Search results for "Quantum"
showing 10 items of 9714 documents
The module structure of Hochschild homology in some examples
2008
Abstract In this Note we give a simple proof of a conjecture by A. Caldararu stating the compatibility between the modified Hochschild–Kostant–Rosenberg isomorphism and the action of Hochschild cohomology on Hochschild homology in the case of Calabi–Yau manifolds and smooth projective curves. To cite this article: E. Macri` et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).
Kontsevich formality and cohomologies for graphs
2004
A formality on a manifold M is a quasi isomorphism between the space of polyvector fields (Tpoly(M)) and the space of multidifferential operators (Dpoly(M)). In the case M=R d , such a mapping was explicitly built by Kontsevich, using graphs drawn in configuration spaces. Looking for such a construction step by step, we have to consider several cohomologies (Hochschild, Chevalley, and Harrison and Chevalley) for mappings defined on Tpoly. Restricting ourselves to the case of mappings defined with graphs, we determine the corresponding coboundary operators directly on the spaces of graphs. The last cohomology vanishes.
The Dynamical Problem for a Non Self-adjoint Hamiltonian
2012
After a compact overview of the standard mathematical presentations of the formalism of quantum mechanics using the language of C*- algebras and/or the language of Hilbert spaces we turn attention to the possible use of the language of Krein spaces.I n the context of the so-called three-Hilbert-space scenario involving the so-called PT-symmetric or quasi- Hermitian quantum models a few recent results are reviewed from this point of view, with particular focus on the quantum dynamics in the Schrodinger and Heisenberg representations.
Quantum Groups, Star Products and Cyclic Cohomology
1993
After some historical remarks, we start with a rapid overview of the star-product theory (deformation of algebras of functions on phase space) and its applications to deformation-quantization. We then concentrate on Poisson-Lie groups and their “quantization”, give a star-product realization of quantum groups and discuss uniqueness and the rigidity as bialgebra of a universal model for the quantum SL(2) groups. In the last part we develop the notion of closed star-product (for which a trace can be defined on the algebra), show that it is classified by cyclic cohomology, permits to define a character and that there always exists one; finally we show that the pseudodifferential calculus on a …
Algebraic Results on Quantum Automata
2004
We use tools from the algebraic theory of automata to investigate the class of languages recognized by two models of Quantum Finite Automata (QFA): Brodsky and Pippenger’s end-decisive model, and a new QFA model whose definition is motivated by implementations of quantum computers using nucleo-magnetic resonance (NMR). In particular, we are interested in the new model since nucleo-magnetic resonance was used to construct the most powerful physical quantum machine to date. We give a complete characterization of the languages recognized by the new model and by Boolean combinations of the Brodsky-Pippenger model. Our results show a striking similarity in the class of languages recognized by th…
The new results on lattice deformation of current algebra
2008
The topic “Quantum Integrable Models” was reviewed in the literature and presented to the conferences and schools many times. Only the reports of our own have been done on quite a few occasions (see, e.g., [1], [2]). So here we shall try to present a fresh approach to the description of the ingredients of construction of integrable models. It has gradually evolved in the process of our joint work. Whereas our goal was the Sugawara construction for the lattice affine algebra (known now as the St.Petersburg algebra), (see, e.g., [1]), some technical developments happen to be new and useful for the already developed subjects. Here we shall underline this development.
Analytic vectors, anomalies and star representations
1989
It is hinted that anomalies are not really anomalous since (at least in characteristic examples) they can be related to a lack of common analytic vectors for the Hamiltonian and the observables. We reanalyze the notions of analytic vectors and of local representations of Lie algebras in this light, and show how the notion of preferred observables introduced in the deformation (star product) approach to quantization may help give an anomaly-free formulation to physical problems. Finally, some remarks are made concerning the applicability of these considerations to field theory, especially in two dimensions.
Electronic excitations of 1,4-disilyl-substituted 1,4-disilabicycloalkanes: a MS-CASPT2 study of the influence of cage size.
2007
We present a multistate complete active space second-order perturbation theory computational study aimed to predict the low-lying electronic excitations of four compounds that can be viewed as two disilane units connected through alkane bridges in a bicyclic cage. The analysis has focused on 1,4-disilyl-1,4-disilabicyclo[2.2.1]heptane (1a), 1,4-bis(trimethylsilyl)-1,4-disilabicyclo[2.2.1]heptane (1b), 1,4-disilyl-1,4-disilabicyclo[2.1.1]hexane (2a), and 1,4-bis(trimethylsilyl)-1,4-disilabicyclo[2.1.1]hexane (2b). The aim has been to find out the nature of the lowest excitations with significant oscillator strengths and to investigate how the cage size affects the excitation energies and the…
Improving the local vertex invariants in alkane graphs through a standard molecular orbital approach
2007
Abstract In this work, novel topological indices are introduced by the application of algorithms based on molecular orbital theory. Actually, the novel indices are obtained by computing new values of the local vertex invariants (LOVIs) in alkane graphs. The most significant result is the dramatic increase in the predictive capability achieved with the topological charge indices weighted according the new LOVIs’ values in the prediction of four key properties in the set of octane isomers, namely heat of atomization, molar refraction, heat of vaporization and boiling point.
Supramolecular Aggregates in Vacuum: Positively Mono-Charged Sodium Alkanesulfonate Clusters
2010
The formation and structural features of positively mono-charged aggregates of sodium bis(2-ethylhexyl) sulfosuccinate (AOT) and sodium methane—(MetS), butane—(ButS) and octane—(OctS) sulfonate molecules in the gas phase have been investigated by electrospray ionization mass spectrometry, energy-resolved mass spectrometry and density functional theory (DFT) calculations. The experimental results show that the center-of-mass collision energy required to dissociate 50% of these mono-charged aggregates scantly depends on the length of the alkyl chain as well as on the aggregation number. This, together with the large predominance of mono-charged species in the mass spectra, was rationalized i…