- November 4,
2011, Friday - 15h00 (Room
P
3.10):
David Krejcirik
(Nuclear Physics Institute of Academy of Sciences, ASCR, Czech
Republic)
" Non-Hermitian
operators in quantum theory and PT-symmetry "
Abstract. We give an introductory talk on a recent
progress in the so-called "PT-symmetric quantum theory", in which the
usual self-adjointness of observables requirement is replaced by their
simultaneous Parity-Time invariance. The latter "often" implies that
the spectrum is real and that the time evolution is unitary when
reconsidered in a Hilbert space with appropriately changed inner
product. The relevance of PT-symmetry has been suggested in various
domains of physics, however, so far, there has been no experimental
evidence proving that quantum systems defined by PT-symmetric
Hamiltonians do exist in nature.
In this talk, inter alia, we propose a simple PT-symmetric
interpretation of a class of Sturm-Liouville operators with
non-Hermitian Robin-type boundary conditions as a (physical)
perfect-transmission scattering problem. Moreover, we establish
closed integral-type formulae for similarity transformations relating
the non-Hermitian operators with self-adjoint Hamiltonians, succeed in
writing down the latter as a simple integro-differential operator and
also find the associated "charge conjugation" operator, which plays the
role of fundamental symmetry in a Krein-space reformulation of the
problem.
Past Seminars
2011/12
2010/11
2009/10
2008/09
2007/08
2006/07
2005/06
2004/05
2003/04
2002/03
2001/02
2000/01
1999/2000
1998/99
1997/98
1996/97
1995/96
Seminars take place in
Lisbon, I.S.T. -
Post Graduation Building
