Triangle Seminars
Wednesday, 15 Oct 2008
Unfolding of higher order exceptional points in a PT-symmetric Bose-Hubbard model
Eva-Maria Graefe
(Technische Universitaet Kaiserslautern)
Abstract:
We study an N-particle, two-mode Bose-Hubbard system, modelling a Bose-Einstein condensate in a double-well potential. By introducing effective complex energies to the modes we describe a coupling to a continuum. The eigenvalues of the resulting non-Hermitian matrix model are in general complex where the imaginary parts (resonance widths) describe the decay rate into the continuum.
In dependence on the parameters the spectrum shows an intricate structure of exceptional points, at which two or more eigenvalues as well as the corresponding eigenstates are degenerate. In the present talk the effect of the interplay between the particle interaction and the non-Hermiticity on the spectrum is analysed, drawing special attention to the occurrence and unfolding of exceptional points. Some peculiarities are clarified using perturbational methods.
We study an N-particle, two-mode Bose-Hubbard system, modelling a Bose-Einstein condensate in a double-well potential. By introducing effective complex energies to the modes we describe a coupling to a continuum. The eigenvalues of the resulting non-Hermitian matrix model are in general complex where the imaginary parts (resonance widths) describe the decay rate into the continuum.
In dependence on the parameters the spectrum shows an intricate structure of exceptional points, at which two or more eigenvalues as well as the corresponding eigenstates are degenerate. In the present talk the effect of the interplay between the particle interaction and the non-Hermiticity on the spectrum is analysed, drawing special attention to the occurrence and unfolding of exceptional points. Some peculiarities are clarified using perturbational methods.
Posted by: KCL
Gluon Scattering in N=4 Super-Yang-Mills Theory from Weak to Strong Coupling
📍 London
Lance Dixon
(SLAC)
Abstract:
Scattering amplitudes in N=4 super-Yang-Mills theory can be defined in dimensional regularization near four dimensions, and have a number of remarkable features. There is good evidence for an exact, all-loop formula for the planar four- and five-point scattering amplitudes in terms of four functions of the coupling alone, one of which is the cusp anomalous dimension. For six gluons this particular formula fails. However, for the 'MHV' helicity configuration, an equivalence to a Wilson line expectation value on a hexagon persists at two loops, as does a certain 'dual conformal invariance'. These properties are connected to features of string propagation in AdS(5) x S5, in particular T duality.
Scattering amplitudes in N=4 super-Yang-Mills theory can be defined in dimensional regularization near four dimensions, and have a number of remarkable features. There is good evidence for an exact, all-loop formula for the planar four- and five-point scattering amplitudes in terms of four functions of the coupling alone, one of which is the cusp anomalous dimension. For six gluons this particular formula fails. However, for the 'MHV' helicity configuration, an equivalence to a Wilson line expectation value on a hexagon persists at two loops, as does a certain 'dual conformal invariance'. These properties are connected to features of string propagation in AdS(5) x S5, in particular T duality.
Posted by: KCL
Dual superconformal invariance from AdS5 x S5
📍 London
Riccardo Ricci
(Imperial)
Abstract:
In this talk we discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. We will see that combining T-duality along four directions in Poincare parametrization of AdS5 with a similar duality transformation on some of the fermionic variables maps the superstring action into itself. One implication is that, after duality, the superstring has a 'dual' superconformal symmetry group. Furthermore this dual superconformal symmetry can be seen as a consequence of the integrability of the superstring. This will also suggest that the dual superconformal charges correspond to non-local charges of the original model before T-duality.
In this talk we discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. We will see that combining T-duality along four directions in Poincare parametrization of AdS5 with a similar duality transformation on some of the fermionic variables maps the superstring action into itself. One implication is that, after duality, the superstring has a 'dual' superconformal symmetry group. Furthermore this dual superconformal symmetry can be seen as a consequence of the integrability of the superstring. This will also suggest that the dual superconformal charges correspond to non-local charges of the original model before T-duality.
Posted by: KCL