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

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

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 ($Q$) and an anti-quark ($\bar{Q}$) 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 $Q\bar{Q}$ 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 $Q\bar{Q}$ can also be checked from the structure of the SPF. To test this idea, quenched QCD simulations on anisotropic lattices ($a_\sigma=4a_\tau=0.039\rm fm$, $N^3_\sigma \times N_{\tau} =20^2 \times (96-32)$) are performed. The real part of the proper potential below the deconfinement temperature ($T=0.78T_c$) exhibits the well known Coulombic and confining behavior. At ($T=2.33T_c$) 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

Population of the Galactic X-ray binaries and eRosita

The population of the Galactic X-ray binaries has been mostly probed with moderately sensitive hard X-ray surveys so far. The eRosita mission will provide, for the first time a sensitive all-sky X-ray survey in the 2-10 keV energy range, where the X-ray binaries emit most of the flux and discover the still unobserved low-luminosity population of these objects. In this paper, we briefly review the current constraints for the X-ray luminosity functions of high- and low-mass X-ray binaries and present our own analysis based the INTEGRAL 9-year Galactic survey, which yields improved constraints. Based on these results, we estimate the number of new XRBs to be detected in the eRosita all-sky surveyComment: accepted for publication in A&

Generalised Calogero-Moser models and universal Lax pair operators

Calogero-Moser models can be generalised for all of the finite reflection groups. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H_3, H_4, and the dihedral group I_2(m), besides the well-known ones based on crystallographic root systems, namely those associated with Lie algebras. Universal Lax pair operators for all of the generalised Calogero-Moser models and for any choices of the potentials are constructed as linear combinations of the reflection operators. The consistency conditions are reduced to functional equations for the coefficient functions of the reflection operators in the Lax pair. There are only four types of such functional equations corresponding to the two-dimensional sub-root systems, A_2, B_2, G_2, and I_2(m). The root type and the minimal type Lax pairs, derived in our previous papers, are given as the simplest representations. The spectral parameter dependence plays an important role in the Lax pair operators, which bear a strong resemblance to the Dunkl operators, a powerful tool for solving quantum Calogero-Moser models.Comment: 37 pages, LaTeX2e, no macro, no figur

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