Related papers: Exactly solvable Richardson-Gaudin models for many…
The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows for its eigenstates to be constructed algebraically. In this work we show that quantum…
Three families of exact solutions for 2-dimensional gravity minimally coupled to electrodynamics are obtained in the context of ${\cal R}=T$ theory. It is shown, by supersymmetric formalism of quantum mechanics, that the quantum dynamics of…
The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.
We introduce an exactly solvable model for interacting bosons that extend up to high spin and interact through a repulsive pairing force. The model exhibits a phase transition to a state with almost complete $sd$ dominance. The repulsive…
We have found the elementary excitations of the exactly solvable BCS model for a fixed number of particles. These turn out to have a peculiar dispersion relation, some of them with no counterpart in the Bogoliubov picture, and unusual…
We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from the non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to the well-known symmetric exclusion…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occur in a pairwise fashion. It is also…
Bogomol'nyi-Prasad-Sommerfield solitons in models with spontaneously broken gauge symmetry have been intensively studied at infinite gauge coupling limit, where the governing equation -- so-called master equation -- is exactly solvable.…
We construct a class of exactly solvable generalized Kitaev spin-$1/2$ models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An…
We construct a new class of quasi-exactly solvable many-body Hamiltonians in arbitrary dimensions, whose ground states can have any correlations we choose. Some of the known correlations in one dimension and some recent novel correlations…
A model for the coherent output coupler of the Bose-Einstein condensed atoms from a trap in the recent MIT experiment (Phys. Rev. Lett., 78 (1997) 582) is established with a simple many-boson system of two states with linear coupling. Its…
We determine the exact asymptotic many-body wavefunction of a spin-$s$ Richardson-Gaudin model with a coupling inversely proportional to time, for time evolution starting from the ground state at $t = 0^+$ and for arbitrary $s$. Contrary to…
We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known…
Spin-boson Hamiltonians are an effective description for numerous quantum many-body systems such as atoms coupled to cavity modes, quantum electrodynamics in circuits and trapped ion systems. While reaching the limit of strong coupling is…
Some results for two distinct but complementary exactly solvable algebraic models for pairing in atomic nuclei are presented: 1) binding energy predictions for isotopic chains of nuclei based on an extended pairing model that includes…
Background: The reduced, level-independent, Bardeen-Cooper-Schrieffer Hamiltonian is exactly diagonalizable by means of a Bethe Ansatz wavefunction, provided the free variables in the Ansatz are the solutions of the set of Richardson-Gaudin…
We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum…
We establish quantum and classical exact solvability for two large classes of maximally superintegrable Benenti systems in $n$ dimensions with arbitrarily large $n$. Namely, we solve the Hamilton--Jacobi and Schr\"odinger equations for the…
There has been increasing interest in studying the Richardson model from which one can derive the exact solution for certain pairing Hamiltonians. However, it is still a numerical challenge to solve the nonlinear equations involved. In this…