Quantum Analysis and Nonequilibrium Response

The quantum derivatives of $e^{-A}, A^{-1}$ and $\log A$, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator $A$ in a Hilbert space. Using the quantum analysis based on these quantum derivatives, a basic equation for the entropy operator in nonequilibrium systems is derived, and Zubarev's theory is extended to infinite order with respect to a perturbation. Using the first-order term of this general perturbational expansion of the entropy operator, Kubo's linear response is rederived and expressed in terms of the inner derivation $\delta_{{\cal H}}$ for the relevant Hamiltonian ${\cal H}$. Some remarks on the conductivity $\sigma (\omega)$ are given.Comment: Latex, 16 pages, no figures, to be published in Prog. Theor. Phys. (1998

General Formulation of Quantum Analysis

A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the G\^ateaux derivative or commutators. This yields a unified formulation of quantum analysis, namely the invariance of quantum derivatives, which are expressed by multiple integrals of ordinary higher derivatives with hyperoperator variables. Multivariate quantum analysis is also formulated in the present unified scheme by introducing a partial inner derivation and a rearrangement formula. Operator Taylor expansion formulas are also given by introducing the two hyperoperators $\delta_{A \to B} \equiv -\delta_A^{-1} \delta_B$ and $d_{A \to B} \equiv \delta_{(-\delta_A^{-1}B) ; A}$ with the inner derivation $\delta_A : Q \mapsto [A,Q] \equiv AQ-QA$. Physically the present noncommutative derivatives express quantum fluctuations and responses.Comment: Latex file, 29 pages, no figur

Quantum Statistical Mechanics of Ideal Gas Obeying Fractional Exclusion Statistics: A Systematic Study

The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and internal energy, the equation of state, as well as the thermodynamic properties are thoroughly discussed. Some novel results are obtained.Comment: Revtex, one figure in EPS format include

Determining equations for higher-order decompositions of exponential operators

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of the coefficients are derived.Comment: 30 page

Statistical Mechanics of Non-Equilibrium Systems : Extensive Property, Fluctuation and Nonlinear Response

この論文は国立情報学研究所の電子図書館事業により電子化されました

New Types of Phase Transitions in Magnetic Materials

The present paper reviews the recent work on the quantum effective-field theory by M.Suzuki (in Physica B, 1994). This new theory is shown to be very useful in studying new types of phase transitions in strongly correlated systems and in quantum magnetic systems

Towards Bose-Einstein Condensation of Electron Pairs: Role of Schwinger Bosons

It can be shown that the bosonic degree of freedom of the tightly bound on-site electron pairs could be separated as Schwinger bosons. This is implemented by projecting the whole Hilbert space into the Hilbert subspace spanned by states of two kinds of Schwinger bosons (to be called binon and vacanon) subject to a constraint that these two kinds of bosonic quasiparticles cannot occupy the same site. We argue that a binon is actually a kind of quantum fluctuations of electron pairs, and a vacanon corresponds to a vacant state. These two bosonic quasiparticles may be responsible for the Bose-Einstein condensation (BEC) of the system associated with electron pairs. These concepts are also applied to the attractive Hubbard model with strong coupling, showing that it is quite useful. The relevance of the present arguments to the existing theories associated with the BEC of electron pairs is briefly commented.Comment: Revtex, one figur

Parametric Wind Velocity Vector Estimation Method for Single Doppler LIDAR Model

Doppler lidar (LIght Detection And Ranging) can provide accurate wind velocity vector estimates by processing the time delay and Doppler spectrum of received signals. This system is essential for real-time wind monitoring to assist aircraft taking off and landing. Considering the difficulty of calibration and cost, a single Doppler lidar model is more attractive and practical than a multiple lidar model. In general, it is impossible to estimate two or three dimensional wind vectors from a single lidar model without any prior information, because lidar directly observes only a 1-dimensional (radial direction) velocity component of wind. Although the conventional VAD (Velocity Azimuth Display) and VVP (Velocity Volume Processing) methods have been developed for single lidar model, both of them are inaccurate in the presence of local air turbulence. This paper proposes an accurate wind velocity estimation method based on a parametric approach using typical turbulence models such as tornado, micro-burst and gust front. The results from numerical simulation demonstrate that the proposed method remarkably enhances the accuracy for wind velocity estimation in the assumed modeled turbulence cases, compared with that obtained by the VAD or other conventional method