Thermodynamics of two-colour QCD

We discuss the thermodynamics of two-colour QCD with four flavours of staggered quarks on 8^3x4 and 16^3x4 lattices. In our simulations we use the Naik action for the fermions and a (1,2) tree-level improved gauge action. We analyze the deconfinement and chiral phase transitions for four different quark masses (m=0.1,0.05,0.025,0.015). Contrary to three-colour QCD the peak in the Polyakov loop susceptibility decreases with decreasing quark mass. This reflects an early breaking of the string in the heavy quark potential, which we verify explicitly by calculating the heavy quark potential at finite temperature using Polyakov loop correlations.Comment: LATTICE98(hightemp), 3 pages, LaTeX2e File, 5 EPS-figures, espcrc2.st

A Gauge-fixed Hamiltonian for Lattice QCD

We study the gauge fixing of lattice QCD in 2+1 dimensions, in the Hamiltonian formulation. The technique easily generalizes to other theories and dimensions. The Hamiltonian is rewritten in terms of variables which are gauge invariant except under a single global transformation. This paper extends previous work, involving only pure gauge theories, to include matter fields.Comment: 7 pages of LaTeX, RU-92-45 and BUHEP-92-3

The non-zero baryon number formulation of QCD

We discuss the non-zero baryon number formulation of QCD in the quenched limit at finite temperature. This describes the thermodynamics of gluons in the background of static quark sources. Although a sign problem remains in this theory, our simulation results show that it can be handled quite well numerically. The transition region gets shifted to smaller temperatures and the transition region broadens with increasing baryon number. Although the action is in our formulation explicitly Z(3) symmetric the Polyakov loop expectation value becomes non-zero already in the low temperature phase and the heavy quark potential gets screened at non-vanishing number density already this phase.Comment: LATTICE99(Finite Temperature and Density), Latex2e using espcrc2.sty, 3 pages, 7 figure

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

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 ($64 \times 16^3$) 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

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

Search For Unresolved Sources In The COBE-DMR Two-Year Sky Maps

We have searched the temperature maps from the COBE Differential Microwave Radiometers (DMR) first two years of data for evidence of unresolved sources. The high-latitude sky (|b| > 30\deg) contains no sources brighter than 192 uK thermodynamic temperature (322 Jy at 53 GHz). The cumulative count of sources brighter than threshold T, N(> T), is consistent with a superposition of instrument noise plus a scale-invariant spectrum of cosmic temperature fluctuations normalized to Qrms-PS = 17 uK. We examine the temperature maps toward nearby clusters and find no evidence for any Sunyaev-Zel'dovich effect, \Delta y < 7.3 x 10^{-6} (95% CL) averaged over the DMR beam. We examine the temperature maps near the brightest expected radio sources and detect no evidence of significant emission. The lack of bright unresolved sources in the DMR maps, taken with anisotropy measurements on smaller angular scales, places a weak constraint on the integral number density of any unresolved Planck-spectrum sources brighter than flux density S, n(> S) < 2 x 10^4 (S/1 Jy)^{-2} sr^{-1}.Comment: 16 pages including 2 figures, uuencoded PostScript, COBE preprint 94-0

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

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) ∩ L∞(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 ε-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 ε-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 (ε, k)-level as the parameters tend to zero and infinity, respectively.This author’s research was supported by the DFG-EC315 “Engineering of Advanced Materials” and by the Spanish Ministerio de Economía y Competitividad under projects MTM2011-22711 and MTM2014-57531-P