Article

# Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field

Modern Physics Letters A (Impact Factor: 1.11). 01/2005; DOI: 10.1142/S0217732305016488

Source: arXiv

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**ABSTRACT:**To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating pos- itive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.Communications in Theoretical Physics 05/2013; 59(5). · 0.95 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems fully consistent quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such evolution ceases at exceptional points of the pseudo-Hermitian system.Journal of Physics A Mathematical and Theoretical 02/2012; 45(35). · 1.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider a 2d anisotropic SHO with {\bf ixy} interaction and a 3d SHO in an imaginary magnetic field with $\vec\mu_l$.$\vec B$ interaction to study the $PT$ phase transition analytically in higher dimension.Unbroken $PT$ symmetry in the first case is complementary to the rotational symmetry of the original Hermitian system .$PT$ 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.Physics Letters A 01/2013; 377(14). · 1.77 Impact Factor

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