Momentum isotropisation in random potentials

When particles are multiply scattered by a random potential, their momentum distribution becomes isotropic on average. We study this quantum dynamics numerically and with a master equation. We show how to measure the elastic scattering time as well as characteristic isotropisation times, which permit to reconstruct the scattering phase function, even in rather strong disorder.Comment: 5 pages, paper contributed to Lyon BEC 2012; v2 minor changes, version published in prin

Strong Anderson localization in cold atom quantum quenches

Signatures of strong Anderson localization in the momentum distribution of a cold atom cloud after a quantum quench are studied. We consider a quasi one-dimensional cloud initially prepared in a well defined momentum state, and expanding for some time in a disorder speckle potential. Anderson localization leads to a formation of a coherence peak in the \emph{forward} scattering direction (as opposed to the common weak localization backscattering peak). We present a microscopic, and fully time resolved description of the phenomenon, covering the entire diffusion--to--localization crossover. Our results should be observable by present day technology.Comment: 4 pages, 2 figures, published versio

Echo spectroscopy of Anderson localization

We propose a conceptually new framework to study the onset of Anderson localization in disordered systems. The idea is to expose waves propagating in a random scattering environment to a sequence of short dephasing pulses. The system responds through coherence peaks forming at specific echo times, each echo representing a particular process of quantum interference. We suggest a concrete realization for cold gases, where quantum interferences are observed in the momentum distribution of matter waves in a laser speckle potential. This defines a challenging, but arguably realistic framework promising to yield unprecedented insight into the mechanisms of Anderson localization.Comment: 14 pages, 7 figures; published versio

The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. Moreover, we describe an algorithm to compute $\mu$

Symmetric Diblock Copolymers in Thin Films (I): Phase stability in Self-Consistent Field Calculations and Monte Carlo Simulations

We investigate the phase behavior of symmetric AB diblock copolymers confined into a thin film. The film boundaries are parallel, impenetrable and attract the A component of the diblock copolymer. Using a self-consistent field technique [M.W. Matsen, J.Chem.Phys. {\bf 106}, 7781 (1997)], we study the ordered phases as a function of incompatibility $\chi$ and film thickness in the framework of the Gaussian chain model. For large film thickness and small incompatibility, we find first order transitions between phases with different number of lamellae which are parallel oriented to the film boundaries. At high incompatibility or small film thickness, transitions between parallel oriented and perpendicular oriented lamellae occur. We compare the self-consistent field calculations to Monte Carlo simulations of the bond fluctuation model for chain length N=32. In the simulations we quench several systems from $\chi N=0$ to $\chi N=30$ and monitor the morphology into which the diblock copolymers assemble. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Good agreement between self-consistent field calculations and Monte Carlo simulations is found.Comment: to appear in J.Chem.Phy

Anomalous Viscosity of an Expanding Quark-Gluon Plasma

We argue that an expanding quark-gluon plasma has an anomalous viscosity, which arises from interactions with dynamically generated color fields. We derive an expression for the anomalous viscosity in the turbulent plasma domain and apply it to the hydrodynamic expansion phase, when the quark-gluon plasma is near equilibrium. The anomalous viscosity dominates over the collisional viscosity for weak coupling and not too late times. This effect may provide an explanation for the apparent ``nearly perfect'' liquidity of the matter produced in nuclear collisions at the Relativistic Heavy Ion Collider without the assumption that it is a strongly coupled state.Comment: Final version accepted for publicatio

Supernova Simulations from a 3D Progenitor Model -- Impact of Perturbations and Evolution of Explosion Properties

We study the impact of large-scale perturbations from convective shell burning on the core-collapse supernova explosion mechanism using three-dimensional (3D) multi-group neutrino hydrodynamics simulations of an 18 solar mass progenitor. Seed asphericities in the O shell, obtained from a recent 3D model of O shell burning, help trigger a neutrino-driven explosion 330ms after bounce whereas the shock is not revived in a model based on a spherically symmetric progenitor for at least another 300ms. We tentatively infer a reduction of the critical luminosity for shock revival by ~20% due to pre-collapse perturbations. This indicates that convective seed perturbations play an important role in the explosion mechanism in some progenitors. We follow the evolution of the 18 solar mass model into the explosion phase for more than 2s and find that the cycle of accretion and mass ejection is still ongoing at this stage. With a preliminary value of 0.77 Bethe for the diagnostic explosion energy, a baryonic neutron star mass of 1.85 solar masses, a neutron star kick of ~600km/s and a neutron star spin period of ~20ms at the end of the simulation, the explosion and remnant properties are slightly atypical, but still lie comfortably within the observed distribution. Although more refined simulations and a larger survey of progenitors are still called for, this suggests that a solution to the problem of shock revival and explosion energies in the ballpark of observations are within reach for neutrino-driven explosions in 3D.Comment: 23 pages, 22 figures, accepted for publication in MNRA

Emission line models for the lowest-mass core collapse supernovae. I: Case study of a 9 M⊙M_\odot one-dimensional neutrino-driven explosion

A large fraction of core-collapse supernovae (CCSNe), 30-50%, are expected to originate from the low-mass end of progenitors with $M_{\rm ZAMS}~= 8-12~M_\odot$. However, degeneracy effects make stellar evolution modelling of such stars challenging, and few predictions for their supernova light curves and spectra have been presented. Here we calculate synthetic nebular spectra of a 9 $M_\odot$ Fe CCSN model exploded with the neutrino mechanism. The model predicts emission lines with FWHM$\sim$1000 km/s, including signatures from each deep layer in the metal core. We compare this model to observations of the three subluminous IIP SNe with published nebular spectra; SN 1997D, SN 2005cs, and SN 2008bk. The prediction of both line profiles and luminosities are in good agreement with SN 1997D and SN 2008bk. The close fit of a model with no tuning parameters provides strong evidence for an association of these objects with low-mass Fe CCSNe. For SN 2005cs, the interpretation is less clear, as the observational coverage ended before key diagnostic lines from the core had emerged. We perform a parameterised study of the amount of explosively made stable nickel, and find that none of these three SNe show the high $^{58}$Ni/$^{56}$Ni ratio predicted by current models of electron capture SNe (ECSNe) and ECSN-like explosions. Combined with clear detection of lines from O and He shell material, these SNe rather originate from Fe core progenitors. We argue that the outcome of self-consistent explosion simulations of low-mass stars, which gives fits to many key observables, strongly suggests that the class of subluminous Type IIP SNe is the observational counterpart of the lowest mass CCSNe.Comment: Resubmitted to MNRAS after referee comment

Waveform sampling using an adiabatically driven electron ratchet in a two-dimensional electron system

We utilize a time-periodic ratchet-like potential modulation imposed onto a two-dimensional electron system inside a GaAs/Al$_x$Ga$_{1-x}$As heterostructure to evoke a net dc pumping current. The modulation is induced by two sets of interdigitated gates, interlacing off center, which can be independently addressed. When the transducers are driven by two identical but phase-shifted ac signals, a lateral dc pumping current $I(\phi)$ results, which strongly depends on both, the phase shift $\phi$ and the waveform $V(t)$ of the imposed gate voltages. We find that for different periodic signals, the phase dependence $I(\phi)$ closely resembles $V(t)$. A simple linear model of adiabatic pumping in two-dimensional electron systems is presented, which reproduces well our experimental findings.Comment: 3 figure

A simple model of price formation

A simple Ising spin model which can describe the mechanism of price formation in financial markets is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among traders. It is shown via standard Monte Carlo simulations that very simple rules lead to dynamics that duplicate those of asset prices.Comment: Version 2: 4 pages, 4 figures; added more stringent statistical analysis; to appear in Int. J. Modern Physics C, Vol. 13, No. 1 (2002