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Springer eBooks

A General Formula for the Classical Limit of the Interacting Boson Hamiltonian

Jin-Quan Chen, Pieter Van Isacker

Published Jan 1, 1981• 0 citations
Publisher
DOI
10.1007/978-1-4757-1523-1_20

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Abstract. 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 pure initial states, the analytical calculation of certain observables simplifies considerably. Namely, we provide exact formulas for the calculation of the Loschmidt-echo and the emptiness formation probability, where the computational time scales polynomially with the particle number. Moreover, we construct a non-local mapping of the q -boson model to the XX spin chain, and show how this can be utilized to obtain the time evolution of various local bosonic observables for translationally invariant initial states. The results obtained via the bosonic and fermionic picture show perfect agreement. In the infinite volume and large time limits, we rigorously verify the prediction of the generalized Gibbs ensemble for homogeneous initial Fock states.
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 ->infinity. It is shown that, for a particular class of pure initial states, the analytical calculation of certain observables simplifies considerably. Namely, we provide exact formulas for the calculation of the Loschmidt-echo and the emptiness formation probability, where the computational time scales polynomially with the particle number. Moreover, we construct a non-local mapping of the q-boson model to the XX spin chain, and show how this can be utilized to obtain the time evolution of various local bosonic observables for translationally invariant initial states. The results obtained via the bosonic and fermionic picture show perfect agreement. In the infinite volume and large time limits, we rigorously verify the prediction of the generalized Gibbs ensemble for homogeneous initial Fock states.