On the spectrum-generating superalgebras of the deformed one-dimensional quantum oscillators

We investigate the dynamical symmetry superalgebras of the one-dimensional Matrix Superconformal Quantum Mechanics with inverse-square potential. They act as spectrum-generating superalgebras for the systems with the addition of the de Alfaro-Fubini-Furlan oscillator term. The undeformed quantum oscillators are expressed by $2^n\times 2^n$ supermatrices; their corresponding spectrum-generating superalgebras are given by the $osp(2n|2)$ series. For $n=1$ the addition of a inverse-square potential does not break the $osp(2|2)$ spectrum-generating superalgebra. For $n=2$ two cases of inverse-square potential deformations arise. The first one produces Klein deformed quantum oscillators; the corresponding spectrum-generating superalgebras are given by the $D(2,1;\alpha)$ class, with $\alpha$ determining the inverse-square potential coupling constants. The second $n=2$ case corresponds to deformed quantum oscillators of non-Klein type. In this case the $osp(4|2)$ spectrum-generating superalgebra of the undeformed theory is broken to $osp(2|2)$. The choice of the Hilbert spaces corresponding to the admissible range of the inverse-square potential coupling constants and the possible direct sum of lowest weight representations of the spectrum-generating superalgebras is presented.Comment: Final version to appear in J. Math. Phys.; three references adde

Combining Text and Formula Queries in Math Information Retrieval: Evaluation of Query Results Merging Strategies

Specific to Math Information Retrieval is combining text with mathematical formulae both in documents and in queries. Rigorous evaluation of query expansion and merging strategies combining math and standard textual keyword terms in a query are given. It is shown that techniques similar to those known from textual query processing may be applied in math information retrieval as well, and lead to a cutting edge performance. Striping and merging partial results from subqueries is one technique that improves results measured by information retrieval evaluation metrics like Bpref

Spectral analysis and an area-preserving extension of a piecewise linear intermittent map

We investigate spectral properties of a 1-dimensional piecewise linear intermittent map, which has not only a marginal fixed point but also a singular structure suppressing injections of the orbits into neighborhoods of the marginal fixed point. We explicitly derive generalized eigenvalues and eigenfunctions of the Frobenius--Perron operator of the map for classes of observables and piecewise constant initial densities, and it is found that the Frobenius--Perron operator has two simple real eigenvalues 1 and $\lambda_d \in (-1,0)$, and a continuous spectrum on the real line $[0,1]$. From these spectral properties, we also found that this system exhibits power law decay of correlations. This analytical result is found to be in a good agreement with numerical simulations. Moreover, the system can be extended to an area-preserving invertible map defined on the unit square. This extended system is similar to the baker transformation, but does not satisfy hyperbolicity. A relation between this area-preserving map and a billiard system is also discussed.Comment: 12 pages, 3 figure

Strong parity mixing in the FFLO superconductivity in systems with coexisting spin and charge fluctuations

We study the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of spin fluctuation mediated pairing, and focus on the effect of coexisting charge fluctuations. We find that (i) consecutive transitions from singlet pairing to FFLO and further to $S_z=1$ triplet pairing can generally take place upon increasing the magnetic field when strong charge fluctuations coexist with spin fluctuations, and (ii) the enhancement of the charge fluctuations lead to a significant increase of the parity mixing in the FFLO state, where the triplet/singlet component ratio in the gap function can be close to unity. We propose that such consecutive pairing state transition and strong parity mixing in the FFLO state may take place in a quasi-one-dimensional organic superconductor (TMTSF)$_2X$.Comment: 5 pages, 5 figures. To be published in Phys. Rev. Let

Laughlin states on the Poincare half-plane and its quantum group symmetry

We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.Comment: 9 pages,Late

Quantum group symmetry of the Quantum Hall effect on the non-flat surfaces

After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a first example we show that the $su(2)$ symmetry of the QHE on sphere leads to $su_q(2)$ algebra in the equator . We explain this result by a contraction of $su(2)$ . Secondly , with the help of the symmetry operators of QHE on the Pioncare upper half plane , we will show that the ground state wave functions form a representation of the $su_q(2)$ algebra .Comment: 8 pages,latex,no figur

Mechanism for the Singlet to Triplet Superconductivity Crossover in Quasi-One-Dimensional Organic Conductors

Superconductivity of quasi-one-dimensional organic conductors with a quarter-filled band is investigated using the two-loop renormalization group approach to the extended Hubbard model for which both the single electron hopping t_{\perp} and the repulsive interaction V_{\perp} perpendicular to the chains are included. For a four-patches Fermi surface with deviations to perfect nesting, we calculate the response functions for the dominant fluctuations and possible superconducting states. By increasing V_{\perp}, it is shown that a d-wave (singlet) to f-wave (triplet) superconducting state crossover occurs, and is followed by a vanishing spin gap. Furthermore, we study the influence of a magnetic field through the Zeeman coupling, from which a triplet superconducting state is found to emerge.Comment: 11 pages, 15 figures, published versio

Generalized boson algebra and its entangled bipartite coherent states

Starting with a given generalized boson algebra U_(h(1)) known as the bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ the Hopf duality arguments to provide the dually conjugate function algebra Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a closed form expression of the universal T matrix that caps the duality and generalizes the familiar exponential map relating a Lie algebra with its corresponding group. Subsequently, using an inverse Mellin transform approach, the coherent states of single-node systems subject to the U_(h(1)) symmetry are found to be complete with a positive-definite integration measure. Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur

Patterns in the Fermion Mixing Matrix, a bottom-up approach

We first obtain the most general and compact parametrization of the unitary transformation diagonalizing any 3 by 3 hermitian matrix H, as a function of its elements and eigenvalues. We then study a special class of fermion mass matrices, defined by the requirement that all of the diagonalizing unitary matrices (in the up, down, charged lepton and neutrino sectors) contain at least one mixing angle much smaller than the other two. Our new parametrization allows us to quickly extract information on the patterns and predictions emerging from this scheme. In particular we find that the phase difference between two elements of the two mass matrices (of the sector in question) controls the generic size of one of the observable fermion mixing angles: i.e. just fixing that particular phase difference will "predict" the generic value of one of the mixing angles, irrespective of the value of anything else.Comment: 29 pages, 3 figures, references added, to appear in PR

Isomorphisms between Quantum Group Covariant q-Oscillator Systems Defined for q and 1/q

It is shown that there exists an isomorphism between q-oscillator systems covariant under $SU_q(n)$ and $SU_{q^{-1}}(n)$. By the isomorphism, the defining relations of $SU_{q^{-1}}(n)$ covariant q-oscillator system are transmuted into those of $SU_q(n)$. It is also shown that the similar isomorphism exists for the system of q-oscillators covariant under the quantum supergroup $SU_q(n/m)$. Furthermore the cases of q-deformed Lie (super)algebras constructed from covariant q-oscillator systems are considered. The isomorphisms between q-deformed Lie (super)algebras can not obtained by the direct generalization of the one for covariant q-oscillator systems.Comment: LaTeX 13pages, RCNP-07