Time-dependentq-deformed coherent states for generalized uncertainty relations

Abstract

This is the unspecified version of the paper.This version of the publication may differ from the final published version. 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. Permanent repository link

Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations

“…With reference to figure 1, we suggest that the noncommutative coherent states are slightly nonclassical in nature. While, the classical like manner of the noncommutative states have been investigated by many authors [26,27,30,46]. The dual nature of the coherent states in noncommutative spaces have also been found earlier, rather based on the analytical treatment; see, for instance, [30,47].…”

“…It is well known that one does not obtain the entangled states in the output ports, when one transmits coherent states through the input ports [36]. The reason behind this is that the coherent states are classical in nature [26,30,39], whereas the squeezed states are highly nonclassical [12,13] and very useful for the creation of the entangled states. For further analysis on the nonclassical behaviours of the states, albeit in noncommutative space, one may look at the recent work by one of the authors [27].…”

“…The two different approaches (2.3) and (2.4) become equivalent with the choice k(n) = nf 2 (n). For clarifications on physical reality of the ladder operators A, A † and A f , A † f , we refer the readers to [26,27], where an explicit Hermitian representation of the operators was found in terms of the usual canonical observables. A natural checkpoint is the limit f (n) = 1, where the operators in (2.3) and (2.4) reduce to the usual creation and annihilation operators as expected.…”

Uncertainty relations for a non-canonical phase-space noncommutative algebra

“…If we compute the probability of finding the scale factors near the singularity of the Kantowski-Sachs black hole, we conclude that the probability vanishes (see [9]). Thus, in this case, the singularity is not "erased" by the existence of some minimum length as suggested by various authors [25,26,27,28,36,54,56]. Rather, the singularity is still there, but the probability of reaching it is zero.…”

Unified -deformation of oscillator algebra and two-dimensional conformal field theory

“…The q-deformed oscillator algebras were used in the construction of the threedimensional non-commutative spaces with broken Lorentz invariance [32,33]. The (p, q; α, γ, l)-deformed oscillator algebra may be useful in this area.…”