Quantum Analysis of Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma

Quantum properties of a modified Caldirola-Kanai oscillator model for propagating electromagnetic fields in a plasma medium are investigated using invariant operator method. As a modification, ordinary exponential function in the Hamiltonian is replaced with a modified exponential function, so-called the q-exponential function. The system described in terms of q-exponential function exhibits nonextensivity. Characteristics of the quantized fields, such as quantum electromagnetic energy, quadrature fluctuations, and uncertainty relations are analyzed in detail in the Fock state, regarding the q-exponential function. We confirmed, from their illustrations, that these quantities oscillate with time in some cases. It is shown from the expectation value of energy operator that quantum energy of radiation fields dissipates with time, like a classical energy, on account of the existence of non-negligible conductivity in media.