X _m –EOP/PDEM connection for Scarf I potentials and their coherent states revivals

Abstract The revival structures for X m -exceptional orthogonal polynomials (EOP) of Scarf I potentials endowed with position-dependent effective mass (PDEM) are studied in the context of the generalized Gazeau-Klauder coherent states. It is shown that the deduced coherent states mimic full and fractional revivals phenomena in the case of the constant-mass. However, in the case of position-dependent effective mass, although full revivals take place during their time evolution, there is no trace of fractional revivals as defined in the common sense. These properties are illustrated numerically by means of some specific profiles of the mass-function, with and without singularities. We have also observed a close connection between the coherence time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">coh</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mi>m</mml:mi> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and the mass-parameter λ . We suspect the effect that a larger mass-parameter λ contributes significantly to a longer coherence time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">coh</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mi>m</mml:mi> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> .