PT - symmetric deformations of Calogero models
نویسنده
چکیده
We demonstrate that Coxeter groups allow for complex PT -symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero-MoserSutherland models invariant under the extended Coxeter groups. The eigenspecta for the deformed models are real and contain the spectra of the undeformed case as subsystem.
منابع مشابه
On PT-symmetric extensions of the Calogero and Sutherland models
The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinussquare potential. They are well known to be integrable and solvable. Here we extend the Calogero and Sutherland Hamiltonians by means of new interactions which are PT-symmetric but not self adjoint. Some of these new interactions lead to integra...
متن کاملar X iv : 0 70 8 . 24 05 v 1 [ qu an t - ph ] 1 7 A ug 2 00 7 PT - symmetry and Integrability ∗
We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT -symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT -symmetry as a guiding principle to construct deformations of some integrable systems, the Calogero-Moser-Sutherland model and the Korteweg deVries equation. Some properties of these models ar...
متن کاملOn PT-symmetric extensions of the Calogero model
The original Calogero model describes N quantum particles on the line interacting pairwise through a inverse square potential. It is well known to be integrable and solvable. Here we extend the Calogero Hamiltonian by means of new interactions which are PT-symmetric but not self adjoint. Some of these new interactions lead to integrable PT-symmetric Hamiltonians; the algebraic properties furthe...
متن کاملPT -symmetric extensions of the supersymmetric Korteweg-de Vries equation
We discuss several PT -symmetric deformations of superderivatives. Based on these various possibilities, we propose new families of complex PT -symmetric deformations of the supersymmetric Korteweg-de Vries equation. Some of these new models are mere fermionic extensions of the former in the sense that they are formulated in terms of superspace valued superfields containing bosonic and fermioni...
متن کاملPT −symmetric regularizations in supersymmetric quantum mechanics
Within the supersymmetric quantum mechanics the necessary regularization of the poles of the superpotentials on the real line of coordinates x may be most easily mediated by a small constant shift of this axis into complex plane. Detailed attention is paid here to the resulting recipe which works, in effect, with non-Hermitian (a. k. a. PT −symmetric or pseudo-Hermitian) Hamiltonians. Besides a...
متن کامل