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

Molecular Dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition

In this paper we describe a version of London Langevin molecular dynamics simulations that allows for investigations of the vortex lattice melting transition in the highly anisotropic high-temperature superconductor material Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We include the full electromagnetic interaction as well as the Josephson interaction among pancake vortices. We also implement periodic boundary conditions in all directions, including the z-axis along which the magnetic field is applied. We show how to implement flux cutting and reconnection as an analog to permutations in the multilevel Monte Carlo scheme and demonstrate that this process leads to flux entanglement that proliferates in the vortex liquid phase. The first-order melting transition of the vortex lattice is observed to be in excellent agreement with previous multilevel Monte Carlo simulations.Comment: 4 figure

Magnetism and local distortions near carbon impurity in γ\gamma-iron

Local perturbations of crystal and magnetic structure of $\gamma$-iron near carbon interstitial impurity is investigated by {\it ab initio} electronic structure calculations. It is shown that the carbon impurity creates locally a region of ferromagnetic ordering with substantial tetragonal distortions. Exchange integrals and solution enthalpy are calculated, the latter being in a very good agreement with experimental data. Effect of the local distortions on the carbon-carbon interactions in $\gamma$-iron is discussed.Comment: 4 pages 3 figures. Final version, accepted to Phys.Rev. Let

Localization of a polymer in random media: Relation to the localization of a quantum particle

In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be {\it localized} inside a low minimum of the potential. We show how the end-to-end distance of a polymer which is free to move can be obtained from the density of states of the quantum particle using extreme value statistics. We give a physical interpretation to the recently discovered one-step replica-symmetry-breaking solution for the polymer (Phys. Rev. E{\bf 61}, 1729 (2000)) in terms of the statistics of localized tail states. Numerical solutions of the variational equations for chains of different length are performed and compared with quenched averages computed directly by using the eigenfunctions and eigenenergies of the Schr\"odinger equation for a particle in a one-dimensional random potential. The quantities investigated are the radius of gyration of a free gaussian chain, its mean square distance from the origin and the end-to-end distance of a tethered chain. The probability distribution for the position of the chain is also investigated. The glassiness of the system is explained and is estimated from the variance of the measured quantities.Comment: RevTex, 44 pages, 13 figure

Presymplectic current and the inverse problem of the calculus of variations

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon and Lawson and generalizes an older result of Henneaux from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.Comment: v2: 17 pages, no figures, BibTeX; minor corrections, close to published versio

Magic wavelengths for the 5s−18s5s-18s transition in rubidium

Magic wavelengths, for which there is no differential ac Stark shift for the ground and excited state of the atom, allow trapping of excited Rydberg atoms without broadening the optical transition. This is an important tool for implementing quantum gates and other quantum information protocols with Rydberg atoms, and reliable theoretical methods to find such magic wavelengths are thus extremely useful. We use a high-precision all-order method to calculate magic wavelengths for the $5s-18s$ transition of rubidium, and compare the calculation to experiment by measuring the light shift for atoms held in an optical dipole trap at a range of wavelengths near a calculated magic value

The dusty environment of Quasars. Far-IR properties of Optical Quasars

We present the ISO far-IR photometry of a complete sub-sample of optically selected bright quasars belonging to two complete surveys selected through multicolour (U,B,V,R,I) techniques. The ISOPHOT camera on board of the ISO Satellite was used to target these quasars at wavelengths of 7.3, 11.5, 60, 100 and 160 micron. Almost two thirds of the objects were detected at least in one ISOPHOT band. The detection rate is independent of the source redshift, very likely due to the negative K-correction of the far-IR thermal emission. More than a half of the optically selected QSOs show significant emission between 4 and 100 micron in the quasar rest-frame. These fluxes have a very likely thermal origin, although in a few objects an additional contribution from a non-thermal component is plausible in the long wavelength bands. In a colour-colour diagram these objects span a wide range of properties from AGN-dominated to ULIRG-like. The far-IR composite spectrum of the quasar population presents a broad far-IR bump between 10 and 30 micron and a sharp drop at wavelengths greater than 100 micron in the quasar restframe. The amount of energy emitted in the far-IR, is on average a few times larger than that emitted in the blue and the ratio L(FIR)/L(B) increases with the bolometric luminosity. Objects with fainter blue magnitudes have larger ratios between the far-IR (wavelengths > 60 micron) fluxes and the blue band flux, which is attributed to extinction by dust around the central source. No relation between the blue absolute magnitude and the dust colour temperature is seen, suggesting that the dominant source of FIR energy could be linked to a concurrent starburst rather than to gravitational energy produced by the central engine.Comment: Astronomical Journal, in pres

Solvable model of a polymer in random media with long ranged disorder correlations

We present an exactly solvable model of a Gaussian (flexible) polymer chain in a quenched random medium. This is the case when the random medium obeys very long range quadratic correlations. The model is solved in $d$ spatial dimensions using the replica method, and practically all the physical properties of the chain can be found. In particular the difference between the behavior of a chain that is free to move and a chain with one end fixed is elucidated. The interesting finding is that a chain that is free to move in a quadratically correlated random potential behaves like a free chain with $R^2 \sim L$, where $R$ is the end to end distance and $L$ is the length of the chain, whereas for a chain anchored at one end $R^2 \sim L^4$. The exact results are found to agree with an alternative numerical solution in $d=1$ dimensions. The crossover from long ranged to short ranged correlations of the disorder is also explored.Comment: REVTeX, 28 pages, 12 figures in eps forma

Observations of the Hubble Deep Field with the Infrared Space Observatory. I. Data reduction, maps and sky coverage

We present deep imaging at 6.7 micron and 15 micron from the CAM instrument on the Infrared Space Observatory (ISO), centred on the Hubble Deep Field (HDF). These are the deepest integrations published to date at these wavelengths in any region of sky. We discuss the observation strategy and the data reduction. The observed source density appears to approach the CAM confusion limit at 15 micron, and fluctuations in the 6.7 micron sky background may be identifiable with similar spatial fluctuations in the HDF galaxy counts. ISO appears to be detecting comparable field galaxy populations to the HDF, and our data yields strong evidence that future IR missions (such as SIRTF, FIRST and WIRE) as well as SCUBA and millimetre arrays will easily detect field galaxies out to comparably high redshifts.Comment: 7 pages, LaTeX (using mn.sty), 9 figures included as GIFs. Gzipped Postscipt version available from http://artemis.ph.ic.ac.uk/hdf/papers/ps/. Further information on ISO-HDF project can be found at http://artemis.ph.ic.ac.uk/hdf