7,591 research outputs found
The quantum integrable system
The quantum integrable system is a 3D system with rational potential
related to the non-crystallographic root system . It is shown that the
gauge-rotated Hamiltonian as well as one of the integrals, when written
in terms of the invariants of the Coxeter group , is in algebraic form: it
has polynomial coefficients in front of derivatives. The Hamiltonian has
infinitely-many finite-dimensional invariant subspaces in polynomials, they
form the infinite flag with the characteristic vector \vec \al\ =\ (1,2,3).
One among possible integrals is found (of the second order) as well as its
algebraic form. A hidden algebra of the Hamiltonian is determined. It is
an infinite-dimensional, finitely-generated algebra of differential operators
possessing finite-dimensional representations characterized by a generalized
Gauss decomposition property. A quasi-exactly-solvable integrable
generalization of the model is obtained. A discrete integrable model on the
uniform lattice in a space of -invariants "polynomially"-isospectral to
the quantum model is defined.Comment: 32 pages, 3 figure
Finite Temperature Transitions in Lattice QCD with Wilson Quarks --- Chiral Transitions and the Influence of the Strange Quark ---
The nature of finite temperature transitions in lattice QCD with Wilson
quarks is studied near the chiral limit for the cases of 2, 3, and 6 flavors of
degenerate quarks (, 3, and 6) and also for the case of massless up and
down quarks and a light strange quark (). Our simulations mainly
performed on lattices with the temporal direction extension indicate
that the finite temperature transition in the chiral limit (chiral transition)
is continuous for , while it is of first order for and 6. We
find that the transition is of first order for the case of massless up and down
quarks and the physical strange quark where we obtain a value of
consistent with the physical value. We also discuss the phase
structure at zero temperature as well as that at finite temperatures.Comment: uuencoded compressed tar file, 70 pages, 32 figure
Pole dynamics for the Flierl-Petviashvili equation and zonal flow
We use a systematic method which allows us to identify a class of exact
solutions of the Flierl-Petvishvili equation. The solutions are periodic and
have one dimensional geometry. We examine the physical properties and find that
these structures can have a significant effect on the zonal flow generation.Comment: Latex 40 pages, seven figures eps included. Effect of variation of
g_3 is studied. New references adde
Non-perturbative renormalization of vector and axial vector currents in quenched QCD for a renormalization group improved gauge action
Renormalization constants of vector () and axial-vector () currents
are determined non-perturbatively in quenched QCD for an RG-improved gauge
action and a tadpole-improved clover quark action using the Schr\"odinger
functional method. Meson decay constants and show much better
scaling when and estimated for infinite physical volume are used
instead of -factors from tadpole-improved one-loop perturbation theory.Comment: Lattice2003(improve), 3 page
Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to the -particle quantum boson system with
attractive interactions. We find the full set of eigenfunctions and eigenvalues
of this many-body system and perform the summation over the entire spectrum of
excited states. It is shown that in the thermodynamic limit the problem is
reduced to the Fredholm determinant with the Airy kernel yielding the universal
Tracy-Widom distribution, which is known to describe the statistical properties
of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page
Non-perturbative renormalization of meson decay constants in quenched QCD for a renormalization group improved gauge action
Renormalization constants (-factors) of vector and axial-vector currents
are determined non-perturbatively in quenched QCD for a renormalization group
improved gauge action and a tadpole improved clover quark action using the
Schr\"odinger functional method. Non-perturbative values of -factors turn
out to be smaller than one-loop perturbative values by at lattice
spacing of 1 GeV. The pseudoscalar and vector meson decay
constants calculated with the non-perturbative -factors show a much better
scaling behavior compared to previous results obtained with tadpole improved
one-loop -factors. In particular, the non-perturbative -factors
normalized at infinite physical volume show that scaling violation of the decay
constants are within about 10% up to the lattice spacing GeV.
The continuum estimates obtained from data in the range 1 -- 2 GeV
agree with those determined from finer lattices ( GeV) with the
standard action.Comment: 19 pages, 18 eps figures. Corrected addres
I=2 Pion Scattering Length and Phase Shift with Wilson Fermions
We present preliminary results of scattering length and phase shift for I=2
S-wave system with the Wilson fermions in the quenched approximation.
The finite size method presented by L\"uscher is employed, and calculations are
carried out at on a and lattice.Comment: Lattice2001(spectrum
What Thermodynamics tells about QCD Plasma near Phase Transition
Due to a rapid change of the entropy density across the critical
temperature of the QCD phase transition, the pressure and the
energy density above generally deviate from their Stefan-Boltzmann
values. We shall demonstrate this both analytically and numerically for a
general class of consistent with thermodynamical constraints and make a
qualitative comparison of the result with the lattice QCD data. Quantities
related to such as the specific heat and sound velocity are also
discussed.Comment: 6 pages revtex, 4 postscript figure
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