Density dependence of valley polarization energy for composite fermions

In two-dimensional electron systems confined to wide AlAs quantum wells, composite fermions around the filling factor $\nu$ = 3/2 are fully spin polarized but possess a valley degree of freedom. Here we measure the energy needed to completely valley polarize these composite fermions as a function of electron density. Comparing our results to the existing theory, we find overall good quantitative agreement, but there is an unexpected trend: The measured composite fermion valley polarization energy, normalized to the Coulomb energy, decreases with decreasing density

Hypothesis of path integral duality: Applications to QED

We use the modified propagator for quantum field based on a ``principle of path integral duality" proposed earlier in a paper by Padmanabhan to investigate several results in QED. This procedure modifies the Feynman propagator by the introduction of a fundamental length scale. We use this modified propagator for the Dirac particles to evaluate the first order radiative corrections in QED. We find that the extra factor of the modified propagator acts like a regulator at the Planck scales thereby removing the divergences that otherwise appear in the conventional radiative correction calculations of QED. We find that:(i) all the three renormalisation factors $Z_1$, $Z_2$, and $Z_3$ pick up finite corrections and (ii) the modified propagator breaks the gauge invariance at a very small level of ${\mathcal{O}}(10^{-45})$. The implications of this result to generation of the primordial seed magnetic fields are discussed.Comment: 15 pages, LaTeX2e (uses ijmpd.sty); To appear in IJMP-D; References adde

Effective mass suppression upon complete spin-polarization in an isotropic two-dimensional electron system

We measure the effective mass (m*) of interacting two-dimensional electrons confined to a 4.5 nm-wide AlAs quantum well. The electrons in this well occupy a single out-of-plane conduction band valley with an isotropic in-plane Fermi contour. When the electrons are partially spin polarized, m* is larger than its band value and increases as the density is reduced. However, as the system is driven to full spin-polarization via the application of a strong parallel magnetic field, m* is suppressed down to values near or even below the band mass. Our results are consistent with the previously reported measurements on wide AlAs quantum wells where the electrons occupy an in-plane valley with an anisotropic Fermi contour and effective mass, and suggest that the effective mass suppression upon complete spin polarization is a genuine property of interacting two-dimensional electrons.Comment: 6 pages, 7 figures, accepted for publication in Phys. Rev.

The structure of dark matter halos in hierarchical clustering theories

During hierarchical clustering, smaller masses generally collapse earlier than larger masses and so are denser on the average. The core of a small mass halo could be dense enough to resist disruption and survive undigested, when it is incorporated into a bigger object. We explore the possibility that a nested sequence of undigested cores in the center of the halo, which have survived the hierarchical, inhomogeneous collapse to form larger and larger objects, determines the halo structure in the inner regions. For a flat universe with $P(k) \propto k^n$, scaling arguments then suggest that the core density profile is, $\rho \propto r^{-\alpha}$ with $\alpha = (9+3n)/(5+n)$. But whether such behaviour obtains depends on detailed dynamics. We first examine the dynamics using a fluid approach to the self-similar collapse solutions for the dark matter phase space density, including the effect of velocity dispersions. We highlight the importance of tangential velocity dispersions to obtain density profiles shallower than $1/r^2$ in the core regions. If tangential velocity dispersions in the core are constrained to be less than the radial dispersion, a cuspy core density profile shallower than 1/r cannot obtain, in self-similar collapse. We then briefly look at the profiles of the outer halos in low density cosmological models where the total halo mass is convergent. Finally, we analyze a suite of dark halo density and velocity dispersion profiles obtained in cosmological N-body simulations of models with n= 0, -1 and -2. We find that the core-density profiles of dark halos, show considerable scatter in their properties, but nevertheless do appear to reflect a memory of the initial power spectrum, with steeper initial spectra producing flatter core profiles. (Abridged)Comment: 31 pages, 7 figures, submitted to Ap

The hypothesis of path integral duality II: corrections to quantum field theoretic results

In the path integral expression for a Feynman propagator of a spinless particle of mass $m$, the path integral amplitude for a path of proper length ${\cal R}(x,x'| g_{\mu\nu})$ connecting events $x$ and $x'$ in a spacetime described by the metric tensor $g_{\mu\nu}$ is $\exp-[m {\cal R}(x,x'| g_{\mu\nu})]$. In a recent paper, assuming the path integral amplitude to be invariant under the duality transformation ${\cal R} \to (L_P^2/{\cal R})$, Padmanabhan has evaluated the modified Feynman propagator in an arbitrary curved spacetime. He finds that the essential feature of this `principle of path integral duality' is that the Euclidean proper distance $(\Delta x)^2$ between two infinitesimally separated spacetime events is replaced by $[(\Delta x)^2 + 4L_P^2 ]$. In other words, under the duality principle the spacetime behaves as though it has a `zero-point length' $L_P$, a feature that is expected to arise in a quantum theory of gravity. In the Schwinger's proper time description of the Feynman propagator, the weightage factor for a path with a proper time $s$ is $\exp-(m^2s)$. Invoking Padmanabhan's `principle of path integral duality' corresponds to modifying the weightage factor $\exp-(m^2s)$ to $\exp-[m^2s + (L_P^2/s)]$. In this paper, we use this modified weightage factor in Schwinger's proper time formalism to evaluate the quantum gravitational corrections to some of the standard quantum field theoretic results in flat and curved spacetimes. We find that the extra factor $\exp-(L_P^2/s)$ acts as a regulator at the Planck scale thereby `removing' the divergences that otherwise appear in the theory. Finally, we discuss the wider implications of our analysis.Comment: 26 pages, Revte

Valley polarization and susceptibility of composite fermions around nu=3/2

We report magnetotransport measurements of fractional quantum Hall states in an AlAs quantum well around Landau level filling factor nu = 3/2, demonstrating that the quasiparticles are composite Fermions (CFs) with a valley degree of freedom. By monitoring the valley level crossings for these states as a function of applied symmetry-breaking strain, we determine the CF valley susceptibility and polarization. The data can be explained well by a simple Landau level fan diagram for CFs, and are in nearly quantitative agreement with the results reported for CF spin polarization.Comment: to appear in Phys. Rev. Let

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure

Tuning of Fermi Contour Anisotropy in GaAs (001) 2D Holes via Strain

We demonstrate tuning of the Fermi contour anisotropy of two-dimensional (2D) holes in a symmetric GaAs (001) quantum well via the application of in-plane strain. The ballistic transport of high-mobility hole carriers allows us to measure the Fermi wavevector of 2D holes via commensurability oscillations as a function of strain. Our results show that a small amount of in-plane strain, on the order of $10^{-4}$, can induce significant Fermi wavevector anisotropy as large as 3.3, equivalent to a mass anisotropy of 11 in a parabolic band. Our method to tune the anisotropy \textit{in situ} provides a platform to study the role of anisotropy on phenomena such as the fractional quantum Hall effect and composite fermions in interacting 2D systems.Comment: Accepted to Applied Physics Letter

Observational constraints on low redshift evolution of dark energy: How consistent are different observations?

The dark energy component of the universe is often interpreted either in terms of a cosmological constant or as a scalar field. A generic feature of the scalar field models is that the equation of state parameter w= P/rho for the dark energy need not satisfy w=-1 and, in general, it can be a function of time. Using the Markov chain Monte Carlo method we perform a critical analysis of the cosmological parameter space, allowing for a varying w. We use constraints on w(z) from the observations of high redshift supernovae (SN), the WMAP observations of CMB anisotropies and abundance of rich clusters of galaxies. For models with a constant w, the LCDM model is allowed with a probability of about 6% by the SN observations while it is allowed with a probability of 98.9% by WMAP observations. The LCDM model is allowed even within the context of models with variable w: WMAP observations allow it with a probability of 99.1% whereas SN data allows it with 23% probability. The SN data, on its own, favors phantom like equation of state (w<-1) and high values for Omega_NR. It does not distinguish between constant w (with w<-1) models and those with varying w(z) in a statistically significant manner. The SN data allows a very wide range for variation of dark energy density, e.g., a variation by factor ten in the dark energy density between z=0 and z=1 is allowed at 95% confidence level. WMAP observations provide a better constraint and the corresponding allowed variation is less than a factor of three. Allowing for variation in w has an impact on the values for other cosmological parameters in that the allowed range often becomes larger. (Abridged)Comment: 21 pages, PRD format (Revtex 4), postscript figures. minor corrections to improve clarity; references, acknowledgement adde

An Approach to Improve Multi objective Path Planning for Mobile Robot Navigation using the Novel Quadrant Selection Method

Currently, automated and semi-automated industries need multiple objective path planning algorithms for mobile robot applications. The multi-objective optimisation algorithm takes more computational effort to provide optimal solutions. The proposed grid-based multi-objective global path planning algorithm [Quadrant selection algorithm (QSA)] plans the path by considering the direction of movements from starting position to the target position with minimum computational effort. Primarily, in this algorithm, the direction of movements is classified into quadrants. Based on the selection of the quadrant, the optimal paths are identified. In obstacle avoidance, the generated feasible paths are evaluated by the cumulative path distance travelled, and the cumulative angle turned to attain an optimal path. Finally, to ease the robot’s navigation, the obtained optimal path is further smoothed to avoid sharp turns and reduce the distance. The proposed QSA in total reduces the unnecessary search for paths in other quadrants. The developed algorithm is tested in different environments and compared with the existing algorithms based on the number of cells examined to obtain the optimal path. Unlike other algorithms, the proposed QSA provides an optimal path by dramatically reducing the number of cells examined. The experimental verification of the proposed QSA shows that the solution is practically implementable