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Quantum diffusion and generalized Rényi dimensions of spectral measures

Jean-Marie Barbaroux, François Germinet, Serguei Tcheremchantsev (2000)

Journées équations aux dérivées partielles

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 p at time T for the state ψ defined by [ 1 T ∫ 0 T ∥ | X | p / 2 e - i t H ψ ∥ 2 d t ] . We show that this lower bound can be expressed in term of the generalized Rényi dimension of the spectral measure μ ψ associated to the hamiltonian H and the state ψ . We especially concentrate on continuous models.

Quantum Fibre Bundles. An Introduction

Tomasz Brzeziński (1997)

Banach Center Publications

An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

Quantum finite automata with control language

Carlo Mereghetti, Beatrice Palano (2006)

RAIRO - Theoretical Informatics and Applications

Bertoni et al.  introduced in Lect. Notes Comput. Sci.2710 (2003) 1–20 a new model of 1-way quantum finite automaton (1qfa) called 1qfa with control language (1qfc). This model, whose recognizing power is exactly the class of regular languages, generalizes main models of 1qfa's proposed in the literature. Here, we investigate some properties of 1qfc's. In particular, we provide algorithms for constructing 1qfc's accepting the inverse homomorphic images and quotients of languages accepted...

Quantum graph spectra of a graphyne structure

Ngoc T. Do, Peter Kuchment (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

We study the dispersion relations and spectra of invariant Schrödinger operators on a graphyne structure (lithographite). In particular, description of different parts of the spectrum, band-gap structure, and Dirac points are provided.

Quantum homogeneous superspaces and quantum duality principle

Rita Fioresi (2015)

Banach Center Publications

We define the concept of quantum section of a line bundle of a homogeneous superspace and we employ it to define the concept of quantum homogeneous projective superspace. We also suggest a generalization of the QDP to the quantum supersetting.

Currently displaying 41 – 60 of 110