citations

(e,{e}^{'}p)

experiments at large values of missing energy and momentum is pointed out.