Found 3 result(s)

12.10.2011 (Wednesday)

Non-Hermitian Hamiltonian systems and antilinear deformations of integrable systems

Regular Seminar Andreas Fring (City University)

at:
13:15 KCL
room S4.23
abstract:

I will provide a brief general introduction into non-Hermitian Hamiltonian systems with real eigenvalue spectra, arguing that they represent well defined self consistent physical systems. Such type of models possess usually an antilinear symmetry, as for instance PT-invariance (simultaneous parity and time reversal) and/or are quasi/pseudo Hermitian. Most crucial is that they allow for a consistent quantum mechanical framework possessing a unitary time evolution. The general framework will be applied to some integrable models, such a quantum spin chains, classical integrable systems associated to differential equations and Calogero-Moser-Sutherland models. I will present some recent results.

18.11.2008 (Tuesday)

Integrable models from PT-symmetric deformations

Regular Seminar Andreas Fring (City University London)

at:
16:00 Brunel U.
room M128
abstract:

I will give a brief account of some examples of non-Hermitian Hamiltonian systems with real spectra, which have appeared in the literature over the last four decades. I will discuss the spectral properties of these type of Hamiltonians and explain how their reality results from PT-symmetry, quasi-Hermiticity, pseudo-Hermiticity or supersymmetry. Subsequently I review the general technicalities needed to formulate a consistent quantum mechanical system in this context by constructing an appropriate metric and domain. I will provide some Lie algebraic examples. Taking PT-symmetry as a guiding principle one may construct deformations of integrable models, such as Calogero-Moser-Sutherland models, the Korteweg-deVries or Burgers equation. It turns out that some of these deformations are supersymmetry preserving. Others even leave the integrabilty in tact and therefore lead to new types of integrable system.

06.07.2005 (Wednesday)

Affine Toda field theories related to Coxeter groups of non-crystallographic type

Regular Seminar Andreas Fring (City University)

at:
13:15 KCL
room 423
abstract:

We propose affine Toda field theories related to the non-crystallographic Coxeter groups H_2, H_3 and H_4. The classical mass spectrum, the classical three-point couplings and the one-loop corrections to the mass renormalisation are determined. The construction is carried out by means of a reduction procedure from crystallographic to non-crystallographic Coxeter groups. The embedding structure explains for various affine Toda field theories that their particles can be organised in pairs, such that their relative masses differ by the golden ratio.