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$R$ -matrice universelle pour $U_{h} (D (2, 1, x))$ et invariant d’entrelacs associé

Henrik Thys (2002)

Bulletin de la Société Mathématique de France

En utilisant la méthode du double quantique, nous construisons une $R$ -matrice universelle pour la quantification de la superalgèbre de Lie $D (2, 1, x)$ . Nous utilisons ce résultat pour construire un invariant d’entrelacs et nous montrons qu’il est égal à une spécialisation du polynôme de Dubrovnik introduit par Kauffman.

Racks and orbits of dressing transformations

A. A. Balinsky (2000)

Commentationes Mathematicae Universitatis Carolinae

A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.

Radiation conditions and resolvent estimates for relativistic Schrödinger operators

Tomio Umeda (1995)

Annales de l'I.H.P. Physique théorique

Radiation conditions and scattering theory for $N$ -particle hamiltonians (main ideas of the approach)

Dimitri R. Yafaev (1992)

Journées équations aux dérivées partielles

Radiation conditions and scattering theory for $N$ -particle quantum systems

D. Yafaev (1991/1992)

Séminaire Équations aux dérivées partielles (Polytechnique)

Radiation reaction, renormalization and Poincaré symmetry.

Yaremko, Yurij (2005)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Random fields on the adele ring and Wilson's renormalization group

M. D. Missarov (1989)

Annales de l'I.H.P. Physique théorique

Rapidities and observable 3-velocities in the flat Finslerian event space with entirely broken 3D isotropy.

Bogoslovsky, George Yu. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Rate of convergence for large coupling limits by brownian motion

M. Demuth, F. Jeske, W. Kirsch (1993)

Annales de l'I.H.P. Physique théorique

Rational BV-algebra in string topology

Yves Félix, Jean-Claude Thomas (2008)

Bulletin de la Société Mathématique de France

Let $M$ be a 1-connected closed manifold of dimension $m$ and $L M$ be the space of free loops on $M$ . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of $L M$ , $H_{*} (L M; k)$ . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology $H H^{*} (C^{*} (M); C^{*} (M))$ which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between $H H^{*} (C^{*} (M); C^{*} (M))$ and the shifted homology $H_{* + m} (L M; k)$ . We also prove that the...

Rational string topology

Yves Félix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2007)

Journal of the European Mathematical Society

We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold $M$ . We prove that the loop homology of $M$ is isomorphic to the Hochschild cohomology of the cochain algebra $C^{*} (M)$ with coefficients in $C^{*} (M)$ . Some explicit computations of the loop product and the string bracket are given.

Realisation of a class of Markov processes through unitary evolutions in Fock space

Kalyanapuram Rangachari Parthasarathy (1991)

Séminaire de probabilités de Strasbourg

Rearrangement of lattice particles.

Muraskin, M. (1993)

International Journal of Mathematics and Mathematical Sciences

Recent developments in instantons in noncommutative $ℝ^{4}$ .

Sako, Akifumi (2010)

Advances in Mathematical Physics

Recent results on Lieb-Thirring inequalities

Ari Laptev, Timo Weidl (2000)

Journées équations aux dérivées partielles

We give a survey of results on the Lieb-Thirring inequalities for the eigenvalue moments of Schrödinger operators. In particular, we discuss the optimal values of the constants therein for higher dimensions. We elaborate on certain generalisations and some open problems as well.

Recent Results on the Cauchy Problem for Focusing and Defocusing Gross-Pitaevskii Hierarchies

Thomas Chen, Nataša Pavlović (2010)

Mathematical Modelling of Natural Phenomena

In this paper, we review some of our recent results in the study of the dynamics of interacting Bose gases in the Gross-Pitaevskii (GP) limit. Our investigations focus on the well-posedness of the associated Cauchy problem for the infinite particle system described by the GP hierarchy.

Recovering quantum graphs from their Bloch spectrum

Ralf Rueckriemen (2013)

Annales de l’institut Fourier

We define the Bloch spectrum of a quantum graph to be the map that assigns to each element in the deRham cohomology the spectrum of an associated magnetic Schrödinger operator. We show that the Bloch spectrum determines the Albanese torus, the block structure and the planarity of the graph. It determines a geometric dual of a planar graph. This enables us to show that the Bloch spectrum indentifies and completely determines planar $3$ -connected quantum graphs.

Recovering the total singularity of a conormal potential from backscattering data

Mark S. Joshi (1998)

Annales de l'institut Fourier

The problem of recovering the singularities of a potential from backscattering data is studied. Let $Ω$ be a smooth precompact domain in $ℝ^{n}$ which is convex (or normally accessible). Suppose $V_{i} = v + w_{i}$ with $v \in C_{c}^{\infty} (ℝ^{n})$ and $w_{i}$ conormal to the boundary of $Ω$ and supported inside $\overline{Ω}$ then if the backscattering data of $V_{1}$ and $V_{2}$ are equal up to smoothing, we show that $w_{1} - w_{2}$ is smooth.

Rectangular potentials in a semi-harmonic background: spectrum, resonances and dwell time.

Fernández-García, Nicolás, Rosas-Ortiz, Oscar (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Recurrent versus diffusive dynamics for a kicked quantum oscillator

M. Combescure (1992)

Annales de l'I.H.P. Physique théorique

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