Macro-deformed coherent states and the q-analogue quantized field

The q-analogue coherent states vertical bar z>a are used to identify some of the canonical physical properties of the single-mode of the q-analogue quantized radiation field. Macro-deformed coherent states (CSs) with striking number and phase signatures are found to arise as q→∞, equivalently as q→0. In particular, the CS expectation value of the mean number of particles, qq∼Sq (log10 vertical bar z vertical bar2) where Sq(log10 vertical bar z vertical bar2) is a 'stair function' with equally spaced, integer steps as log10 vertical bar z vertical bar2) increases. Macro q-deformation provides a simple model with one region which simultaneously exhibits features from two distinct regions in the well known bosonic case: the quantum mechanical limit with occupation number vertical bar n> states and the semi-classical limit with vertical bar z> coherent states where vertical bar z vertical bar is large. The role of the deformation parameter 'q' is to enable a smooth interpolation between the classic bosonic CSs (q=1) and the fermionic CSs (q=∞ or 0). (author)