Pseudo-hermitian Interaction Research Articles

Quantum Work from a Pseudo-Hermitian Hamiltonian

In this work, we study the thermodynamics of a hybrid system based on the Da Providencia–Schütte Hamiltonian. The model consists of bosons, i.e., photons in a cavity, interacting with an ensemble of spins through a pseudo-Hermitian Hamiltonian. We compute the exact partition function of the system, and from it, we derive the statistical properties of the system. Finally, we evaluate the work that can be extracted from the system by performing an Otto cycle and discuss the advantages of the proposed pseudo-Hermitian interaction.

Pseudo-Hermitian Matrix Exactly Solvable Hamiltonian

The non PT-symmetric exactly solvable Hamiltonian describing a system of a fermion in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction is considered. We point out all properties of both of the original Mandal and the original Jaynes-Cummings Hamitonians. It is shown that these Hamiltonians are respectively pseudo-hermitian and hermitian REF _Ref536606452 \r \h \* MERGEFORMAT [1] REF _Ref536606454 \r \h [2]. Like the direct approach to invariant vector spaces used in Refs. REF _Ref536606456 \r \h [3] REF _Ref536606457 \r \h [4], we reveal the exact solvability of both the Mandal and Jaynes-Cummings Hamiltonians after expressing them in the position operator and the impulsion operator.

Pseudo-Hermitian Interaction Between an Oscillator and a Spin-1/2 Particle in an External Magnetic Field: A Path Integral Approach

We use the coherent-state path integral and an angular model for the spin to solve the pseudo-hermitian interaction between an oscillator and a spin-1/2 particle in an external magnetic field. The propagators are given explicitly as a perturbation series and are summed up exactly. The energy spectrum and the bi-orthonormal basis of states are deduced.

PSEUDO-HERMITIAN INTERACTIONS IN DIRAC THEORY: EXAMPLES

We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example we consider parity pseudo-Hermitian scalar interaction with arbitrary parameter in Dirac theory. In both cases we show that the energy spectrum is real and all the other features of nonrelativistic pseudo-Hermitian formulation are present. Using the spectral method, the positive definite metric operator (η) has been calculated explicitly for both the models to ensure positive definite norms for the state vectors.

PSEUDO-HERMITIAN INTERACTION BETWEEN AN OSCILLATOR AND A SPIN-1/2 PARTICLE IN THE EXTERNAL MAGNETIC FIELD

We consider a spin-1/2 particle in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction. We find that the energy eigenvalues for this system are real even though the interaction is not PT-invariant.