(1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups

All Lie bialgebra structures for the (1+1)-dimensional centrally extended Schrodinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family of Schrodinger Poisson-Lie groups can be deduced by means of the Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended Galilei and gl(2) Lie bialgebras within the Schrodinger classification are studied. As an application, new quantum (Hopf algebra) deformations of the Schrodinger algebra, including their corresponding quantum universal R-matrices, are constructed.Comment: 25 pages, LaTeX. Possible applications in relation with integrable systems are pointed; new references adde

Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions

A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra. In this way several examples of N-body dynamical systems obtained from q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2) Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of Ruijsenaars type arising from the same (non co-boundary) q-deformation of the (1+1) Poincare' algebra. Also, a unified interpretation of all these systems as different Poisson-Lie dynamics on the same three dimensional solvable Lie group is given.Comment: 19 Latex pages, No figure

Classical Lie algebras and Drinfeld doubles

The Drinfeld double structure underlying the Cartan series An, Bn, Cn, Dn of simple Lie algebras is discussed. This structure is determined by two disjoint solvable subalgebras matched by a pairing. For the two nilpotent positive and negative root subalgebras the pairing is natural and in the Cartan subalgebra is defined with the help of a central extension of the algebra. A new completely determined basis is found from the compatibility conditions in the double and a different perspective for quantization is presented. Other related Drinfeld doubles on C are also considered.Comment: 11 pages. submitted for publication to J. Physics

Correlation length of the two-dimensional Ising spin glass with bimodal interactions

We study the correlation length of the two-dimensional Edwards-Anderson Ising spin glass with bimodal interactions using a combination of parallel tempering Monte Carlo and a rejection-free cluster algorithm in order to speed up equilibration. Our results show that the correlation length grows ~ exp(2J/T) suggesting through hyperscaling that the degenerate ground state is separated from the first excited state by an energy gap ~4J, as would naively be expected.Comment: 5 pages, 4 figures, 2 table

Evaluation of additional head of biceps brachii: a study with autopsy material

Additional head of the biceps brachii (AHBB) has been reported in different population groups with a frequency of 1–25%. The purpose of this study was to determine the incidence and morphologic expression of the AHBB as determined in a sample of the Colombian population. An exploration was conducted with 106 arms corresponding to unclaimed corpses autopsied at Institute of Legal and Forensic Medicine of Bucaramanga, Colombia. Using medial incision involvingskin, subcutaneous tissue, and brachial fascia, the heads of the biceps and their innervating branches were visualised. One AHBB was observed in 21 (19.8%) of the arms evaluated, with non-significant difference (p = 0.568) per side of presentation: 11 (52.4%) cases on the right side and 10 (47.6%) on the left side. All AHBBs were originated in the infero-medial segment of the humerus, with a mean thickness of 17.8 ± 6.8 mm. In 4 (19%) cases the fascicle was thin, less than 10 mm; in 7 (33.3%) cases it was of medium thickness, between 11 and 20 mm, whereas in 47.6% it was longer than 20 mm. The length of the AHBB was 118.3 ± 26.8 mm; its motor point supplied by the musculocutaneous nerve was located at 101.3 ± 20.9 mm of the bi-epicondylar line. The incidence of AHBB in this study is located at the upper segment of what has been reportedin the literature and could be a morphologic trait of the Colombian population; in agreement with prior studies, the origin was the infero-medial surface of the humerus

Characterisation of myocardial bridges in pigs: a comparative anatomical analysis with the human heart

Background: Few studies have been conducted in pigs concerning the presence of myocardial bridges (MB) on the coronary arteries and their branches, and some of them have evaluated small samples. The objective of this study was to characterise MB in pigs of commercial breeds. Materials and methods: One hundred and fifty eight hearts of pigs destined to the slaughterhouse with stunning method were studied. The coronary arteries were perfused with polyester resin (palatal 85% and styrene 15%) and then subjected to potassium hydroxide infusion to remove the subepicardial fat. Results: Ninety three MB were found in 67 (42.4%) specimens, 43 (46%) of which were located on branches of the right coronary artery, 38 (41%) on branches of the left coronary artery and 12 (13%) on both vessels. The MB occurred in 26 (38.8%) females and 41 (61.2%) males, but the difference was not statistically significant (p = 0.23). Single MB were most common (70%), followed by the presence of 2 (21%) MB in different vessels. the subsinusal interventricular artery was the vascular structure with the largest number of MB (46.2%), with its middle third being the most compromised segment (79%). The mean length of the MB was 11.23 ± 5.67 mm and the thickness of the suprapontine myocardium was 1.13 ± 0.48 mm. Conclusions: The frequency, localisation, and length of the MB reported in pigs are consistent with the findings of the present study, whereas in humans the MB involve mainly the anterior interventricular artery and are longer

A systematic construction of completely integrable Hamiltonians from coalgebras

A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum deformations can be interpreted as generating structures for integrable deformations of Hamiltonian systems with coalgebra symmetry. In order to illustrate this general method, the $so(2,1)$ algebra and the oscillator algebra $h_4$ are used to derive new classical integrable systems including a generalization of Gaudin-Calogero systems and oscillator chains. Quantum deformations are then used to obtain some explicit integrable deformations of the previous long-range interacting systems and a (non-coboundary) deformation of the $(1+1)$ Poincar\'e algebra is shown to provide a new Ruijsenaars-Schneider-like Hamiltonian.Comment: 26 pages, LaTe

Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits

Multiparametric quantum deformations of $gl(2)$ are studied through a complete classification of $gl(2)$ Lie bialgebra structures. From them, the non-relativistic limit leading to harmonic oscillator Lie bialgebras is implemented by means of a contraction procedure. New quantum deformations of $gl(2)$ together with their associated quantum $R$-matrices are obtained and other known quantizations are recovered and classified. Several connections with integrable models are outlined.Comment: 21 pages, LaTeX. To appear in J. Phys. A. New contents adde

Quantum E(2) groups and Lie bialgebra structures

Lie bialgebra structures on $e(2)$ are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical $r$-matrix) we solve the cocycle condition, find the Lie-Poisson brackets and obtain quantum group relations. There is one to one correspondence between Lie bialgebra structures on $e(2)$ and possible quantum deformations of $U(e(2))$ and $E(2)$.Comment: 8 pages, plain TEX, harvmac, to appear in J. Phys.

Integrable deformations of oscillator chains from quantum algebras

A family of completely integrable nonlinear deformations of systems of N harmonic oscillators are constructed from the non-standard quantum deformation of the sl(2,R) algebra. Explicit expressions for all the associated integrals of motion are given, and the long-range nature of the interactions introduced by the deformation is shown to be linked to the underlying coalgebra structure. Separability and superintegrability properties of such systems are analysed, and their connection with classical angular momentum chains is used to construct a non-standard integrable deformation of the XXX hyperbolic Gaudin system.Comment: 15 pages, LaTe