Invitation to Seminar Talk A generalized relative entropy and a BCS functional without artificial boundary conditions Andreas Deuchert IST Austria, Klosterneuburg Host: Laszlo Erdös In the first part of this talk we consider a recently introduced generalized relative entropy for bounded and not necessarily compact linear operators on a separable Hilbert space. Defined is this object by a limiting procedure that resembles a thermodynamic limit. A natural question in this context is whether there exists a formula that allows one to compute the resulting limit without going through the relatively complicated limiting procedure. We answer this question affirmatively and provide a general formula for this limit. Under weak additional regularity assumptions on the operators, we show that it takes a form that is particularly suited for explicit computations. In the second part of the talk we use the relative entropy from the first part to define a version of the BCS functional of superconductivity without artificial boundary conditions. We investigate this functional in the parameter regime close to the critical temperature where Ginzburg-Landau theory is assumed to be valid and show that it is bounded from below. A direct consequence of our lower bound are a -priori estimates for states with energy lower or equal than that of a certain reference state. These bounds are a crucial ingredient for the derivation of Ginzburg -Landau theory in our set-up. Tuesday, October 25, 2016, 04:00pm Seminar Room Big Ground Floor / Office Building West Thi s invi tation is va lid as a ti cket for the IST Shuttle from a nd to Heiligenstadt Station. Pl ease find a s chedule of the IST Shuttle on our webpage (note that the IST Shuttle ti mes a re highlighted i n dark green): http://i st.ac.at/fileadmin/user_upload/pdfs/IST_shuttle_bus.pdf The IST Shuttle bus is marked IST Shuttle (#242) and has the Institute Logo printed on the s ide. Institute of Science and Technology Austria | Am Campus 1 | 3400 Klosterneuburg www.ist.ac.at

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