Quantum Monte Carlo simulations of a particle in a random potential

In this paper we carry out Quantum Monte Carlo simulations of a quantum particle in a one-dimensional random potential (plus a fixed harmonic potential) at a finite temperature. This is the simplest model of an interface in a disordered medium and may also pertain to an electron in a dirty metal. We compare with previous analytical results, and also derive an expression for the sample to sample fluctuations of the mean square displacement from the origin which is a measure of the glassiness of the system. This quantity as well as the mean square displacement of the particle are measured in the simulation. The similarity to the quantum spin glass in a transverse field is noted. The effect of quantum fluctuations on the glassy behavior is discussed.Comment: 23 pages, 7 figures included as eps files, uses RevTeX. Accepted for publication in J. of Physics A: Mathematical and Genera

Discrete element modelling of fluidised bed spray granulation

A novel discrete element spray granulation model capturing the key features of fluidised bed hydrodynamics, liquid-solid contacting and agglomeration is presented. The model computes the motion of every individual particle and droplet in the system, considering the gas phase as a continuum. Micro scale processes such as particle-particle collisions, droplet-particle coalescence and agglomeration are directly taken into account by simple closure models. Simulations of the hydrodynamic behaviour of a batch granulation process are presented to demonstrate the potential of the model for creating\ud insight into the influence of several key process conditions such as fluidisation velocity, spray rate and spray pattern on powder product characteristics

Replica field theory for a polymer in random media

In this paper we revisit the problem of a (non self-avoiding) polymer chain in a random medium which was previously investigated by Edwards and Muthukumar (EM). As noticed by Cates and Ball (CB) there is a discrepancy between the predictions of the replica calculation of EM and the expectation that in an infinite medium the quenched and annealed results should coincide (for a chain that is free to move) and a long polymer should always collapse. CB argued that only in a finite volume one might see a ``localization transition'' (or crossover) from a stretched to a collapsed chain in three spatial dimensions. Here we carry out the replica calculation in the presence of an additional confining harmonic potential that mimics the effect of a finite volume. Using a variational scheme with five variational parameters we derive analytically for d<4 the result R~(g |ln \mu|)^{-1/(4-d)} ~(g lnV)^{-1/(4-d)}, where R is the radius of gyration, g is the strength of the disorder, \mu is the spring constant associated with the confining potential and V is the associated effective volume of the system. Thus the EM result is recovered with their constant replaced by ln(V) as argued by CB. We see that in the strict infinite volume limit the polymer always collapses, but for finite volume a transition from a stretched to a collapsed form might be observed as a function of the strength of the disorder. For d<2 and for large V>V'~exp[g^(2/(2-d))L^((4-d)/(2-d))] the annealed results are recovered and R~(Lg)^(1/(d-2)), where L is the length of the polymer. Hence the polymer also collapses in the large L limit. The 1-step replica symmetry breaking solution is crucial for obtaining the above results.Comment: Revtex, 32 page

Quantum fluctuations and glassy behavior: The case of a quantum particle in a random potential

In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known ``toy'' model for an interface in a random medium. It also applies to a single quantum particle like an an electron subject to random interactions, where the harmonic potential can be tuned to mimic the effect of a finite box. Using the variational approximation, or alternatively, the limit of large spatial dimensions, together with the use the replica method, and are able to solve the model and obtain its phase diagram in the $T - (\hbar^2/m)$ plane, where $m$ is the particle's mass. The phase diagram is similar to that of a quantum spin-glass in a transverse field, where the variable $\hbar^2/m$ plays the role of the transverse field. The glassy phase is characterized by replica-symmetry-breaking. The quantum transition at zero temperature is also discussed.Comment: revised version, 23 pages, revtex, 5 postscript figures in a separate file figures.u

Dynamical solutions of a quantum Heisenberg spin glass model

We consider quantum-dynamical phenomena in the $\mathrm{SU}(2)$, $S=1/2$ infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical self-consistency equations. Using the Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic states we study in particular the isotropic model variant on the spin space. Two complementary approximation schemes are applied: one restricts the quantum spin dynamics to a manageable number of Matsubara frequencies while the other employs an expansion in terms of the dynamical local spin susceptibility. We accurately determine the critical temperature $T_c$ of the spin glass to paramagnet transition. We find that the dynamical correlations cause an increase of $T_c$ by 2% compared to the result obtained in the spin-static approximation. The specific heat $C(T)$ exhibits a pronounced cusp at $T_c$. Contradictory to other reports we do not observe a maximum in the $C(T)$-curve above $T_c$.Comment: 8 pages, 7 figure

Lorentz and CPT Invariance Violation In High-Energy Neutrinos

High-energy neutrino astronomy will be capable of observing particles at both extremely high energies and over extremely long baselines. These features make such experiments highly sensitive to the effects of CPT and Lorentz violation. In this article, we review the theoretical foundation and motivation for CPT and Lorentz violating effects, and then go on to discuss the related phenomenology within the neutrino sector. We describe several signatures which might be used to identify the presence of CPT or Lorentz violation in next generation neutrino telescopes and cosmic ray experiments. In many cases, high-energy neutrino experiments can test for CPT and Lorentz violation effects with much greater precision than other techniques.Comment: 27 pages, 8 figure

Disorder effects in the quantum Heisenberg model: An Extended Dynamical mean-field theory analysis

We investigate a quantum Heisenberg model with both antiferromagnetic and disordered nearest-neighbor couplings. We use an extended dynamical mean-field approach, which reduces the lattice problem to a self-consistent local impurity problem that we solve by using a quantum Monte Carlo algorithm. We consider both two- and three-dimensional antiferromagnetic spin fluctuations and systematically analyze the effect of disorder. We find that in three dimensions for any small amount of disorder a spin-glass phase is realized. In two dimensions, while clean systems display the properties of a highly correlated spin-liquid (where the local spin susceptibility has a non-integer power-low frequency and/or temperature dependence), in the present case this behavior is more elusive unless disorder is very small. This is because the spin-glass transition temperature leaves only an intermediate temperature regime where the system can display the spin-liquid behavior, which turns out to be more apparent in the static than in the dynamical susceptibility.Comment: 15 pages, 7 figure

Radio Properties of z>4 Optically-Selected Quasars

We report on two programs to address differential evolution between the radio-loud and radio-quiet quasar populations at high (z>4) redshift. Both programs entail studying the radio properties of optically-selected quasars. First, we have observed 32 optically-selected, high-redshift (z>4) quasars with the VLA at 6 cm (5 GHz). These sources comprise a statistically complete and well-understood sample. We detect four quasars above our 3-sigma limit of ~0.15 mJy, which is sufficiently sensitive to detect all radio-loud quasars at the probed redshift range. Second, we have correlated 134 z>4 quasars, comprising all such sources that we are aware of as of mid-1999, with FIRST and NVSS. These two recent 1.4 GHz VLA sky surveys reach 3-sigma limits of approximately 0.6 mJy and 1.4 mJy respectively. We identify a total of 15 z>4 quasars, of which six were not previously known to be radio-loud. The depth of these surveys does not reach the radio-loud/radio-quiet demarcation luminosity density (L(1.4 GHz) = 10^32.5 h(50)^(-2) ergs/s/Hz) at the redshift range considered; this correlation therefore only provides a lower limit to the radio-loud fraction of quasars at high-redshift. The two programs together identify eight new radio-loud quasars at z>4, a significant increase over the seven currently in the published literature. We find no evidence for radio-loud fraction depending on optical luminosity for -25 > M_B > -28 at z~2, or for -26>M_B>-28 at z>4. Our results also show no evolution in the radio-loud fraction between z~2 and z>4 (-26>M_B>-28).Comment: 19 pages, 7 figures; to appear in The Astronomical Journal (April 2000

Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class

The probability P(alpha, N) that search algorithms for random Satisfiability problems successfully find a solution is studied as a function of the ratio alpha of constraints per variable and the number N of variables. P is shown to be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and exponentially small in N above. The critical behaviour is universal for all algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon) alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to the critical behaviour of random graphs, and the scaling function Phi is exactly calculated through a mapping onto a diffusion-and-death problem.Comment: 7 pages; 3 figure

Quantitative Analysis of the Publishing Landscape in High-Energy Physics

World-wide collaboration in high-energy physics (HEP) is a tradition which dates back several decades, with scientific publications mostly coauthored by scientists from different countries. This coauthorship phenomenon makes it difficult to identify precisely the ``share'' of each country in HEP scientific production. One year's worth of HEP scientific articles published in peer-reviewed journals is analysed and their authors are uniquely assigned to countries. This method allows the first correct estimation on a ``pro rata'' basis of the share of HEP scientific publishing among several countries and institutions. The results provide an interesting insight into the geographical collaborative patterns of the HEP community. The HEP publishing landscape is further analysed to provide information on the journals favoured by the HEP community and on the geographical variation of their author bases. These results provide quantitative input to the ongoing debate on the possible transition of HEP publishing to an Open Access model.Comment: For a better on-screen viewing experience this paper can also be obtained at: http://doc.cern.ch/archive/electronic/cern/preprints/open/open-2006-065.pd