Let h be a finite dimensional complex Hilbert space, b(h)+ be the set of all positive semi-definite operators on h and Phi is a (not necessarily linear) unital map of B(H) + preserving the Entropy-Gibbs transformation. Then there exists either a unitary or an anti-unitary operator U on H such that Phi(A) = UAU* for any B(H) +. Thermodynamics, a branch of physics that is concerned with the study...

0. Introduction 1. Affine Weyl groups (Reduction modulo W ) 2. Double Hecke algebras (Automorphisms, Demazure-Lusztig operators) 3. Macdonald polynomials (Intertwining operators) 4. Fourier transform on polynomials (Four transforms) 5. Jackson integrals (Macdonald’s η-identities) 6. Semisimple and pseudo-unitary representations (Main Theorem) 7. Spherical representations (Semisimple spherical r...

Using the winding of measures on torus in "rational directions" special classes unitary operators and pairs isometries are defined. This provides nontrivial examples generalized powers. Operators related to Szegö-singular shown have specific properties their invariant subspaces.

Linear optical systems acting on photon number states produce many interesting evolutions, but cannot give all the allowed quantum operations input state. Using Toponogov's theorem from differential geometry, we propose an iterative method that, for any arbitrary operator $U$ $n$ photons in $m$ modes, returns $\widetilde{U}$ which can be implemented with linear optics. The approximation is loca...

We investigate the correlators in unitary minimal conformal models coupled to two-dimensional gravity from the two-matrix model. We show that simple fusion rules for all of the scaling operators exist. We demonstrate the role played by the boundary operators and discuss its connection to how loops touch each other. PACS nos.: 04.60.Nc, 11.25.Pm

The paper interprets the concept “operator in separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined “classical” quantum mechanics) by that of “quantum information”. As far wave function characteristic probability (density) distribution for all possible values a certain quantity to be measured, definition mechanics means any unitary change distribution. It c...