Quantum Multibaker Maps: Extreme Quantum Regime

We introduce a family of models for quantum mechanical, one-dimensional random walks, called quantum multibaker maps (QMB). These are Weyl quantizations of the classical multibaker models previously considered by Gaspard, Tasaki and others. Depending on the properties of the phases parametrizing the quantization, we consider only two classes of the QMB maps: uniform and random. Uniform QMB maps are characterized by phases which are the same in every unit cell of the multibaker chain. Random QMB maps have phases that vary randomly from unit cell to unit cell. The eigenstates in the former case are extended while in the latter they are localized. In the uniform case and for large $\hbar$, analytic solutions can be obtained for the time dependent quantum states for periodic chains and for open chains with absorbing boundary conditions. Steady state solutions and the properties of the relaxation to a steady state for a uniform QMB chain in contact with ``particle'' reservoirs can also be described analytically. The analytical results are consistent with, and confirmed by, results obtained from numerical methods. We report here results for the deep quantum regime (large $\hbar$) of the uniform QMB, as well as some results for the random QMB. We leave the moderate and small $\hbar$ results as well as further consideration of the other versions of the QMB for further publications.Comment: 17 pages, referee's and editor's comments addresse

Observations of Stripped Edge-on Virgo Cluster Galaxies

We present observations of highly inclined, HI deficient, Virgo cluster spiral galaxies. Our high-resolution VLA HI observations of edge-on galaxies allow us to distinguish extraplanar gas from disk gas. All of our galaxies have truncated H-alpha disks, with little or no disk gas beyond a truncation radius. While all the gas disks are truncated, the observations show evidence for a continuum of stripping states: symmetric, undisturbed truncated gas disks indicate galaxies that were stripped long ago, while more asymmetric disks suggest ongoing or more recent stripping. We compare these timescale estimates with results obtained from two-dimensional stellar spectroscopy of the outer disks of galaxies in our sample. One of the galaxies in our sample, NGC 4522 is a clear example of active ram-pressure stripping, with 40% of its detected HI being extraplanar. As expected, the outer disk stellar populations of this galaxy show clear signs of recent (and, in fact, ongoing) stripping. Somewhat less expected, however, is the fact that the spectrum of the outer disk of this galaxy, with very strong Balmer absorption and no observable emission, would be classified as ``k+a'' if observed at higher redshift. Our observations of NGC 4522 and other galaxies at a range of cluster radii allow us to better understand the role that clusters play in the structure and evolution of disk galaxies.Comment: 4 pages, 2 figures, to appear in the proceedings of the Island Universes conference held in Terschelling, Netherlands, July 2005, ed. R. de Jong, version with high resolution figures can be downloaded from ftp://ftp.astro.yale.edu/pub/hugh/papers/iu_crowl_h.ps.g

Connecting the timescales in picosecond remagnetization experiments

In femtosecond demagnetization experiments, one gains access to the elementary relaxation mechanisms of a magnetically ordered spin system on a time scale of 100 fs. Following these experiments, we report a combined micromagnetic and experimental study that connects the different regimes known from all-optical pump-probe experiments by employing a simple micromagnetic model. We identify spin-wave packets on the nanometer scale that contribute to the remagnetization process on the intermediate time scale between single-spin relaxation and collective precession.Comment: 12 pages, 3 figures, submitted to Phys. Rev. Lett, changes made with regard to review proces

Logarithmic periodicities in the bifurcations of type-I intermittent chaos

The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I intermittency is studied and a log-periodic dependence is numerically obtained for the average time between laminar events, the Lyapunov exponent and attractor moments. The origin of the oscillations is built in the natural probabilistic measure of the map and can be traced back to the existence of logarithmically distributed discrete values of the control parameter giving Markov partition. Reinjection and noise effect dependences are discussed and indications are given on how the oscillations are potentially applicable to complement predictions made with the usual critical exponents, taken from data in critical phenomena.Comment: 4 pages, 6 figures, accepted for publication in PRL (2004

Detecting the orientation of magnetic fields in galaxy clusters

Clusters of galaxies, filled with hot magnetized plasma, are the largest bound objects in existence and an important touchstone in understanding the formation of structures in our Universe. In such clusters, thermal conduction follows field lines, so magnetic fields strongly shape the cluster's thermal history; that some have not since cooled and collapsed is a mystery. In a seemingly unrelated puzzle, recent observations of Virgo cluster spiral galaxies imply ridges of strong, coherent magnetic fields offset from their centre. Here we demonstrate, using three-dimensional magnetohydrodynamical simulations, that such ridges are easily explained by galaxies sweeping up field lines as they orbit inside the cluster. This magnetic drape is then lit up with cosmic rays from the galaxies' stars, generating coherent polarized emission at the galaxies' leading edges. This immediately presents a technique for probing local orientations and characteristic length scales of cluster magnetic fields. The first application of this technique, mapping the field of the Virgo cluster, gives a startling result: outside a central region, the magnetic field is preferentially oriented radially as predicted by the magnetothermal instability. Our results strongly suggest a mechanism for maintaining some clusters in a 'non-cooling-core' state.Comment: 48 pages, 21 figures, revised version to match published article in Nature Physics, high-resolution version available at http://www.cita.utoronto.ca/~pfrommer/Publications/pfrommer-dursi.pd

Non-Fermi-Liquid Scaling in Ce(Ru_{0.5}Rh_{0.5})_2Si_2

We study the temperature and field dependence of the magnetic and transport properties of the non-Fermi-liquid compound Ce(Ru_{1-x}Rh_x)_2Si_2 at x=0.5. For fields $\lesssim$0.1T the experimental results show signatures of the presence of Kondo-disorder, expected to be large at this concentration. For larger fields, however, magnetic and transport properties are controlled by the coupling of the conduction electrons to critical spin-fluctuations. The temperature dependence of the susceptibility as well as the scaling properties of the magnetoresistance are in very good agreement with the predictions of recent dynamical mean-field theories of Kondo alloys close to a spin-glass quantum critical point.Comment: 4 pages, 4 figures. Improved discussion. To appear in Phys. Rev. Let

Model Checking CTL is Almost Always Inherently Sequential

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+

Exciton Mediated Superconductivity in PrOs4Sb12

The most important character of the exotic superconductor PrOs4Sb12 is the existence of low-lying excitations (excitons) with a finite energy gap and it appears as the magnetic field-induced order above 4.5 T. We focus on the a_u conduction band, which hybridizes with a Pr 4f^2 state strongly, coupled to the excitons. It results in an attractive interaction between the conduction electrons. The symmetry of the superconducting order parameter is determined by dispersion relation of the exciton. For the bcc system PrOs4Sb12, a d-wave state [kx ky + omega ky kz + omega^2 kz kx, omega=exp(pm i 2 pi/3)] is stabilized with broken time reversal symmetry.Comment: 4 page

Particle tracking for polydisperse sedimenting droplets in phase separation

When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between the two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4 -- 40 micrometers are detected and tracked. Based on this data we resolve the oscillations in the droplet size distribution which are coupled to the convective flow.Comment: 13 pages; 16 figures including 3 photographs and 3 false-color plot

Single virus detection on silicon photonic crystal random cavities

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this recordData Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.On-chip silicon microcavity sensors are advantageous for the detection of virus and biomolecules due to their compactness and the enhanced light–matter interaction with the analyte. While their theoretical sensitivity is at the single-molecule level, the fabrication of high quality (Q) factor silicon cavities and their integration with optical couplers remain as major hurdles in applications such as single virus detection. Here, label-free single virus detection using silicon photonic crystal random cavities is proposed and demonstrated. The sensor chips consist of free-standing silicon photonic crystal waveguides and do not require pre-fabricated defect cavities or optical couplers. Residual fabrication disorder results in Anderson-localized cavity modes which are excited by a free space beam. The Q ≈105 is sufficient for observing discrete step-changes in resonance wavelength for the binding of single adenoviruses (≈50 nm radius). The authors’ findings point to future applications of CMOS-compatible silicon sensor chips supporting Anderson-localized modes that have detection capabilities at the level of single nanoparticles and molecules.Engineering and Physical Sciences Research Council (EPSRC