A phase effect in the harmonic oscillator

Arun Kumar Pati, S. V. Lawande

It is shown that the state vector of a harmonic oscillator in a finite-dimensional Hilbert space changes sign only when the Hilbert space is of even dimension. The cyclic geometric phase for this finite-dimensional Hilbert-space harmonic oscillator is calculated. The effect of the finiteness of the Hilbert space on the dynamical and geometric phase change of a harmonic oscillator during a complete cycle is studied. In the limit of an infinite-dimensional case, the expressions reduce to the well known results.

Edward B. Manoukian

Bingsheng Lin, Jian Xu, Taihua Heng

We study the entanglement entropy of harmonic oscillators in non-commutative phase space (NCPS). We propose a new definition of quantum Rényi entropy based on Wigner functions in NCPS. Using the Rényi entropy, we calculate the entanglement entropy of the ground state of the 2D isotropic harmonic oscillators. We find that for some values of the non-commutative parameters, the harmonic oscillators can be entangled in NCPS. This is a new entanglement-like effect caused by the non-commutativity of the phase space.

B. B. Varga, S. Ø. Aks

Stephen P. Martin

Paul Bracken

Abstract An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.