1,704 research outputs found
A model for the continuous q-ultraspherical polynomials
We provide an algebraic interpretation for two classes of continuous
-polynomials. Rogers' continuous -Hermite polynomials and continuous
-ultraspherical polynomials are shown to realize, respectively, bases for
representation spaces of the -Heisenberg algebra and a -deformation of
the Euclidean algebra in these dimensions. A generating function for the
continuous -Hermite polynomials and a -analog of the Fourier-Gegenbauer
expansion are naturally obtained from these models
Temperature effects on the universal equation of state of solids
Recently it has been argued based on theoretical calculations and experimental data that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. It is shown that for many solids the input data needed to predict high temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P=0) isothermal bulk modulus; (2)it P=0 pressure derivative; (3) the P=0 volume; and (4) the P=0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found
Universality in the compressive behavior of solids
It was discovered that the isothermal equation of state for solids in compression is a simple, universal form. This single form accurately describes the pressure and bulk modulus as a function of volume for tonic, metallic, covalent, and rare gas solids
A Super-Integrable Discretization of the Calogero Model
A time-discretization that preserves the super-integrability of the Calogero
model is obtained by application of the integrable time-discretization of the
harmonic oscillator to the projection method for the Calogero model with
continuous time. In particular, the difference equations of motion, which
provide an explicit scheme for time-integration, are explicitly presented for
the two-body case. Numerical results exhibit that the scheme conserves all
the conserved quantities of the (two-body) Calogero model with a
precision of the machine epsilon times the number of iterations.Comment: 22 pages, 5 figures. Added references. Corrected typo
An Algebraic Model for the Multiple Meixner Polynomials of the First Kind
An interpretation of the multiple Meixner polynomials of the first kind is
provided through an infinite Lie algebra realized in terms of the creation and
annihilation operators of a set of independent oscillators. The model is used
to derive properties of these orthogonal polynomials
The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)
The algebra H of the dual -1 Hahn polynomials is derived and shown to arise
in the Clebsch-Gordan problem of sl_{-1}(2). The dual -1 Hahn polynomials are
the bispectral polynomials of a discrete argument obtained from a q-> -1 limit
of the dual q-Hahn polynomials. The Hopf algebra sl_{-1}(2) has four generators
including an involution, it is also a q-> -1 limit of the quantum algebra
sl_{q}(2) and furthermore, the dynamical algebra of the parabose oscillator.
The algebra H, a two-parameter generalization of u(2) with an involution as
additional generator, is first derived from the recurrence relation of the -1
Hahn polynomials. It is then shown that H can be realized in terms of the
generators of two added sl_{-1}(2) algebras, so that the Clebsch-Gordan
coefficients of sl_{-1}(2) are dual -1 Hahn polynomials. An irreducible
representation of H involving five-diagonal matrices and connected to the
difference equation of the dual -1 Hahn polynomials is constructed.Comment: 15 pages, Some minor changes from version #
The Dynamics of Sustained Reentry in a Loop Model with Discrete Gap Junction Resistance
Dynamics of reentry are studied in a one dimensional loop of model cardiac
cells with discrete intercellular gap junction resistance (). Each cell is
represented by a continuous cable with ionic current given by a modified
Beeler-Reuter formulation. For below a limiting value, propagation is found
to change from period-1 to quasi-periodic () at a critical loop length
() that decreases with . Quasi-periodic reentry exists from
to a minimum length () that is also shortening with .
The decrease of is not a simple scaling, but the bifurcation can
still be predicted from the slope of the restitution curve giving the duration
of the action potential as a function of the diastolic interval. However, the
shape of the restitution curve changes with .Comment: 6 pages, 7 figure
How to construct spin chains with perfect state transfer
It is shown how to systematically construct the quantum spin chains with
nearest-neighbor interactions that allow perfect state transfer (PST). Sets of
orthogonal polynomials (OPs) are in correspondence with such systems. The key
observation is that for any admissible one-excitation energy spectrum, the
weight function of the associated OPs is uniquely prescribed. This entails the
complete characterization of these PST models with the mirror symmetry property
arising as a corollary. A simple and efficient algorithm to obtain the
corresponding Hamiltonians is presented. A new model connected to a special
case of the symmetric -Racah polynomials is offered. It is also explained
how additional models with PST can be derived from a parent system by removing
energy levels from the one-excitation spectrum of the latter. This is achieved
through Christoffel transformations and is also completely constructive in
regards to the Hamiltonians.Comment: 7 page
A CMOS silicon spin qubit
Silicon, the main constituent of microprocessor chips, is emerging as a
promising material for the realization of future quantum processors. Leveraging
its well-established complementary metal-oxide-semiconductor (CMOS) technology
would be a clear asset to the development of scalable quantum computing
architectures and to their co-integration with classical control hardware. Here
we report a silicon quantum bit (qubit) device made with an industry-standard
fabrication process. The device consists of a two-gate, p-type transistor with
an undoped channel. At low temperature, the first gate defines a quantum dot
(QD) encoding a hole spin qubit, the second one a QD used for the qubit
readout. All electrical, two-axis control of the spin qubit is achieved by
applying a phase-tunable microwave modulation to the first gate. Our result
opens a viable path to qubit up-scaling through a readily exploitable CMOS
platform.Comment: 12 pages, 4 figure
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