Fractionalization of minimal excitations in integer quantum Hall edge channels

A theoretical study of the single electron coherence properties of Lorentzian and rectangular pulses is presented. By combining bosonization and the Floquet scattering approach, the effect of interactions on a periodic source of voltage pulses is computed exactly. When such excitations are injected into one of the channels of a system of two copropagating quantum Hall edge channels, they fractionalize into pulses whose charge and shape reflects the properties of interactions. We show that the dependence of fractionalization induced electron/hole pair production in the pulses amplitude contains clear signatures of the fractionalization of the individual excitations. We propose an experimental setup combining a source of Lorentzian pulses and an Hanbury Brown and Twiss interferometer to measure interaction induced electron/hole pair production and more generally to reconstruct single electron coherence of these excitations before and after their fractionalization.Comment: 18 pages, 10 figures, 1 tabl

Influence of surfactants on the structure of titanium oxide gels : experiments and simulations

We report here on experimental and numerical studies of the influence of surfactants on mineral gel synthesis. The modification of the gel structure when the ratios water-precursor and water-surfactant vary is brought to the fore by fractal dimension measures. A property of {\em polydispersity of the initial hydrolysis} is proposed to explain these results, and is successfuly tested through numerical experiments of three dimensional chemically limited aggregation.Comment: 12 pages, 4 Postscript figures, uses RevTe

Work-rate of substitutes in elite soccer: A preliminary study

The aim of this study was to investigate the work-rate of substitutes in professional soccer. A computerised player tracking system was used to assess the work-rates of second-half substitutes (11 midfielders and 14 forwards) in a French Ligue 1 club. Total distance, distance covered in five categories of movement intensity and recovery time between high-intensity efforts were evaluated. First- and second-half work-rates of the replaced players were compared. The performance of substitutes was compared to that of the players they replaced, to team-mates in the same position who remained on the pitch after the substitution and in relation to their habitual performances when starting games. No differences in work-rate between first- and second-halves were observed in all players who were substituted. In the second-half, a non-significant trend was observed in midfield substitutes who covered greater distances than the player they replaced whereas no differences were observed in forwards. Midfield substitutes covered a greater overall distance and distance at high-intensities (p<0.01) and had a lower recovery time between high-intensity efforts (p<0.01) compared to other midfield team-mates who remained on the pitch. Forwards covered less distance (p<0.01) in their first 10-minutes as a substitute compared to their habitual work-rate profile in the opening 10-minutes when starting matches while this finding was not observed in midfielders. These findings suggest that compared to midfield substitutes, forward substitutes did not utilise their full physical potential. Further investigation is warranted into the reasons behind this finding in order to optimise the work-rate contributions of forward substitutes

Integer and fractional charge Lorentzian voltage pulses analyzed in the frame of Photon-assisted Shot Noise

The periodic injection $n$ of electrons in a quantum conductor using periodic voltage pulses applied on a contact is studied in the energy and time-domain using shot noise computation in order to make comparison with experiments. We particularly consider the case of periodic Lorentzian voltage pulses. When carrying integer charge, they are known to provide electronic states with a minimal number of excitations, while other type of pulses are all accompanied by an extra neutral cloud of electron and hole excitations. This paper focuses on the low frequency shot noise which arises when the pulse excitations are partitioned by a single scatterer in the framework of the Photo Assisted Shot Noise (PASN) theory. As a unique tool to count the number of excitations carried per pulse, shot noise reveals that pulses of arbitrary shape and arbitrary charge show a marked minimum when the charge is integer. Shot noise spectroscopy is also considered to perform energy-domain characterization of the charge pulses. In particular it reveals the striking asymmetrical spectrum of Lorentzian pulses. Finally, time-domain information is obtained from Hong Ou Mandel like noise correlations when two trains of pulses generated on opposite contacts collide on the scatterer. As a function of the time delay between pulse trains, the noise is shown to measure the electron wavepacket autocorrelation function for integer Lorentzian thanks to electron antibunching. In order to make contact with recent experiments all the calculations are made at zero and finite temperature

Magnetic phase diagram of the spin-1/2 antiferromagnetic zigzag ladder

We study the one-dimensional spin-1/2 Heisenberg model with antiferromagnetic nearest-neighbor J_1 and next-nearest-neighbor J_2 exchange couplings in magnetic field h. With varying dimensionless parameters J_2/J_1 and h/J_1, the ground state of the model exhibits several phases including three gapped phases (dimer, 1/3-magnetization plateau, and fully polarized phases) and four types of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2, spin-density-wave (SDW_2), and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various (multiple-)spin correlation functions in detail, and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1, SDW_2, and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs, and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons (central charge c=1+1), which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-one-dimensional compounds are also discussed.Comment: 22 pages, 17 figures. v2: published versio

Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field

We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighbor J_2 exchange couplings in the presence of magnetic field. We use both numerical approaches (the density matrix renormalization group method and exact diagonalization) and effective field-theory approach, and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J_1/J_2. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferro-nematic spin correlation, and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed through binding of p magnons near the saturation fields, showing quasi-LRO of antiferro-multipolar spin correlations. The multipolar phases cross over to spin density wave phases as the magnetic field is decreased, before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO_4) are discussed.Comment: v1. 20 pages, 18 figures: v2: 21 pages, 19 figures, Title modified slightly. Some references, Fig.16, and a note are added. To appear in Phys. Rev.

Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction

Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than the expected square of the velocity. It was also found that, for a given inclination of the plane, the velocity of the ball scales as a power of its radius. We present here a one dimensional stochastic model based on the microscopic equations of motion of the ball, which exhibits the same behaviour as the experiments. This model yields a mechanism for the origins of the viscous friction force and the scaling of the velocity with the radius. It also reproduces other aspects of the phase diagram of the motion which we will discuss.Comment: 19 pages, latex, 11 postscript figures in separate uuencoded fil

Fluctuating Bond Aggregation: a Model for Chemical Gel Formation

The Diffusion-Limited Cluster-Cluster Aggregation (DLCA) model is modified by including cluster deformations using the {\it bond fluctuation} algorithm. From 3$d$ computer simulations, it is shown that, below a given threshold value $c_g$ of the volumic fraction $c$, the realization of all intra-aggregate bonding possibilities prevents the formation of a gelling network. For $c>c_g$, the sol-gel transition occurs at a time $t_g$ which, in contrast to DLCA, doesnot diverge with the box size. Several results are reported including small angle scattering curves and possible applications are discussed.Comment: RevTex, 9 pages + 3 postscript figures appended using "uufiles". To appear in Phys. Rev. Let

New universality class for the three-dimensional XY model with correlated impurities: Application to 4^4He in aerogels

Encouraged by experiments on $^4$He in aerogels, we confine planar spins in the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behavior of the three-dimensional XY model. Monte Carlo simulations and finite-size scaling are used to determine critical couplings $K_c$ and exponents. In agreement with experiments, clear evidence of change in the thermal critical exponents $\nu$ and $\alpha$ is found at nonzero volume fractions of impurities. These changes are explained in terms of {\it hidden} long-range correlations within disorder distributions.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let