All coboundary Lie bialgebras and their corresponding Poisson–Lie structures are constructed for the oscillator algebra generated by {N,A+, A−,M}. Quantum oscillator algebras are derived from these bialgebras by using the Lyakhovsky and Mudrov formalism and, for some cases, quantizations at both algebra and group levels are obtained, including their universal R–matrices.

This series is absolutely convergent in the region Rs > 1, and defines a holomorphic function in s there. We call this function ζQ(s) the spectral zeta function for the non-commutative harmonic oscillator Q, which is introduced and studied by Ichinose and Wakayama [1]. The zeta function ζQ(s) is analytically continued to the whole complex plane as a single-valued meromorphic function which is h...

All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular Lie bialgebra, and a universal R-matrix linked to this new quantum algebra is presented.

We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is connected to Ohmic heat reservoirs at different temperatures. We use an approach following from a direct solution of the Langevin equations of motion. This work...