28,150 research outputs found
Energy Spectra for Fractional Quantum Hall States
Fractional quantum Hall states (FQHS) with the filling factor nu = p/q of q <
21 are examined and their energies are calculated. The classical Coulomb energy
is evaluated among many electrons; that energy is linearly dependent on 1/nu.
The residual binding energies are also evaluated. The electron pair in nearest
Landau-orbitals is more affected via Coulomb transition than an electron pair
in non-nearest orbitals. Each nearest electron pair can transfer to some empty
orbital pair, but it cannot transfer to the other empty orbital pair because of
conservation of momentum. Counting the numbers of the allowed and forbidden
transitions, the binding energies are evaluated for filling factors of 126
fraction numbers. Gathering the classical Coulomb energy and the pair
transition energy, we obtain the spectrum of energy versus nu. This energy
spectrum elucidates the precise confinement of Hall resistance at specific
fractional filling factors.Comment: 5 pages, 3 figure
Optimal phase estimation and square root measurement
We present an optimal strategy having finite outcomes for estimating a single
parameter of the displacement operator on an arbitrary finite dimensional
system using a finite number of identical samples. Assuming the uniform {\it a
priori} distribution for the displacement parameter, an optimal strategy can be
constructed by making the {\it square root measurement} based on uniformly
distributed sample points. This type of measurement automatically ensures the
global maximality of the figure of merit, that is, the so called average score
or fidelity. Quantum circuit implementations for the optimal strategies are
provided in the case of a two dimensional system.Comment: Latex, 5 figure
Calogero-Moser Models III: Elliptic Potentials and Twisting
Universal Lax pairs of the root type with spectral parameter and independent
coupling constants for twisted non-simply laced Calogero-Moser models are
constructed. Together with the Lax pairs for the simply laced models and
untwisted non-simply laced models presented in two previous papers, this
completes the derivation of universal Lax pairs for all of the Calogero-Moser
models based on root systems. As for the twisted models based on B_n, C_n and
BC_nroot systems, a new type of potential term with independent coupling
constants can be added without destroying integrability. They are called
extended twisted models. All of the Lax pairs for the twisted models presented
here are new, except for the one for the F_4 model based on the short roots.
The Lax pairs for the twisted G_2 model have some novel features. Derivation of
various functions, twisted and untwisted, appearing in the Lax pairs for
elliptic potentials with the spectral parameter is provided. The origin of the
spectral parameter is also naturally explained. The Lax pairs with spectral
parameter, twisted and untwisted, for the hyperbolic, the trigonometric and the
rational potential models are obtained as degenerate limits of those for the
elliptic potential models.Comment: LaTeX2e with amsfonts.sty, 36 pages, no figure
Realization of a collective decoding of codeword states
This was also extended from the previous article quant-ph/9705043, especially
in a realization of the decoding process.Comment: 6 pages, RevTeX, 4 figures(EPS
I=2 Two-Pion Wave Function and Scattering Phase Shift
We calculate a two-pion wave function for the I=2 -wave two-pion system
with a finite scattering momentum and estimate the interaction range between
two pions, which allows us to examine the validity of a necessary condition for
the finite size formula presented by Rummukainen and Gottlieb. We work in the
quenched approximation employing the plaquette gauge action for gluons and the
improved Wilson action for quarks at on
lattice. The quark masses are chosen to give , 0.488 and . We find that the energy dependence of the interaction range is
small and the necessary condition is satisfied for our range of the quark mass
and the scattering momentum, . We also find that the
scattering phase shift can be obtained with a smaller statistical error from
the two-pion wave function than from the two-pion time correlator.Comment: 23 pages, 7 figures, added a reference (Phys.Rev.D73:054503,2006) in
v
Proper heavy-quark potential from a spectral decomposition of the thermal Wilson loop
We propose a non-perturbative and gauge invariant derivation of the static
potential between a heavy-quark () and an anti-quark () at finite
temperature. This proper potential is defined through the spectral function
(SPF) of the thermal Wilson loop and can be shown to satisfy the
Schr\"{o}dinger equation for the heavy pair in the thermal medium.
In general, the proper potential has a real and an imaginary part,corresponding
to the peak position and width of the SPF. The validity of using a
Schr\"{o}dinger equation for heavy can also be checked from the
structure of the SPF. To test this idea, quenched QCD simulations on
anisotropic lattices (, ) are performed. The real part of the proper
potential below the deconfinement temperature () exhibits the well
known Coulombic and confining behavior. At () we find that it
coincides with the Debye screened potential obtained from Polyakov-line
correlations in the color-singlet channel under Coulomb gauge fixing. The
physical meaning of the spectral structure of the thermal Wilson loop and the
use of the maximum entropy method (MEM) to extract the real and imaginary part
of the proper potential are also discussed.Comment: 7 pages, 8 figures, Talk given at the XXVII International Symposium
on Lattice Field Theory (LATTICE 2009), July 25-31, 2009, Beijing, Chin
Dirty two-band superconductivity with interband pairing order
We study theoretically the effects of random nonmagnetic impurities on the
superconducting transition temperature in a two-band superconductor
characterized by an equal-time s-wave interband pairing order parameter. The
Fermi-Dirac statistics of electrons allows a spin-triplet s-wave pairing order
as well as a spin-singlet s-wave order parameter due to the two-band degree of
freedom. In a spin-singlet superconductor, is insensitive to the impurity
concentration when we estimate the self-energy due to the random impurity
potential within the Born approximation. On the other hand in a spin-triplet
superconductor, decreases with the increase of the impurity
concentration. We conclude that Cooper pairs belonging to odd-band-parity
symmetry class are fragile under the random impurity potential even though they
have s-wave pairing symmetry.Comment: 7 pages, 2 figures embedde
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