Solvable glassy system: static versus dynamical transition

A directed polymer is considered on a flat substrate with randomly located parallel ridges. It prefers to lie inside wide regions between the ridges. When the transversel width $W=\exp(\lambda L^{1/3})$ is exponential in the longitudinal length $L$, there can be a large number $\sim \exp L^{1/3}$ of available wide states. This ``complexity'' causes a phase transition from a high temperature phase where the polymer lies in the widest lane, to a glassy low temperature phase where it lies in one of many narrower lanes. Starting from a uniform initial distribution of independent polymers, equilibration up to some exponential time scale induces a sharp dynamical transition. When the temperature is slowly increased with time, this occurs at a tunable temperature. There is an asymmetry between cooling and heating. The structure of phase space in the low temperature non-equilibrium glassy phase is of a one-level tree.Comment: 4 pages revte

Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals

It is shown that density-of-states fluctuations, which can be interpreted as the order-parameter susceptibility \chi_OP in a Fermi liquid, are anomalously strong as a result of the existence of Goldstone modes and associated strong fluctuations. In a 2-d system with a long-range Coulomb interaction, a suitably defined \chi_OP diverges as 1/T^2 as a function of temperature in the limit of small wavenumber and frequency. In contrast, standard statistics suggest \chi_OP = O(T), a discrepancy of three powers of T. The reasons behind this surprising prediction, as well as ways to observe it, are discussed.Comment: 4 pp, revised version contains a substantially expanded derivatio

To maximize or not to maximize the free energy of glassy systems, !=?

The static free energy of glassy systems can be expressed in terms of the Parisi order parameter function. When this function has a discontinuity, the location of the step is determined by maximizing the free energy. In dynamics a transition is found at larger temperature, while the location of the step satisfies a marginality criterion. It is shown here that in a replica calculation this criterion minimizes the free energy. This leads to first order phase transitions at the dynamic transition point. Though the order parameter function is the same as in the long-time limit of a dynamical analysis, thermodynamics is different.Comment: 4 pages PostScript, one figur

Finite size effects and localization properties of disordered quantum wires with chiral symmetry

Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral symmetry. For quasi one-dimensional geometries and low concentration of vacancies, an exponential decay of the mean conductance with the wire length is obtained even at the center of the energy band. For wide wires, finite size effects cause the conductance to decay following a non-pure exponential law. We propose an analytical formula for the mean conductance that reproduces accurately the numerical data for both geometries. However, when the concentration of vacancies increases above a critical value, a transition towards the suppression of the conductance occurs. This is a signature of the presence of ultra-localized states trapped in finite regions of the sample.Comment: 5 figures, revtex

Competition between glassiness and order in a multi-spin glass

A mean-field multi-spin interaction spin glass model is analyzed in the presence of a ferromagnetic coupling. The static and dynamical phase diagrams contain four phases (paramagnet, spin glass, ordinary ferromagnet and glassy ferromagnet) and exhibit reentrant behavior. The glassy ferromagnet phase has anomalous dynamical properties. The results are consistent with a nonequilibrium thermodynamics that has been proposed for glasses.Comment: revised version, 4 pages Revtex, 2 eps-figures. Phys. Rev. E, Rapid Communication, to appea

Metastable states in glassy systems

Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs to cast them in a form involving states with finite lifetimes. Starting from elementary examples and using results of Gaveau and Schulman, we propose a simple expression for the configurational entropy and revisit the question of taking flat averages over metastable states. The construction is applicable to finite dimensional systems, and we explicitly show that for simple mean-field glass models it recovers, justifies and generalises the known results. The calculation emphasises the appearance of new dynamical order parameters.Comment: 4 fig., 20 pages, revtex; added references and minor change

Resolving the L/T transition binary SDSS J2052-1609 AB

Binaries provide empirical key constraints for star formation theories, like the overall binary fraction, mass ratio distribution and the separation distribution. They play a crucial role to calibrate the output of theoretical models, like absolute magnitudes, colors and effective temperature depending on mass, metallicity and age. We present first results of our on-going high-resolution imaging survey of late type brown dwarfs. The survey aims at resolving tight brown dwarf binary systems to better constrain the T dwarf binary fraction. We intent to follow-up the individual binaries to determine orbital parameters. Using NACO at the VLT we performed AO-assisted near-infrared observations of SDSS J2052-1609. High-spatial resolution images of the T1 dwarf were obtained in H and Ks filters. We resolved SDSS J2052-1609 into a binary system with a separation of 0.101" \pm 0.001". Archival data from HST/NICMOS taken one year previous to our observations proves the components to be co-moving. Using the flux ratio between the components we infer J, H and Ks magnitudes for the resolved system. From the near-IR colors we estimate spectral types of T1 +1 -4 and T2.5 \pm 1 for component A and B, respectively. A first estimate of the total system mass yields Mtot > 78 Mjup, assuming a circular orbit.Comment: 5 pages, 3 figures, 3 tables, accepted for publication by A&

2MASS J03105986+1648155AB - A new binary at the L/T transition

The transition from the L to the T spectral type of brown dwarfs is marked by a very rapid transition phase, remarkable brightening in the J-band and a higher binary frequency. Despite being an active area of inquiry, this transition regime still remains one of the most poorly understood phases of brown dwarf evolution. We resolved the L dwarf 2MASS J03105986+1648155 for the first time into two almost equally bright components straddling the L/T transition. Since such a co-eval system with common age and composition provides crucial information of this special transition phase, we monitored the system over 3 years to derive first orbital parameters and dynamical mass estimates, as well as a spectral type determination. We obtained resolved high angular resolution, near-IR images with HST and the adaptive optics instrument NACO at the VLT including the laser guide star system PARSEC. Based on two epochs of astrometric data we derive a minimum semi-major axis of 5.2 +- 0.8 AU. The assumption of a face-on circular orbit yields an orbital period of 72 +- 4 years and a total system mass of 30-60 Mjup. This places the masses of the individual components of the system at the lower end of the mass regime of brown dwarfs. The achieved photometry allowed a first spectral type determination of L9 +- 1 for each component. In addition, this seems to be only the fifth resolved L/T transition binary with a flux reversal. While ultimate explanations for this effect are still owing, the 2MASS J03105986+1648155 system adds an important benchmark object for improving our understanding of this remarkable evolutionary phase of brown dwarfs. Additionally, the observational results of 2MASS J03105986+1648155 AB derived with the new PARSEC AO system at the VLT show the importance of this technical capability. The updated AO system allows us to significantly extend the sample of brown dwarfs observable with high-resolution from the ground and hence to reveal more of their physical properties.Comment: 6 pages, 2 figures, 3 tables, accepted for publication by A&

Emergence of macroscopic temperatures in systems that are not thermodynamical microscopically: towards a thermodynamical description of slow granular rheology

A scenario for systems with slow dynamics is characterised by stating that there are several temperatures coexisting in the sample, with a single temperature shared by all observables at each (widely separate) time-scale. In preparation for the study of granular rheology, we show within this framework that glassy systems with driving and friction that are generic and do not correspond to a thermal bath --- and whose microscopic `fast' motion is hence not thermal --- have a well-defined macroscopic temperature associated to the slow degrees of freedom. This temperature is what a thermometer coupled to the system will measure if tuned to respond to low frequencies, and since it can be related to the number of stationary configurations, it is the formalisation of Edwards' `compactivity' ideas.Comment: Revised version: treatment of `tapping' deferre

Damage spreading transition in glasses: a probe for the ruggedness of the configurational landscape

We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of meta-stable states. For systems evolving under identical but arbitrarily correlated noises we demonstrate that there exists a critical temperature $T_0$ which separates two different dynamical regimes depending on whether damage spreads or not in the asymptotic long-time limit. This transition exists for generic noise correlations such that the zero damage solution is stable at high-temperatures being minimal for maximal noise correlations. Although this dynamical transition depends on the type of noise correlations we show that the asymptotic damage has the good properties of an dynamical order parameter such as: 1) Independence on the initial damage; 2) Independence on the class of initial condition and 3) Stability of the transition in the presence of asymmetric interactions which violate detailed balance. For maximally correlated noises we suggest that damage spreading occurs due to the presence of a divergent number of saddle points (as well as meta-stable states) in the thermodynamic limit consequence of the ruggedness of the free energy landscape which characterizes the glassy state. These results are then compared to extensive numerical simulations of a mean-field glass model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom of choosing arbitrary noise correlations for Langevin dynamics makes damage spreading a interesting tool to probe the ruggedness of the configurational landscape.Comment: 25 pages, 13 postscript figures. Paper extended to include cross-correlation