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Quantum Integrability and its Application to the Dicke Model
Christoph Sträter (LMU)
11.10.2011 at 14:00
Integrability is a well known concept in classical mechanics. There is actually a quantum analogue of it, and the Algebraic Bethe Ansatz allows us to easily solve the Schroedinger equation of many quantum integrable systems. Instead of a full diagonalization of the Hamiltonian, one has to solve a system of a few coupled equations, the Bethe equations. One example of an integrable system is the Dicke model, which describes a bosonic mode coupled to a collection of spins. In my talk, I will show how easy the Algebraic Bethe Ansatz can be applied to this model. By a special substitution the Bethe equations take a simple form and become numerically easily solvable. From the numerical solution, we can directly extract physics: We look at how bosons decay into the system of unexcited spins. This example of non-equilibrium dynamics has so far been explored for only a few bosons. Instead, we now look into regimes where the number of bosons is of the same order as the number of spins. Furthermore, by the integrability of the system we have easy access to the correlation functions of the system, giving us further insight into the dynamics.
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