Freitag, 12.06.2015: Flow Equations for Operators
Prof. Dr. Volker Bach (TU Braunschweig)
A basic problem in theoretical physics is the determination
of the ground state energy $$E_{\mathrm{gs}} := \inf\sigma(H)$$ and the
corresponding eigenvector(s) $$\Psi_0 \in \mathcal{H}$$ of a given
physical system defined by a self-adjoint Hamiltonian operator $$H$$
that acts on the Hilbert space $$\mathcal{H}$$ of physical states (wave
functions), or better yet, the diagonalized form $$\widetilde{H}$$ of
the Hamiltonian together with the unitary $$U$$ that implements the
diagonalization, $$\widetilde{H} = U H U^*$$.
The lecture reviews progress on the solution of this problem by
(continuous) flows, focussing on two methods:
* The Brockett-Wegner diagonalizing flow for matrices and operators
and its application to quadratic operators will be discussed.
* The Renormalization Group flow based on the isospectral
Feshbach-Schur map that has been used to construct ground states of,
e.g., atoms that interact with photons, will be described, as well.
| Uhrzeit: |
17:15 |
| Ort: |
N14 |
| Gruppe: |
Kolloquium |
| Einladender: |
Loose, Teufel |
