Transport in Luttinger Liquids

We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some important results on tunneling through barriers in a one-dimensional quantum wire and the phenomena of persistent currents in mesoscopic rings. We give a brief description of our own work on transport through doubly-crossed Luttinger liquids and transport in the Schulz-Shastry exactly solvable Luttinger-like model.Comment: Latex file, 15 pages, four eps figure

Electronic phase separation in the rare earth manganates, (La1-xLnx)0.7Ca0.3MnO3 (Ln = Nd, Gd and Y)

All the three series of manganates showsaturation magnetization characteristic of ferromagnetism, with the ferromagnetic Tc decreasing with increasing in x up to a critical value of x, xc (xc = 0.6, 0.3, 0.2 respectively for Nd, Gd, Y). For x > xc, the magnetic moments are considerably smaller showing a small increase around TM, the value of TM decreasing slightly with increase in x or decrease in . The ferromagnetic compositions (x xc) show insulator-metal (IM) transitions, while the compositions with x > xc are insulating. The magnetic and electrical resistivity behavior of these manganates is consistent with the occurrence of phase separation in the compositions around xc, corresponding to a critical average radius of the A-site cation, , of 1.18 A. Both Tc and TIM increase linearly when < rA > > or x xc as expected of a homogenous ferromagnetic phase. Both Tc and TM decrease linearly with the A-site cation size disorder at the A-site as measured by the variance s2. Thus, an increase in s2 favors the insulating AFM state. Percolative conduction is observed in the compositions with > < rAc >. Electron transport properties in the insulating regime for x > xc conforms to the variable range hopping mechanism. More interestingly, when x > xc, the real part of dielectric constant (e') reaches a high value (104-106) at ordinary temperatures dropping to a very small (~500) value below a certain temperature, the value of which decreases with decreasing frequency.Comment: 27 pages; 11 figures, Submitted to J.Phys:Condens Matte

Non-singular radiation cosmological models

In this paper we analyse the possibility of constructing singularity-free inhomogeneous cosmological models with a pure radiation field as matter content. It is shown that the conditions for regularity are very easy to implement and therefore there is a huge number of such spacetimes.Comment: 13 pages, LaTex, ws-mpla, to appear in Modern Physics Letters

A Theory of Errors in Quantum Measurement

It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an observable are distributed normally. We obtain the probability distribution this implies for the outcome of a measurement, exactly for the case of 2x2 matrices and in the steepest descent approximation in general. Due to the phenomenon of `level repulsion', the probability distributions obtained are quite different from the Gaussian.Comment: Based on talk at "Spacetime and Fundamental Interactions: Quantum Aspects" A conference to honor A. P. Balachandran's 65th Birthda

Theory of Hysteresis Loop in Ferromagnets

We consider three mechanisms of hysteresis phenomena in alternating magnetic field: the domain wall motion in a random medium, the nucleation and the retardation of magnetization due to slow (critical) fluctuations. We construct quantitative theory for all these processes. The hysteresis is characterized by two dynamic threshold fields, by coercive field and by the so-called reversal field. Their ratios to the static threshold field is shown to be function of two dimensionless variables constituted from the frequency and amplitude of the ac field as well as from some characteristics of the magnet. The area and the shape of the hysteresis loop are found. We consider different limiting cases in which power dependencies are valid. Numerical simulations show the domain wall formation and propagation and confirm the main theoretical predictions. Theory is compared with available experimental data.Comment: RevTex, 13 pages, 8 figures (PostScript), acknowledgements adde

Droplet Fluctuations in the Morphology and Kinetics of Martensites

We derive a coarse grained, free-energy functional which describes droplet configurations arising on nucleation of a product crystal within a parent. This involves a new `slow' vacancy mode that lives at the parent-product interface. A mode-coupling theory suggests that a {\it slow} quench from the parent phase produces an equilibrium product, while a {\it fast} quench produces a metastable martensite. In two dimensions, the martensite nuclei grow as `lens-shaped' strips having alternating twin domains, with well-defined front velocities. Several empirically known structural and kinetic relations drop out naturally from our theory.Comment: 4 pages, REVTEX, and 3 .eps figures, compressed and uuencoded, Submitted to Phys. Rev. Let

Diffuse Neutron Scattering Study of Magnetic Correlations in half-doped La0.5Ca0.5-xSrxMnO3 (x = 0.1, 0.3 and 0.4) Manganites

The short range ordered magnetic correlations have been studied in half doped La0.5Ca0.5-xSrxMnO3 (x = 0.1, 0.3 and 0.4) compounds by polarized neutron scattering technique. On doping Sr2+ for Ca2+ ion, these compounds with x = 0.1, 0.3, and 0.4 exhibit CE-type, mixture of CE-type and A-type, and A-type antiferromagnetic ordering, respectively. Magnetic diffuse scattering is observed in all the compounds above and below their respective magnetic ordering temperatures and is attributed to magnetic polarons. The correlations are primarily ferromagnetic in nature above T\_N, although a small antiferromagnetic contribution is also evident. Additionally, in samples x = 0.1 and 0.3 with CE-type antiferromagnetic ordering, superlattice diffuse reflections are observed indicating correlations between magnetic polarons. On lowering temperature below T\_N the diffuse scattering corresponding to ferromagnetic correlations is suppressed and the long range ordered antiferromagnetic state is established. However, the short range ordered correlations indicated by enhanced spin flip scattering at low Q coexist with long range ordered state down to 3K. In x = 0.4 sample with A-type antiferromagnetic ordering, superlattice diffuse reflections are absent. Additionally, in comparison to x = 0.1 and 0.3 sample, the enhanced spin flip scattering at low Q is reduced at 310K, and as temperature is reduced below 200K, it becomes negligibly low. The variation of radial correlation function, g(r) with temperature indicates rapid suppression of ferromagnetic correlations at the first nearest neighbor on approaching TN. Sample x = 0.4 exhibits growth of ferromagnetic phase at intermediate temperatures (~ 200K). This has been further explored using SANS and neutron depolarization techniques.Comment: 13 pages, 12 figures, To appear in Physical Review

Autonomous detection and anticipation of jam fronts from messages propagated by inter-vehicle communication

In this paper, a minimalist, completely distributed freeway traffic information system is introduced. It involves an autonomous, vehicle-based jam front detection, the information transmission via inter-vehicle communication, and the forecast of the spatial position of jam fronts by reconstructing the spatiotemporal traffic situation based on the transmitted information. The whole system is simulated with an integrated traffic simulator, that is based on a realistic microscopic traffic model for longitudinal movements and lane changes. The function of its communication module has been explicitly validated by comparing the simulation results with analytical calculations. By means of simulations, we show that the algorithms for a congestion-front recognition, message transmission, and processing predict reliably the existence and position of jam fronts for vehicle equipment rates as low as 3%. A reliable mode of operation already for small market penetrations is crucial for the successful introduction of inter-vehicle communication. The short-term prediction of jam fronts is not only useful for the driver, but is essential for enhancing road safety and road capacity by intelligent adaptive cruise control systems.Comment: Published in the Proceedings of the Annual Meeting of the Transportation Research Board 200

Renormalization group study of the conductances of interacting quantum wire systems with different geometries

We examine the effect of interactions between the electrons on the conductances of some systems of quantum wires with different geometries. The systems include a wire with a stub in the middle, a wire containing a ring which can enclose a magnetic flux, and a system of four wires which are connected in the middle through a fifth wire. Each of the wires is taken to be a weakly interacting Tomonaga-Luttinger liquid, and scattering matrices are introduced at all the junctions. Using a renormalization group method developed recently for studying the flow of scattering matrices for interacting systems in one dimension, we compute the conductances of these systems as functions of the temperature and the wire lengths. We present results for all three regimes of interest, namely, high, intermediate and low temperature. These correspond respectively to the thermal coherence length being smaller than, comparable to and larger than the smallest wire length in the different systems, i.e., the length of the stub or each arm of the ring or the fifth wire. The renormalization group procedure and the formulae used to compute the conductances are different in the three regimes. We present a phenomenologically motivated formalism for studying the conductances in the intermediate regime where there is only partial coherence. At low temperatures, we study the line shapes of the conductances versus the electron energy near some of the resonances; the widths of the resonances go to zero with decreasing temperature. Our results show that the conductances of various systems of experimental interest depend on the temperature and lengths in a non-trivial way when interactions are taken into account.Comment: Revtex, 17 pages including 15 figure

Understanding of the phase transformation from fullerite to amorphous carbon at the microscopic level

We have studied the shock-induced phase transition from fullerite to a dense amorphous carbon phase by tight-binding molecular dynamics. For increasing hydrostatic pressures P, the C60-cages are found to polymerise at P<10 GPa, to break at P~40 GPa and to slowly collapse further at P>60 GPa. By contrast, in the presence of additional shear stresses, the cages are destroyed at much lower pressures (P<30 GPa). We explain this fact in terms of a continuum model, the snap-through instability of a spherical shell. Surprisingly, the relaxed high-density structures display no intermediate-range order.Comment: 5 pages, 3 figure