Search results for "quantum [statistics]"
showing 10 items of 4295 documents
Finite Braid Groups for the SU(2) Knizhnik Zamolodchikov Equation
1995
We consider the monodromy representations of the mapping class group B 4 of the 2-sphere with 4 punctures acting in the solutions space of the zu(2) Knizhnik-Zamolodchikov equation [3] (note that the monodromy representations of the braid group have a more general geometric definition [4]).
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.
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.
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…
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…
Unsaturated syn- and anti-1,2-Amino Alcohols by Cyclization of Allylic Bis-trichloroacetimidates. Stereoselectivity Dependence on Substrate Configura…
2014
Disubstituted allylic bis-imidates undergo Lewis acid catalyzed or spontaneous cyclization to oxazolines, which are precursors of unsaturated amino alcohols. Stereoselectivity of the cyclization is mainly determined by the substrate configuration. Highly selective cis-oxazoline formation is achieved starting from anti-E-bis-imidates while trans-oxazoline predominantly forms from anti-Z-bis-imidates. On the basis of DFT calculations, the stereoselectivity trends can be explained by the formation of the energetically most stable carbenium ion conformation, followed by the cyclization via most favorable bond rotations.
Properties of native ultrathin aluminium oxide tunnel barriers
2003
We have investigated planar metal–insulator–metal tunnel junctions with aluminium oxide as the dielectricum. These oxide barriers were grown on an aluminium electrode in pure oxygen at room temperature till saturation. By applying the Simmons model we derived discrete widths of the tunnelling barrier, separated by Δs ≈ 0.38 nm. This corresponds to the addition of single layers of oxygen atoms. The minimum thickness of s0 ≈ 0.54 nm is then due to a double layer of oxygen. We found a strong and systematic dependence of the barrier height on the barrier thickness. Breakdown fields up to 5 GV m−1 were reached. They decreased strongly with increasing barrier thickness. Electrical breakdown could…