Time-dependent q-deformed coherent states for generalized uncertainty relations

TL;DR

This paper explores time-dependent q-deformed coherent states in a noncommutative harmonic oscillator, revealing their squeezing properties, oscillating uncertainties, and potential revival phenomena, with implications for quantum uncertainty and dynamics.

Contribution

It introduces and analyzes a novel class of time-dependent q-deformed coherent states that satisfy generalized uncertainty relations and exhibit revival behaviors.

Findings

States are initially squeezed and saturate uncertainty inequalities.

Uncertainty products oscillate over time but always respect the relations.

Explicit calculations show potential for infinite-order revival times.

Abstract

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.