Prof. Tomaž Prosen: Exact Solutions in Quantum Physics Far from Equilibrium

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Povzetek:

    Exact Solutions in Quantum Physics Far from Equilibrium

    Prof. Tomaž Prosen, Fakulteta za matematiko in fiziko, Univerza v Ljubljani

In classical and quantum mechanics the term integrability usually refers to an algebraic procedure which reduces an interacting system to a non-interacting one.  Even though the situation of integrability is exceptional in nature it is often encountered in important phenomenological and fundamental models of many-body physics and field theory. A particularly appealing mathematical framework of integrability has ben put forward by C. N. Yang and R. Baxter which unified the treatment of exactly solvable systems in d+1 dimensional equilibrium classical statistical mechanics and d dimensional quantum mechanics. These techniques, known also as algebraic Bethe ansatz or quantum soliton theory, have been further elaborated by the celebrated Leningrad school of mathematical physics.

After giving a historical overview I shall focus on the problem of quantum transport in one dimension. I will explain how integrability structures can be relevant or irrelevant for the observable phenomena. In particular, I will show how the steady state problem for the quantum Heisenberg chain driven far from equilibrium can bring into the game new fundamental structures, such as quasi-local conservation laws, which lead to new results on ballistic transport at finite temperature.