Berlin 2018 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 81: Nonequilibrium Quantum Many-Body Systems III
TT 81.7: Vortrag
Donnerstag, 15. März 2018, 11:00–11:15, H 3010
From two Algebraic Bethe Ansätze to the dynamics of Dicke-Jaynes-Cummings-Gaudin quantum integrable models through eigenvalue-based determinants — Hugo Tschirhart1, •Alexandre Faribault2, and Thierry Platini3 — 1Université du Luxembourg, Luxembourg, Luxembourg — 2Université de Lorraine, Nancy, France — 3Coventry University, Coventry, United Kingdoms
The work in question was inspired by precedent results on the Gaudin models (which are integrable) for spins-1/2 only which, by a change of variables in the algebraic Bethe equations, manage to considerably simplify the numerical treatment of such models.
This numerical optimisation is carried out by the construction of determinants, only depending on the previously mentioned variables, for every scalar products appearing in the expression of the mean value of an observable of interest at a given time.
By showing it is possible to use the Quantum Inverse Scattering Method, even when the vacuum state is not eigenstate of the transfer matrix, the previous results concerning spins-1/2 only are generalised to models including an additional spin-boson interaction.
A numerical treatment of systems describing the interaction of many spins-1/2 with a single bosonic mode has been done. We studied through it the time evolution of bosonic occupation and of local magnetisation for two different Hamiltonians, the Tavis-Cummings Hamiltonian and a central spin-like Hamiltonian. We learn that the dynamics of these systems, relaxing from an initial state to a stationary state, leads to a superradiant-like state for certain initial states.