https://doi.org/10.1140/epjst/e2015-02528-2
Review
The dissipative Bose-Hubbard model
1 University of Athens, Physics Department, Nuclear & Particle Physics Section, Panepistimiopolis, Ilissia 15771, Athens, Greece
2 Forschungszentrum Jülich, Institute for Energy and Climate Research (IEK-STE), 52428 Julich, Germany
3 Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany
4 QSTAR, INO-CNR and LENS, Largo Fermi 2, 50125 Firenze, Italy
5 S3, CNR Istituto di Nanoscienze, via Campi 213A, 41125 Modena, Italy
6 Dipartimento di Fisica e Scienze della Terra, Università di Parma, via G.P. Usberti 7/a, 43124 Parma, Italy
7 INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Parma, Italy
a e-mail: gekordas@phys.uoa.gr
Received: 15 June 2015
Revised: 5 August 2015
Published online: 14 September 2015
Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counter-intuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.
© EDP Sciences, Springer-Verlag, 2015
