We consider a 2d anisotropic SHO with ixy interaction and a 3d SHO in an imaginary magnetic field with µ l . B interaction to study the P T phase transition analytically in higher dimension.Unbroken P T symmetry in the first case is complementary to the rotational symmetry of the original Hermitian system .P T phase transition ceases to occur the moment the 2d oscillator becomes isotropic.Transverse magnetic field in the other system introduces the anisotropy in the system and the system undergoes PT phase transition depending on the strength of the magnetic field and frequency of the oscillator.
We study a massless Dirac particle with PT symmetric non-Hermitian Rashba
interaction in the background of Dirac oscillator potential to show the PT
phase transition in a (2+1) dimensional relativistic system analytically. PT
phase transition occurs when strength of the (i) imaginary Rashba interaction
or (ii) transverse magnetic field exceed their respective critical values.
Small mass gap in the spectrum, consistent with other approaches is generated
as long as the system is in the unbroken phase. Relativistic Landau levels are
constructed explicitly for such a system.Comment: 13 pages, Latex, 2 Figs ( Version to appear in Annals of Physics
We consider a one parameter family of a PT symmetric two dimensional system with quadratic non-linearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this systems by constructing a non-Hermitian Hamiltonian of a particle with position dependent mass. We further construct a canonical transformation which maps this position dependent mass systems to a QES system. First few QES levels are calculated explicitly by using Bender-Dunne (BD) polynomial method.
We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamiltonian of the system is converted to a separable Hamiltonian of Liouville type in parabolic coordinates and is further mapped into a Hamiltonian corresponding to two 2-dimensional simple harmonic oscillators (SHOs). Thus the explicit Green's functions for a general non-central PT symmetric non hermitian potential are calculated in terms of that of 2d SHOs. The entire spectrum for this three dimensional system is shown to be always real leading to the fact that the system remains in unbroken PT phase all the time .
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