Quantization of the cotangent bundle via the tangent groupoid
Quantization of the orientation preserving automorphisms of the torus
Quantization on submanifolds
Quantizations and symbolic calculus over the -adic numbers
We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the -adic numbers. We apply this theory to the study of elliptic operators over the -adic numbers and determine their asymptotic spectral behavior.
Quantized charge in terms of pure geometry
Quantized fields and operators on a partial inner product space
Quantum Affine Algebras and Deformations of the Virasoro and -Algebras
Quantum algebras and associated with certain -Hahn polynomials: a revisited approach.
Quantum Barnes function as the partition function of the resolved conifold.
Quantum Bochner theorems and incompatible observables
A quantum version of Bochner's theorem characterising Fourier transforms of probability measures on locally compact Abelian groups gives a characterisation of the Fourier transforms of Wigner quasi-joint distributions of position and momentum. An analogous quantum Bochner theorem characterises quasi-joint distributions of components of spin. In both cases quantum states in which a true distribution exists are characterised by the intersection of two convex sets. This may be described explicitly...
Quantum cohomology and its application.
Quantum computational structures
Quantum computing.
Quantum computing in decoherence-free subspace constructed by triangulation.
Quantum copying: a review.
Quantum curve in -oscillator model.
Quantum deformations and superintegrable motions on spaces with variable curvature.
Quantum detailed balance
Quantum detailed balance conditions with time reversal: the finite-dimensional case
We classify generators of quantum Markov semigroups on (h), with h finite-dimensional and with a faithful normal invariant state ρ satisfying the standard quantum detailed balance condition with an anti-unitary time reversal θ commuting with ρ, namely for all x,y ∈ and t ≥ 0. Our results also show that it is possible to find a standard form for the operators in the Lindblad representation of the generators extending the standard form of generators of quantum Markov semigroups satisfying the usual...
Quantum diffusion and generalized Rényi dimensions of spectral measures
We estimate the spreading of the solution of the Schrödinger equation asymptotically in time, in term of the fractal properties of the associated spectral measures. For this, we exhibit a lower bound for the moments of order at time for the state defined by . We show that this lower bound can be expressed in term of the generalized Rényi dimension of the spectral measure associated to the hamiltonian and the state . We especially concentrate on continuous models.