Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite difference operators. The physical relevance of our study relies on the fact that coherent states (CS) are indeed formulated in the space of entire analytic functions where they can be rigorously expressed in terms of theta functions on the von Neumann lattice. The r\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the CS system suggest that the $q$--deformation of the WH algebra is an essential tool in the physics of discretized (periodic) systems. In this latter context we define a quantum mechanics formalism for lattice systems.Comment: 22 pages, TEX file, DFF188/9/93 Firenz

Quantum Effects in Biology and Their Applications to Light Harvesting and Sensing

AbstractThis session introduced the novel area of quantum effects in biological systems: it presented its seminal experimental discoveries and theoretical ideas, namely regarding photosynthetic systems and olfactory recognition, and discussed their potential applications to the development of artificial devices for more efficient light harvesting and finer sensing

Q-derivatives, coherent states and squeezing

We show that the q-deformation of the Weyl-Heisenberg (q-WH) algebra naturally arises in discretized systems, coherent states, squeezed states and systems with periodic potential on the lattice. We incorporate the q-WH algebra into the theory of (entire) analytical functions, with applications to theta and Bloch functions

Identical Particles and Permutation Group

Second quantization is revisited and creation and annihilation operators areshown to be related, on the same footing both to the algebra h(1), and to the superalgebra osp(1|2) that are shown to be both compatible with Bose and Fermi statistics. The two algebras are completely equivalent in the one-mode sector but, because of grading of osp(1|2), differ in the many-particle case. The same scheme is straightforwardly extended to the quantum case h_q(1) and osp_q(1|2).Comment: 8 pages, standard TEX, DFF 205/5/94 Firenz

Libri in rete on line: l\u27esperienza toscana di cooperazione tra biblioteche pubbliche e universitarie

The Biblioteca Comunale "Renato Fucini" di Empoli has started, since year 2003, to develop a software to manage Inter Library Loan and Document Delivery transactions among public and university libraries of Region Tuscany, in the framework of the project "Libri in rete". (http://www.cultura.regione.toscana.it/biblioteche/progetti/libri_rete/).La Biblioteca Comunale "Renato Fucini" di Empoli ? stata incaricata dalla Regione Toscana, a partire dal 2003, di mettere a punto un software di gestione per le transazioni di prestito interbibliotecario e document delivery tra le biblioteche pubbliche, statali e universitarie aderenti al progetto di cooperazione "Libri in rete" (http://www.cultura.regione.toscana.it/biblioteche/progetti/libri_rete/). Tale progetto si colloca al cosiddetto "secondo livello" della cooperazione, essendo relativo a transazioni di ILL/DD che, non potendosi esaurire all\u27interno della rete territoriale, richiedono ad una biblioteca di una rete di rivolgersi a biblioteche di reti diverse. Dal 3 marzo 2003 (data di avvio del servizio) al 4 maggio 2005, il sistema ha registrato 102.011 accessi, producendo 49.645 e-mail di informazioni sulle transazioni in corso, che hanno interessato 409 biblioteche aderenti al servizio, di cui 222 ne hanno effettivamente usufruito. Da parte della Regione Toscana la ricerca di partnership con una biblioteca pubblica ha rappresentato una soluzione efficace per la messa a punto di un servizio on line che, oltre a svolgere funzioni gestionali, rispondesse all\u27esigenza originaria di effettuare il controllo sull\u27impiego dei voucher di trasporto acquistati dalla Regione Toscana e distribuiti alle reti di cooperazione. Di questa particolare soluzione organizzativa sono illustrati i punti di forza e di debolezza. La chiara prevalenza quantitativa delle transazioni di ILL su quelle di DD, per l\u27anno 2004, ? illustrata alla luce del peso giocato all\u27interno del servizio dalle biblioteche pubbliche rispetto alle biblioteche universitarie, che esauriscono al proprio interno la stragrande maggioranza delle transazioni di DD. Sono illustrati alcuni dati statistici sulle transazioni di DD delle biblioteche universitarie toscane aderenti a LiR on line, sia al loro interno, sia nei confronti delle reti di pubblica lettura, assenti sia da ACNP che da Nilde. L\u27apertura delle biblioteche pubbliche ai servizi di ACNP e Nilde costituisce una prospettiva importante, alla luce della quale potr? essere sviluppato in chiave di integrazione il servizio LiR on line

Quantum geometry and quantum algorithms

Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on the complete solution of Chern-Simons topological quantum field theory and its connection to Wess-Zumino-Witten conformal field theory. The colored Jones polynomial is expressed as the expectation value of the evolution of the q-deformed spin-network quantum automaton. A quantum circuit is constructed capable of simulating the automaton and hence of computing such expectation value. The latter is efficiently approximated using a standard sampling procedure in quantum computation.Comment: Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirard

Bose-Einstein condensation in inhomogeneous Josephson arrays

We show that spatial Bose-Einstein condensation of non-interacting bosons occurs in dimension d < 2 over discrete structures with inhomogeneous topology and with no need of external confining potentials. Josephson junction arrays provide a physical realization of this mechanism. The topological origin of the phenomenon may open the way to the engineering of quantum devices based on Bose-Einstein condensation. The comb array, which embodies all the relevant features of this effect, is studied in detail.Comment: 4 pages, 5 figure

Spin networks, quantum automata and link invariants

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological quantum computation models. Such a quantum combinatorial scheme, which essentially encodes SU(2) Racah--Wigner algebra and its braided counterpart, is particularly suitable to address problems in topology and group theory and we discuss here a finite states--quantum automaton able to accept the language of braid group in view of applications to the problem of estimating link polynomials in Chern--Simons field theory.Comment: LateX,19 pages; to appear in the Proc. of "Constrained Dynamics and Quantum Gravity (QG05), Cala Gonone (Italy) September 12-16 200

Topological origin of the phase transition in a mean-field model

We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological transition occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N. Furthermore, as in statistical mechanics, also in topology the way the thermodynamic limit is taken is crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the text. To appear in Physical Review Letter