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

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

Short Time Cycles of Purely Quantum Refrigerators

Four stroke Otto refrigerator cycles with no classical analogue are studied. Extremely short cycle times with respect to the internal time scale of the working medium characterize these refrigerators. Therefore these cycles are termed sudden. The sudden cycles are characterized by the stable limit cycle which is the invariant of the global cycle propagator. During their operation the state of the working medium possesses significant coherence which is not erased in the equilibration segments due to the very short time allocated. This characteristic is reflected in a difference between the energy entropy and the Von Neumann entropy of the working medium. A classification scheme for sudden refrigerators is developed allowing simple approximations for the cooling power and coefficient of performance.Comment: 20 pages, 12 figures. Among the figures there are 6 figures which are double, namely with two parts, Top and Botto

How to evaluate ground-state landscapes of disordered systems thermodynamical correctly

Ground states of three-dimensional EA Ising spin glasses are calculated for sizes up to 14^3 using a combination of a genetic algorithm and cluster-exact approximation. For each realization several independent ground states are obtained. Then, by applying ballistic search and T=0 Monte-Carlo simulations, it is ensured that each ground state appears with the same probability. Consequently, the results represent the true T=0 thermodynamic behavior. The distribution P(|q|) of overlaps is evaluated. For increasing size the width of P(|q|) and the fraction of the distribution below q_0=0.5 converge to zero. This indicates that for the infinite system P(|q|) is a delta function, in contrast to previous results. Thus, the ground-state behavior is dominated by few large clusters of similar ground states.Comment: 7 pages revtex, 6 figures, 27 reference

The Hubble Sequence in Groups: The Birth of the Early-Type Galaxies

The physical mechanisms and timescales that determine the morphological signatures and the quenching of star formation of typical (~L*) elliptical galaxies are not well understood. To address this issue, we have simulated the formation of a group of galaxies with sufficient resolution to track the evolution of gas and stars inside about a dozen galaxy group members over cosmic history. Galaxy groups, which harbor many elliptical galaxies in the universe, are a particularly promising environment to investigate morphological transformation and star formation quenching, due to their high galaxy density, their relatively low velocity dispersion, and the presence of a hot intragroup medium. Our simulation reproduces galaxies with different Hubble morphologies and, consequently, enables us to study when and where the morphological transformation of galaxies takes place. The simulation does not include feedback from active galactic nuclei showing that it is not an essential ingredient for producing quiescent, red elliptical galaxies in galaxy groups. Ellipticals form, as suspected, through galaxy mergers. In contrast with what has often been speculated, however, these mergers occur at z>1, before the merging progenitors enter the virial radius of the group and before the group is fully assembled. The simulation also shows that quenching of star formation in the still star-forming elliptical galaxies lags behind their morphological transformation, but, once started, is taking less than a billion years to complete. As long envisaged the star formation quenching happens as the galaxies approach and enter the finally assembled group, due to quenching of gas accretion and (to a lesser degree) stripping. A similar sort is followed by unmerged, disk galaxies, which, as they join the group, are turned into the red-and-dead disks that abound in these environments.Comment: 12 pages, 12 Figures, 1 Table, accepted for publication in AP

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