Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

While it is well-known that the electron-electron (\emph{ee}) interaction cannot affect the resistivity of a Galilean-invariant Fermi liquid (FL), the reverse statement is not necessarily true: the resistivity of a non-Galilean-invariant FL does not necessarily follow a T^2 behavior. The T^2 behavior is guaranteed only if Umklapp processes are allowed; however, if the Fermi surface (FS) is small or the electron-electron interaction is of a very long range, Umklapps are suppressed. In this case, a T^2 term can result only from a combined--but distinct from quantum-interference corrections-- effect of the electron-impurity and \emph{ee} interactions. Whether the T^2 term is present depends on 1) dimensionality (two dimensions (2D) vs three dimensions (3D)), 2) topology (simply- vs multiply-connected), and 3) shape (convex vs concave) of the FS. In particular, the T^2 term is absent for any quadratic (but not necessarily isotropic) spectrum both in 2D and 3D. The T^2 term is also absent for a convex and simply-connected but otherwise arbitrarily anisotropic FS in 2D. The origin of this nullification is approximate integrability of the electron motion on a 2D FS, where the energy and momentum conservation laws do not allow for current relaxation to leading --second--order in T/E_F (E_F is the Fermi energy). If the T^2 term is nullified by the conservation law, the first non-zero term behaves as T^4. The same applies to a quantum-critical metal in the vicinity of a Pomeranchuk instability, with a proviso that the leading (first non-zero) term in the resistivity scales as T^{\frac{D+2}{3}} (T^{\frac{D+8}{3}}). We discuss a number of situations when integrability is weakly broken, e.g., by inter-plane hopping in a quasi-2D metal or by warping of the FS as in the surface states of Bi_2Te_3 family of topological insulators.Comment: Submitted to a special issue of the Lithuanian Journal of Physics dedicated to the memory of Y. B. Levinso

A semi-analytical approach to perturbations in mutated hilltop inflation

We study cosmological perturbations and observational aspects for mutated hilltop model of inflation. Employing mostly analytical treatment, we evaluate observable parameters during inflation as well as post-inflationary perturbations. This further leads to exploring observational aspects related to Cosmic Microwave Background (CMB) radiation. This semi-analytical treatment reduces complications related to numerical computation to some extent for studying the different phenomena related to CMB angular power spectrum for mutated hilltop inflation.Comment: 7 pages, 2 figures. Improved version to appear in IJMP

Flux jumps, Second Magnetization Peak anomaly and the Peak Effect phenomenon in single crystals of YNi2B2CYNi_2B_2C and LuNi2B2CLuNi_2B_2C

We present magnetization measurements in single crystals of the tetragonal $YNi_2B_2C$ compound, which exhibit the phenomenon of peak effect as well as the second magnetization peak anomaly for H $>$ 0.5T (H $||$ c). At the lower field (50mT $<$ H $<$ 200mT), we have observed the presence of flux jumps, which seem to relate to a structural change in the local symmetry of the flux line lattice (a first order re-orientation transition across a local field in some parts of the sample, in the range of 100mT to 150mT). These flux jumps are also observed in a single crystal of $LuNi_2B_2C$ for H $||$ c in the field region from 2 mT to 25 mT, which are compatible with the occurrence of a re-orientation transition at a lower field in a cleaner crystal of this compound, as compared to those of $YNi_2B_2C$. Vortex phase diagrams drawn for H $||$ c in $LuNi_2B_2C$ and $YNi_2B_2C$ show that the ordered elastic glass phase spans a larger part of (H, T) space in the former as compared to latter, thereby, reaffirming the difference in the relative purity of the two samples.Comment: 11 pages, 14 figure

Scale-Dependent Price Fluctuations for the Indian Stock Market

Classic studies of the probability density of price fluctuations $g$ for stocks and foreign exchanges of several highly developed economies have been interpreted using a {\it power-law} probability density function $P(g) \sim g^{-(\alpha+1)}$ with exponent values $\alpha > 2$, which are outside the L\'evy-stable regime $0 < \alpha < 2$. To test the universality of this relationship for less highly developed economies, we analyze daily returns for the period Nov. 1994--June 2002 for the 49 largest stocks of the National Stock Exchange which has the highest volume of trade in India. We find that $P(g)$ decays as an {\it exponential} function $P(g) \sim \exp(-\beta g)$ with a characteristic decay scales $\beta = 1.51 \pm 0.05$ for the negative tail and $\beta = 1.34 \pm 0.04$ for the positive tail, which is significantly different from that observed for developed economies. Thus we conclude that the Indian stock market may belong to a universality class that differs from those of developed countries analyzed previously.Comment: 7 pages, 8 figure

Frustration-induced Emergent Hilbert Space Fragmentation

Although most quantum systems thermalize locally on short timescales independent of initial conditions, recent developments have shown this is not always the case. Lattice geometry and quantum mechanics can conspire to produce constrained quantum dynamics and associated glassy behavior, a phenomenon that falls outside the rubric of the eigenstate thermalization hypothesis. Constraints “fragment” the many-body Hilbert space due to which some states remain insulated from others and the system fails to attain thermal equilibrium. Such fragmentation is a hallmark of geometrically frustrated magnets with low-energy “icelike manifolds” exhibiting a broad range of relaxation times for different initial states. Focusing on the highly frustrated kagome lattice, we demonstrate these phenomena in the Balents-Fisher-Girvin Hamiltonian (easy-axis regime), and a three-coloring model (easy-plane regime), both with constrained Hilbert spaces. We study their level statistics and relaxation dynamics to develop a coherent picture of fragmentation in various limits of the XXZ model on the kagome lattice

Hydrogen Bond Dynamics Near A Micellar Surface: Origin of the Universal Slow Relaxation at Complex Aqueous Interfaces

The dynamics of hydrogen bonds among water molecules themselves and with the polar head groups (PHG) at a micellar surface have been investigated by long molecular dynamics simulations. The lifetime of the hydrogen bond between a PHG and a water molecule is found to be much longer than that between any two water molecules, and is likely to be a general feature of hydrophilic surfaces of organized assemblies. Analyses of individual water trajectories suggest that water molecules can remain bound to the micellar surface for more than a hundred picosecond. The activation energy for such a transition from the bound to a free state for the water molecules is estimated to be about 3.5kcal/mole.Comment: 12 pages. Phys. Rev. Lett. (Accepted) (2002

The extent of strangeness in equilibration in quark-gluon plasma

The evolution and production of strangeness from chemically equilibrating and transversely expanding quark gluon plasma which may be formed in the wake of relativistic heavy ion collisions is studied with initial conditions obtained from the Self Screened Parton Cascade (SSPC) model. The extent of partonic equilibration increases almost linearly with the square of the initial energy density, which can then be scaled with number of participants.Comment: 4 pages including three figures, talk given at ICPAQGP'01, Jaipur, India, to appear in Pramana - Journal of Physics, Indian Academy of Scienc