Lessons from cosmic history: The case for a linear star formation -- H2 relation

Observations show that star formation in galaxies is closely correlated with the abundance of molecular hydrogen. Modeling this empirical relation from first principles proves challenging, however, and many questions regarding its properties remain open. For instance, the exact functional form of the relation is still debated and it is also unknown whether it applies at z>4, where CO observations are sparse. Here, we analyze how the shape of the star formation -- gas relation affects the cosmic star formation history and global galaxy properties using an analytic model that follows the average evolution of galaxies in dark matter halos across cosmic time. We show that a linear relation with an H2 depletion time of ~2.5 Gyr, as found in studies of nearby galaxies, results in good agreement with current observations of galaxies at both low and high redshift. These observations include the evolution of the cosmic star formation rate density, the z~4-9 UV luminosity function, the evolution of the mass -- metallicity relation, the relation between stellar and halo mass, and the gas-to-stellar mass ratios of galaxies. In contrast, the short depletion times that result from adopting a highly super-linear star formation -- gas relation lead to large star formation rates, substantial metal enrichment (~0.1 solar), and low gas-to-stellar mass ratios already at z~10, in disagreement with observations. These results can be understood in terms of an equilibrium picture of galaxy evolution in which gas inflows, outflows, and star formation drive the metallicities and gas fractions toward equilibrium values that are determined by the ratio of the accretion time to the gas depletion time. In this picture, the cosmic modulation of the accretion rate is the primary process that drives the evolution of stellar masses, gas masses, and metallicities of galaxies from high redshift until today.Comment: 22 pages, 13 figures, minor revision after referee repor

Random Magnetic Interactions and Spin Glass Order Competing with Superconductivity: Interference of the Quantum Parisi Phase

We analyse the competition between spin glass (SG) order and local pairing superconductivity (SC) in the fermionic Ising spin glass with frustrated fermionic spin interaction and nonrandom attractive interaction. The phase diagram is presented for all temperatures T and chemical potentials \mu. SC-SG transitions are derived for the relevant ratios between attractive and frustrated-magnetic interaction. Characteristic features of pairbreaking caused by random magnetic interaction and/or by spin glass proximity are found. The existence of low-energy excitations, arising from replica permutation symmetry breaking (RPSB) in the Quantum Parisi Phase, is shown to be relevant for the SC-SG phase boundary. Complete 1-step RPSB-calculations for the SG-phase are presented together with a few results for infinity-step breaking. Suppression of reentrant SG - SC - SG transitions due to RPSB is found and discussed in context of ferromagnet - SG boundaries. The relative positioning of the SC and SG phases presents a theoretical landmark for comparison with experiments in heavy fermion systems and high T_c superconductors. We find a crossover line traversing the SG-phase with (\mu=0,T=0) as its quantum critical (end)point in complete RPSB, and scaling is proposed for its vicinity. We argue that this line indicates a random field instability and suggest Dotsenko-Mezard vector replica symmetry breaking to occur at low temperatures beyond.Comment: 24 pages, 14 figures replaced by published versio

Semi-fermionic representation of SU(N) Hamiltonians

We represent the generators of the SU(N) algebra as bilinear combinations of Fermi operators with imaginary chemical potential. The distribution function, consisting of a minimal set of discrete imaginary chemical potentials, is found for arbitrary N. This representation leads to the conventional temperature diagram technique with standard Feynman codex, except that the Matsubara frequencies are determined by neither integer nor half-integer numbers. The real-time Schwinger-Keldysh formalism is formulated in the framework of complex distribution functions. We discuss the continuous large N and SU(2) large spin limits. We illustrate the application of this technique for magnetic and spin-liquid states of the Heisenberg model.Comment: 11 pages, 7 EPS figures included, extended versio

The Overlap Representation of Skewed Quark and Gluon Distributions

Within the framework of light-cone quantisation we derive the complete and exact overlap representation of skewed parton distributions for unpolarised and polarised quarks and gluons. Symmetry properties and phenomenological applications are discussed.Comment: LaTex, 36 pages. v2: incorrect paper attached originally. v3: erratum adde

Pseudogaps and Charge Band in the Parisi Solution of Insulating and Superconducting Electronic Spin Glasses at Arbitrary Fillings

We report progress in understanding the fermionic Ising spin glass with arbitrary filling. A crossover from a magnetically disordered single band phase via two intermediate bands just below the freezing temperature to a 3-band structure at still lower temperatures - beyond an almost random field instability - is shown to emerge in the magnetic phase. An attempt is made to explain the exact solution in terms of a quantum Parisi phase. A central nonmagnetic band is found and seen to become sharply separated at T=0 by gaps from upper and lower magnetic bands. The gap sizes tend towards zero as the number of replica symmetry breaking steps increases towards infinity. In an extended model, the competition between local pairing superconductivity and spin glass order is discussed.Comment: 3 pages, contribution to "ECRYS-99

A Discrete Four Stroke Quantum Heat Engine Exploring the Origin of Friction

The optimal power performance of a first principle quantum heat engine model shows friction-like phenomena when the internal fluid Hamiltonian does not commute with the external control field. The model is based on interacting two-level-systems where the external magnetic field serves as a control variable.Comment: 4 pages 3 figure

See-Saw Masses for Quarks and Leptons in SU(5)

We build on a recent paper by Grinstein, Redi and Villadoro, where a see-saw like mechanism for quark masses was derived in the context of spontaneously broken gauged flavour symmetries. The see-saw mechanism is induced by heavy Dirac fermions which are added to the Standard Model spectrum in order to render the flavour symmetries anomaly-free. In this letter we report on the embedding of these fermions into multiplets of an SU(5) grand unified theory and discuss a number of interesting consequences.Comment: 15 pages, 4 figures (v3: outline restructured, modified mechanism to cancel anomalies