A microscopic theory of current partition in fractional quantum Hall liquids, described by chiral Luttinger liquids, is developed to compute the noise correlations, using the Keldysh technique. In this Hanbury-Brown and Twiss geometry, at Laughlin filling factors ν = 1/m, the real time noise correlator exhibits oscillations which persist over larger time scales than that of an uncorrelated Hall fluid. The zero frequency noise correlations are negative at filling factor 1/3 as for bare electrons (anti-bunching), but are strongly reduced in amplitude. These correlations become positive (bunching) for ν ≤ 1/5, suggesting a tendency towards bosonic behavior. PACS 72.70+m,71.10.Pm,73.40.Hm Transport experiments in the fractional quantum Hall effect (FQHE) [1] have provided a direct measurement of the fractional charge of the quasi-particles [2,3] associated with these correlated electron fluids. These results constitute a preliminary test of the Luttinger liquid models [4,5] based on chiral edge Lagrangians [6] which describe the low-lying edge excitations. However, the discussion has centered on the charge of the quasiparticles, rather than the statistics. On the other hand, noise correlation experiments [7,8] in branched mesoscopic devices, i.e. fermion analogs of the Hanbury-Brown and Twiss experiments for photons [9], have detected the negative noise correlations predicted by theory [10]. Statistical features in transport are quite explicit in such experiments. So far in the FQHE, the measurement of the noise reduction [2] -smaller than that of fermions -constitutes the only hint that the statistic is not fermionic.Here, it is suggested that the statistics of the underlying excitations of the FQHE can be monitored via a Hanbury-Brown experiment where quasiparticles emitted from one edge and tunneling through the correlated Hall fluid are collected into two receiving edges (see Fig. 1). This constitutes a mesoscopic analogue of a collision process which involves many quasi-particles, and therefore provides a direct probe of their underlying statistics. The Luttinger edge state theory [6] is used to compute the current and noise with the Keldysh technique. The analytic results for the noise in this partition experiment show that: a) upon increasing the magnetic field from the integer quantum Hall effect (IQHE) to filling factor 1/3, the (negative) correlations are strongly reduced in amplitude; b) these correlations change sign and are positive at ν ≤ 1/5. This work attempts to go further than a recent proposal where statistics and scattering properties were dissociated [11], which correlations are fermionic [12].The suggested geometry is depicted in Fig. 1: it requires three edges (two of which are assumed to be decoupled), in contrast to previous noise correlation measurements [2,7] in the IQHE and in the FQHE where a single constriction controlled the transmission between two edge states. There, negative noise correlations between the receiving ends of two edge states (inset Fig 1a) are the consequence of a...
Transport through a metallic carbon nanotube is considered, where electrons are injected in the bulk by a scanning tunneling microscope tip. The charge current and noise are computed both in the absence and in the presence of one dimensional Fermi liquid leads. For an infinite homogeneous nanotube, the shot noise exhibits effective charges different from the electron charge. Noise correlations between both ends of the nanotube are positive, and occur to second order only in the tunneling amplitude. The positive correlations are symptomatic of an entanglement phenomenon between quasiparticles moving right and left from the tip. This entanglement involves many body states of the boson operators which describe the collective excitations of the Luttinger liquid. I. INTRODUCTIONOver the years, the study of current noise and noise correlations has become a respected and useful diagnosis for transport measurements on mesoscopic conductors. Theoretically, noise was first computed mostly for non-interacting systems 1 . However, it soon became clear that low frequency noise could be used to isolate the quasiparticle charge 2,3 and to study the statistical correlations 4,5 in specific quasi one-dimensional correlated electron systems, such as the edge waves in the quantum Hall effect. In these chiral Luttinger liquids, the charge of the collective excitations along the edges corresponds to the electron charge multiplied by the filling factor.Attention is now turning towards conductors -individual nano-objects -which occur naturally, and which can be connected to current/voltage probes in order to perform a transport experiment. The crucial advantage of such nanoobjects is that they are essentially free of defects and in some circumstances they have an inherent one dimensional character. Carbon nanotubes constitute the archetype of such 1D nano-objects: single wall armchair nanotubes have metallic behavior, with two propagating modes at the Fermi level. Incidentally, electronic correlations are known to play an important role in such systems. Carbon nanotubes seem to constitute good candidates to study Luttinger liquid behavior. In particular, their tunneling density of states -and thus the tunneling I(V ) characteristics is known to have a power law behavior 6,7,8 in accordance with Luttinger liquid theory.Luttinger models for nanotubes differ significantly from their quantum Hall effect counterpart, because of their nonchiral character. Forward and backward fields describing collective excitations effectively mix, because the interactions between electrons are spread along the whole length of the nanotube. For this reason, a straightforward transposition of the results obtained for chiral edge system proves difficult. Nevertheless, non-chiral Luttinger liquids can be described with chiral fields 9,10 . Such chiral fields correspond to excitations with anomalous (non-integer) charge, which has eluded detection so far.In the present work, we propose an experimental geometry which allows to probe directly the underlying charg...
We present a theoretical study of the localization phenomenon of gravity waves by a rough bottom in a one-dimensional channel. After recalling localization theory and applying it to the shallow-water case, we give the first study of the localization problem in the framework of the full potential theory; in particular we develop a renormalized-transfer-matrix approach to this problem. Our results also yield numerical estimates of the localization length, which we compare with the viscous dissipation length. This allows the prediction of which cases localization should be observable in and in which cases it could be hidden by dissipative mechanisms.
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