THE EFFECTS OF MACROSCOPIC DISORDER IN CONDENSED MATTER SYSTEMS

Master'sMASTER OF SCIENC

Equivalence of Effective Medium and Random Resistor Network models for disorder-induced unsaturating linear magnetoresistance

A linear unsaturating magnetoresistance at high perpendicular magnetic fields, together with a quadratic positive magnetoresistance at low fields, has been seen in many different experimental materials, ranging from silver chalcogenides and thin films of InSb to topological materials like graphene and Dirac semimetals. In the literature, two very different theoretical approaches have been used to explain this classical magnetoresistance as a consequence of sample disorder. The phenomenological Random Resistor Network model constructs a grid of four-terminal resistors, each with a varying random resistance. The Effective Medium Theory model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. Here, we demonstrate numerically that both models belong to the same universality class and that a restricted class of the Random Resistor Network is actually equivalent to the Effective Medium Theory. Both models are also in good agreement with experiments on a diverse range of materials. Moreover, we show that in both cases, a single parameter, i.e. the ratio of the fluctuations in the carrier density to the average carrier density, completely determines the magnetoresistance profile.Comment: 6 pages, 5 figure

Moderate deviation expansion for fully quantum tasks

The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, where the communication cost approaches a capacity-like quantity and the error vanishes at the same time. We find exact characterisations of these trade-offs for a variety of fully quantum communication tasks, including quantum source coding, quantum state splitting, entanglement-assisted quantum channel coding, and entanglement-assisted quantum channel simulation. The main technical tool we derive is a tight relation between the partially smoothed max-information and the hypothesis testing relative entropy. This allows us to obtain the expansion of the partially smoothed max-information for i.i.d. states in the moderate deviation regime.Comment: 32 page

A multi-station satellite radio beacon study of ionospheric variations during total solar eclipses

Faraday rotation data obtained at Delhi, Kurukshetra, Hyderabad, Bangalore, Waltair, Nagpur and Calcutta during the total solar eclipse of 16 February 1980 and at Delhi during the total solar eclipse of 31 July 1981 have been analysed to detect the gravity waves generated by a total solar eclipse as hypothesized by Chimonas and Hines (1970, J. geophys. Res. 75, 875). It has been found that gravity waves can be generated by a total solar eclipse but their detection at ionospheric heights is critically dependent on the location of the observing station in relation to the eclipse path geometry. The distance of the observing station from the eclipse path should be more than 500 km in order to detect such gravity waves