Sanjib Dey, Andreas Fring, Laure Gouba, Paulo G. Castro
We investigate properties of generalized time-dependent q-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg’s uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e. the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest’s theorem hold at all times. We conjecture that the model exhibits revival times to infinite order. Explicit sample computations for the fractional revival times and superrevival times are presented.
http://arxiv.org/abs/1211.4791
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)
Sanjib Dey, Andreas Fring, Laure Gouba
We provide a systematic procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing noncommutative spaces. The large number of possible free parameters in these calculations is reduced to a manageable amount by imposing various different versions of PT-symmetry on the underlying spaces, which are dictated by the specific physical problem under consideration. The representations for the corresponding operators are in general non-Hermitian with regard to standard inner products and obey algebras whose uncertainty relations lead to minimal length, areas or volumes in phase space. We analyze in particular one three dimensional solution which may be decomposed to a two dimensional noncommutative space plus one commuting space component and also into a one dimensional noncommutative space plus two commuting space components. We study some explicit models on these type of noncommutative spaces.
http://arxiv.org/abs/1205.2291
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)