5,157 research outputs found
Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
We investigate a U(1) gauge invariant quantum mechanical system on a 2D
noncommutative space with coordinates generating a generalized deformed
oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge
covariant derivatives obeying the nonlinear Dolan-Grady relations. This
restricts the structure function of the deformed oscillator algebra to a
quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R)
algebras are investigated in detail. Reducing the Hamiltonian to 1D
finite-difference quasi-exactly solvable operators, we demonstrate partial
algebraization of the spectrum of the corresponding systems on the fuzzy sphere
and noncommutative hyperbolic plane. A completely covariant method based on the
notion of intrinsic algebra is proposed to deal with the spectral problem of
such systems.Comment: 25 pages; ref added; to appear in J. Phys.
Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
In this paper we study the Pettis integral of fuzzy mappings in arbitrary
Banach spaces. We present some properties of the Pettis integral of fuzzy
mappings and we give conditions under which a scalarly integrable fuzzy mapping
is Pettis integrable
Implications of Minimal Length Scale on the Statistical Mechanics of Ideal Gas
Several alternative approaches to quantum gravity problem suggest the
modification of the {\it fundamental volume } of the accessible
phase space for representative points. This modified fundamental volume has a
novel momentum dependence. In this paper, we study the effects of this
modification on the thermodynamics of an ideal gas within the microcanonical
ensemble and using the generalized uncertainty principle(GUP). Although the
induced modifications are important only in quantum gravity era, possible
experimental manifestation of these effects may provides strong support for
underlying quantum gravity proposal.Comment: 14 Pages, No Figures, Title Changed, Revised Versio
String states, loops and effective actions in noncommutative field theory and matrix models
Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string
states as a tool for loop computations in noncommutative field theory and
matrix models. Defined in terms of coherent states, they exhibit the stringy
features of noncommutative field theory. This leads to a closed form for the
1-loop effective action in position space, capturing the long-range non-local
UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces.
The non-locality is tamed in the maximally supersymmetric IKKT or IIB model,
where it gives rise to supergravity. The linearized supergravity interactions
are obtained directly in position space at one loop using string states on
generic noncommutative branes.Comment: 31 pages, 2 figure
Fractional quantum Hall effect on the two-sphere: a matrix model proposal
We present a Chern-Simons matrix model describing the fractional quantum Hall
effect on the two-sphere. We demonstrate the equivalence of our proposal to
particular restrictions of the Calogero-Sutherland model, reproduce the quantum
states and filling fraction and show the compatibility of our result with the
Haldane spherical wavefunctions.Comment: 26 pages, LaTeX, no figures, references adde
Recommended from our members
Aggregation functions with given super-additive and sub-additive transformations
Aggregation functions and their transformations have found numerous applications in various kinds of systems as well as in economics and social science. Every aggregation function is known to be bounded above and below by its super-additive and sub-additive transformations. We are interested in the “inverse” problem of whether or not every pair consisting of a super-additive function dominating a sub-additive function comes from some aggregation function in the above sense. Our main results provide a negative answer under mild extra conditions on the super- and sub-additive pair. We also show that our results are, in a sense, best possible
Weighted lattice polynomials of independent random variables
We give the cumulative distribution functions, the expected values, and the
moments of weighted lattice polynomials when regarded as real functions of
independent random variables. Since weighted lattice polynomial functions
include ordinary lattice polynomial functions and, particularly, order
statistics, our results encompass the corresponding formulas for these
particular functions. We also provide an application to the reliability
analysis of coherent systems.Comment: 14 page
- …