Location of Repository

In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe ansatz solution, into the quasi-exactly solvable spectrum of a one-body Schrodinger operator. Bifurcations of the minima for the potential of the Schrodinger operator determine the crossover couplings. By considering the behaviour of particular ground state correlation functions, these may be identified as quantum phase crossovers in the many-body integrable system with finite particle number. In this approach the existence of the quantum phase crossover is not dependent on the existence of a thermodynamic limit, rendering applications to finite systems feasible. We study two examples of bosonic Hamiltonians which admit second-order crossovers

Topics:
QA

Publisher: IOP Publishing

Year: 2006

OAI identifier:
oai:kar.kent.ac.uk:4712

Provided by:
Kent Academic Repository

Downloaded from
http://kar.kent.ac.uk/4712/1/Dunning_Quantum_Phase.pdf

- (1999). Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations,
- (2001). Bose-Einstein condensation in the alkali gases: Some fundamental concepts,
- (2006). Classical and quantum dynamics of a model for atomic-molecular Bose–Einstein condensates,
- (2003). Entanglement of two-mode Bose– Einstein condensates,
- (2005). Evidence for the super TonksGirardeau gas,
- (2001). Exact quantum phase model for mesoscopic Josephson junctions,
- (2003). Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose–Einstein condensate,
- (2006). Ground state overlap and quantum phase transitions,
- (2005). Instability and entanglement of the ground state of the Dicke model,
- (1992). New methods in the theory of quantum spin systems,
- (1993). On the quantum inverse scattering method for the DST dimer,
- (2002). Oscillatory decay of a two-component Bose–Einstein condensate,
- (2005). Quantum critical behavior of two coupled Bose–Einstein condensates,
- (2001). Quantum eﬀects on the dynamics of a two-mode atom-molecule Bose-Einstein condensate,
- (2005). Quantum entanglement and ﬁxed-point bifurcations,
- (2003). Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions,
- (1999). Quantum phase transitions
- (2004). Quantum phase transitions in mesoscopic systems,
- (1998). Quantum superposition states of Bose–Einstein condensates,
- (1994). Quasi-exactly solvable models in quantum mechanics
- (1998). Some properties of double Morse potentials,
- (2001). Spectral determinants for Schr¨ odinger equation and Q-operators of conformal ﬁeld theory,
- (2001). Spectral determinants for Schro¨dinger equation and Q-operators of conformal field theory,
- (2001). Spectral equivalences, Bethe ansatz equations, and reality properties in PT -symmetric quantum mechanics
- (2001). Spectral equivalences, Bethe ansatz equations, and reality properties in PT-symmetric quantum mechanics
- (1964). Study of exactly soluble one-dimensional N-body problems,
- (1991). The Schro¨dinger equation
- (2000). Theory of coherent photoassociation of a Bose–Einstein condensate,
- (2001). Thermodynamic properties of a small superconducting grain,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.