Very smooth points of spaces of operators

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an $M$-ideal in the space of bounded operators, a very smooth operator $T$ attains its norm at a unique vector $x$ (up to a constant multiple) and $T(x)$ is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon--Nikod\'{y}m property. We give an example of a smooth Banach space without any very smooth points.Comment: 12 pages, no figures, no table

Simulation of mirror inversion of quantum states in an XY spin chain using NMR

We report an experimental quantum simulation of unitary dynamics of an XY spin chain with pre-engineered couplings. Using this simulation, we demonstrate the mirror inversion of quantum states, proposed by Albanese et al. [Phys. Rev. Lett. 93, 230502 (2004)]. The experiment is performed with a 5-qubit dipolar coupled spin system using nuclear magnetic resonance techniques. To perform quantum simulation we make use of the recently proposed unitary operator decomposition algorithm of Ajoy et al. [Phys. Rev. A 85, 030303 (2012)] along with numerical pulse optimization techniques. Further, using mirror inversion, we demonstrate that entangled states can be transferred from one end of the chain to the other end. The simulations are implemented with high experimental fidelity, which implies that these kind of simulations may be possible in larger systems.Comment: 9 pages, 6 figure

Violation of Entropic Leggett-Garg Inequality in Nuclear Spins

We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. (arXiv: 1208.4491v2 (2012)). This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. Here we study ELGI using a two-qubit nuclear magnetic resonance system. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the `ideal negative result measurement' procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we experimentally demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities.Comment: 5 pages, 5 figures, 1 page supplementar

Backward whirl in a simple rotor supported on hydrodynamic bearings

The asymmetric nature of the fluid film stiffness and damping properties in rotors supported on fluid film bearings causes a forward or a backward whirl depending on the bearing parameters and the speed of the rotor. A rotor was designed to exhibit backward synchronous whirl. The rotor-bearing system exhibited split criticals, and a backward whirl was observed between the split criticals. The orbital diagrams show the whirl pattern

Offset fields in perpendicularly magnetized tunnel junctions

We study the offset fields affecting the free layer of perpendicularly magnetized tunnel junctions. In extended films, the free layer offset field results from interlayer exchange coupling with the reference layer through the MgO tunnel oxide. The free layer offset field is thus accompanied with a shift of the free layer and reference layer ferromagnetic resonance frequencies. The shifts depend on the mutual orientation of the two magnetizations. The offset field decreases with the resistance area product of the tunnel oxide. Patterning the tunnel junction into an STT-MRAM disk-shaped cell changes substantially the offset field, as the reduction of the lateral dimension comes with the generation of stray fields by the reference and the hard layer. The experimental offset field compares best with the spatial average of the sum of these stray fields, thereby providing guidelines for the offset field engineering.Comment: Special issue of J. Phys. D: Appl. Phys (2019) on STT-MRA

Radio halos in merging clusters of galaxies

We present the preliminary results of 235 MHz, 327 MHz and 610 MHz observations of the galaxy cluster A3562 in the core of the Shapley Concentration. The purpose of these observations, carried out with the Giant Metrewave Radio Telescope (GMRT, Pune, India) was to study the radio halo located at the centre of A3562 and determine the shape of its radio spectrum at low frequencies, in order to understand the origin of this source. In the framework of the re--acceleration model, the preliminary analysis of the halo spectrum suggests that we are observing a young source (few $10^8$ yrs) at the beginning of the re--acceleration phase.Comment: 3 pages, 2 figures. Proceedings of IAU Colloquium 195 - Outskirts of Galaxy Clusters: intense life in the suburb

Shear flow induced isotropic to nematic transition in a suspension of active filaments

We study the effects of externally applied shear flow on a model of suspensions of motors and filaments, via the equations of active hydrodynamics [PRL {\bf 89} (2002) 058101; {\bf 92} (2004) 118101]. In the absence of shear, the orientationally ordered phase of {\it both} polar and apolar active particles is always unstable at zero-wavenumber. An imposed steady shear large enough to overcome the active stresses stabilises both apolar and moving polar phases. Our work is relevant to {\it in vitro} studies of active filaments, the reorientation of endothelial cells subject to shear flow and shear-induced motility of attached cells.Comment: 8 pages, 4 figures submitted to Europhysics Letter