# A q-deformed completely integrable Bose gas model

@article{Bogoliubov1992AQC, title={A q-deformed completely integrable Bose gas model}, author={Nikolay Bogoliubov and R. K. Bullough}, journal={Journal of Physics A}, year={1992}, volume={25}, pages={4057-4071} }

The authors construct the Hamiltonian of a new quantum integrable 'q-boson' lattice model in 1+1 dimensions which has q-bosons as dynamical variables and solve it for its energy eigenstates and energy eigenvalues under periodic boundary conditions of finite period. This model can be regarded as the q-deformation of the integrable lattice Bose gas (the quantum lattice nonlinear Schrodinger (quantum lattice NLS)) model. In appropriate continuum limits both of these lattice models become the…

## 51 Citations

An integrable q-deformed model for bosons interacting with spin impurities

- Physics
- 1994

A composite quantum model on a lattice which describes the system of q-bosons interacting with Uq(su(2)) spin impurities is introduced and solved exactly under periodic boundary conditions. In one…

Quantum quenches and generalized Gibbs ensemble in a Bethe Ansatz solvable lattice model of interacting bosons

- Mathematics
- 2014

We consider quantum quenches in the so-called q-boson lattice model. We argue that the Generalized Eigenstate Thermalization Hypothesis holds in this model, therefore the Generalized Gibbs Ensemble…

Real-time dynamics in a strongly interacting bosonic hopping model: Global quenches and mapping to the XX chain

- Physics
- 2016

We study the time evolution of an integrable many-particle system, described by the q-boson Hamiltonian in the limit of strong bosonic interactions q→∞. It is shown that, for a particular class of…

Hidden order in bosonic gases confined in one-dimensional optical lattices

- Physics
- 2010

We analyze the effective Hamiltonian arising from a suitable power series expansion of the overlap integrals of Wannier functions for confined bosonic atoms in a one-dimensional (1D) optical lattice.…

Exact solution of a q-boson hopping model.

- PhysicsPhysical review. B, Condensed matter
- 1993

This work solves exactly, for any real q>1, including q=∞, a one-dimensional q-boson lattice «hopping model,» and calculates asymptotically its correlation functions and solves the equivalent quantum difference differential nonlinear Schrodinger model.

Solitons ofq-deformed quantum lattices and the quantum soliton

- Physics
- 2001

We use the classical N-soliton solution of a q-deformed lattice, the Maxwell-Bloch (MB) lattice, which we reported recently (Rybin A V, Varzugin G G, Timonen J and Bullough R K Year 2001 J. Phys. A:…

Integrable spin chain with Hilbert space fragmentation and solvable real-time dynamics.

- Physics, MathematicsPhysical review. E
- 2021

It is argued that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties, and a nonlocal map is constructed that connects the model with the Maassarani-Mathieu spin chain, also known as the SU(3) XX model.

Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas

- Physics
- 2020

We study the out-of-equilibrium properties of a classical integrable non-relativistic theory, with a time evolution initially prepared with a finite energy density in the thermodynamic limit. The…

Statistically induced phase transitions and anyons in 1D optical lattices.

- PhysicsNature communications
- 2011

An experimental setup to create anyons in one-dimensional lattices with fully tuneable exchange statistics and demonstrates how to induce a quantum phase transition from a superfluid into an exotic Mott-like state where the particle distribution exhibits plateaus at fractional densities.

## References

SHOWING 1-10 OF 14 REFERENCES

Quantum groups and generalized statistics in integrable models

- Physics
- 1990

The paper deals with the integrable massive models of quantum field theory. It is shown that generalized statistics of physical particles is closely connected with the invariance under quantum…

EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE

- Physics
- 1963

A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the…

Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model.

- PhysicsPhysical review letters
- 1990

The q-deformations of the quantum harmonic oscillator are used for to describe the generalized Jaynes-Cummings model (JCM) by using the q-analog of the Holstein-Primakoff realization of the su(1,1).…

Quantum nonlinear Schrödinger equation on a lattice

- Physics, Mathematics
- 1986

A local Hamiltonian is constructed for the nonlinear Schrodinger equation on a lattice in both the classical and the quantum variants. This Hamiltonian is an explicit elementary function of the local…

The quantum group SUq(2) and a q-analogue of the boson operators

- Physics
- 1989

A new realisation of the quantum group SUq(2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and q-analogues…

Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum

- Physics
- 1987

An integrable generalisation of the XXZ Heisenberg model with arbitrary spin and with light plane type anisotropy is studied. Integral equations describing the thermodynamics of the model are found.…