A phase operator formalism is presented within the framework of thermo field dynamics (TFD). It is shown that a unitary phase operator (or phase factor) can be defined as a canonical conjugate of the generator of phase shift in TFD since the generator has a lower bounded spectrum. The tilde...

The quantum dissipative dynamics of a phase variable is studied. A phase variable is treated as a quantum mechanical operator in Liouville space. The time translation properties of a phase operator and its eigenstate are investigated in terms of a time-evolution generator describing the phase...

A solvable model of quantum-statistical mechanical frequency modulation is proposed and is solved for the cases of boson and two-state irrelevant subsystems to obtain the intensity distribution for a certain operator of the relevant subsystem. The damping theoretical approach, which is based on...

Within the formalism of non-equilibrium thermo field dynamics (NETFD), a derivation of basic equations is given in their most general and suitable forms to take into account the coarse graining in the kinetic region and in the fluid mechanical region. A new concept, called the connection of...

The framework of multifractal analysis (MFA) is distilled to the most sophisticated one. Within this transparent framework, it is shown that the harmonious representation of MFA utilizing two distinct Tsallis distribution functions, one for the tail part of probability density function (PDF) and...

We provide a unifying axiomatics for Rényi's entropy and non-extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszár's measure of directed divergence known from communication theory.

An analytical formula of the scaling exponents of velocity structure function for fully developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized measures of entropy, the Renyi entropy or the Havrda–Charvat–Tsallis...

An analytical formula for the probability density function (PDF) of the velocity fluctuation in fully-developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized measures of entropy, the Rényi entropy or the Tsallis...

In this paper we extend our recent results [P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain the entropy which accounts both for...

The general scaling theory of transient phenomena near the instability point, which has been proposed by one of the present authors (M.S.), is applied to investigate the fluctuation and relaxation of superradiance near the complete inversion (or instability point). An exact solution for a simple...