2,007 research outputs found
Pathologies of Quenched Lattice QCD at non--zero Density and its Effective Potential
We simulate lattice QCD at non--zero baryon density and zero temperature in
the quenched approximation, both in the scaling region and in the infinite
coupling limit. We investigate the nature of the forbidden region -- the range
of chemical potential where the simulations grow prohibitively expensive, and
the results, when available, are puzzling if not unphysical. At weak coupling
we have explored the sensitivity of these pathologies to the lattice size, and
found that using a large lattice () does not remove them. The
effective potential sheds considerable light on the problems in the
simulations, and gives a clear interpretation of the forbidden region. The
strong coupling simulations were particularly illuminating on this point.Comment: 49 pages, uu-encoded expanding to postscript;also available at
ftp://hlrz36.hlrz.kfa-juelich.de/pub/mpl/hlrz72_95.p
QCD at finite isospin density
QCD at finite isospin chemical potential mu_I has no fermion sign problem and
can be studied on the lattice. We solve this theory analytically in two limits:
at low mu_I where chiral perturbation theory is applicable, and at
asymptotically high mu_I where perturbative QCD works. At low isospin density
the ground state is a pion condensate, whereas at high density it is a Fermi
liquid with Cooper pairing. The pairs carry the same quantum numbers as the
pion. This leads us to a conjecture that the transition from hadron to quark
matter is smooth, which passes several tests. Our results imply a nontrivial
phase diagram in the space of temperature and chemical potentials of isospin
and baryon number.Comment: 4 pages, 1 figure, version to appear in PR
Quantum Simulation of Quantum Field Theories in Trapped Ions
We propose the quantum simulation of a fermion and an antifermion field modes
interacting via a bosonic field mode, and present a possible implementation
with two trapped ions. This quantum platform allows for the scalable add-up of
bosonic and fermionic modes, and represents an avenue towards quantum
simulations of quantum field theories in perturbative and nonperturbative
regimes.Comment: To be published in Physical Review Letter
Approximation of optimal control problems in the coefficient for the p-Laplace equation. I. Convergence result
We study a Dirichlet optimal control problem for a quasi-linear monotone elliptic equation, the so-called weighted p-Laplace problem. The coefficient of the p-Laplacian, the weight u, we take as a control in BV (Ω) â© Lâ(Ω). In this article, we use box-type constraints for the control such that there is a strictly positive lower and some upper bound. In order to handle the inherent degeneracy of the p-Laplacian, we use a regularization, sometimes referred to as the Δ-p-Laplacian. We derive existence and uniqueness of solutions to the underlying boundary value problem and the optimal control problem. In fact, we introduce a two-parameter model for the weighted Δ-p- Laplacian, where we approximate the nonlinearity by a bounded monotone function, parametrized by k. Further, we discuss the asymptotic behavior of the solutions to the regularized problem on each (Δ, k)-level as the parameters tend to zero and infinity, respectively.This authorâs research was supported by the DFG-EC315 âEngineering of Advanced Materialsâ and by the Spanish Ministerio de EconomĂa y Competitividad under projects MTM2011-22711 and MTM2014-57531-P
Microwave Oscillator with the Shielded Dielectric Resonator
A Gunn oscillator with partially shielded hemidisk quasioptical resonator is investigated experimentally in this paper. The investigations of the generation characteristics of oscillations by the semiconductor diode in this resonator are carried out for the different radial co-ordinates of the oscillator active element. The advantages of the investigated oscillator in comparison with the oscillator with an open dielectric resonator are show
Gunn Oscillators Based on Shielded Dielectric Resonators with Mechanical Frequency Tuning
The features of Gunn oscillators based on shielded dielectric resonators with whispering gallery modes and ray oscillations are investigated. Their comparative analysis for oscillators with different dielectric resonant structures is carried out
Quenched QCD at finite density
Simulations of quenched at relatively small but {\it nonzero} chemical
potential on lattices indicate that the nucleon
screening mass decreases linearly as increases predicting a critical
chemical potential of one third the nucleon mass, , by extrapolation.
The meson spectrum does not change as increases over the same range, from
zero to . Past studies of quenched lattice QCD have suggested that
there is phase transition at . We provide alternative
explanations for these results, and find a number of technical reasons why
standard lattice simulation techniques suffer from greatly enhanced
fluctuations and finite size effects for ranging from to
. We find evidence for such problems in our simulations, and suggest
that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte
Thermodynamics of two-colour QCD and the Nambu Jona-Lasinio model
We investigate two-flavour and two-colour QCD at finite temperature and
chemical potential in comparison with a corresponding Nambu and Jona-Lasinio
model. By minimizing the thermodynamic potential of the system, we confirm that
a second order phase transition occurs at a value of the chemical potential
equal to half the mass of the chiral Goldstone mode. For chemical potentials
beyond this value the scalar diquarks undergo Bose condensation and the diquark
condensate is nonzero. We evaluate the behaviour of the chiral condensate, the
diquark condensate, the baryon charge density and the masses of scalar diquark,
antidiquark and pion, as functions of the chemical potential. Very good
agreement is found with lattice QCD (N_c=2) results. We also compare with a
model based on leading-order chiral effective field theory.Comment: 24 pages, 12 figure
High density QCD with static quarks
We study lattice QCD in the limit that the quark mass and chemical potential
are simultaneously made large, resulting in a controllable density of quarks
which do not move. This is similar in spirit to the quenched approximation for
zero density QCD. In this approximation we find that the deconfinement
transition seen at zero density becomes a smooth crossover at any nonzero
density, and that at low enough temperature chiral symmetry remains broken at
all densities.Comment: LaTeX, 18 pages, uses epsf.sty, postscript figures include
Simplicial Chiral Models
Principal chiral models on a d-1 dimensional simplex are introduced and
studied analytically in the large limit. The and
models are explicitly solved. Relationship with standard lattice models and
with few-matrix systems in the double scaling limit are discussed.Comment: 6 pages, PHYZZ
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