Statistical properties of chaotic microcavities in small and large opening cases

We study the crossover behavior of statistical properties of eigenvalues in a chaotic microcavity with different refractive indices. The level spacing distributions change from Wigner to Poisson distributions as the refractive index of a microcavity decreases. We propose a non-hermitian matrix model with random elements describing the spectral properties of the chaotic microcavity, which exhibits the crossover behaviors as the opening strength increases.Comment: 22 pages, 6 figure

Congestion Control and Routing over Challenged Networks

This dissertation is a study on the design and analysis of novel, optimal routing and rate control algorithms in wireless, mobile communication networks. Congestion control and routing algorithms upto now have been designed and optimized for wired or wireless mesh networks. In those networks, optimal algorithms (optimal in the sense that either the throughput is maximized or delay is minimized, or the network operation cost is minimized) can be engineered based on the classic time scale decomposition assumption that the dynamics of the network are either fast enough so that these algorithms essentially see the average or slow enough that any changes can be tracked to allow the algorithms to adapt over time. However, as technological advancements enable integration of ever more mobile nodes into communication networks, any rate control or routing algorithms based, for example, on averaging out the capacity of the wireless mobile link or tracking the instantaneous capacity will perform poorly. The common element in our solution to engineering efficient routing and rate control algorithms for mobile wireless networks is to make the wireless mobile links seem as if they are wired or wireless links to all but few nodes that directly see the mobile links (either the mobiles or nodes that can transmit to or receive from the mobiles) through an appropriate use of queuing structures at these selected nodes. This approach allows us to design end-to-end rate control or routing algorithms for wireless mobile networks so that neither averaging nor instantaneous tracking is necessary

Quasiattractors in coupled maps and coupled dielectric cavities

We study the origin of attracting phenomena in the ray dynamics of coupled optical microcavities. To this end we investigate a combined map that is composed of standard and linear map, and a selection rule that defines when which map has to be used. We find that this system shows attracting dynamics, leading exactly to a quasiattractor, due to collapse of phase space. For coupled dielectric disks, we derive the corresponding mapping based on a ray model with deterministic selection rule and study the quasiattractor obtained from it. We also discuss a generalized Poincar\'e surface of section at dielectric interfaces.Comment: 7 pages, 7 figure

Antiresonance induced by symmetry-broken contacts in quasi-one-dimensional lattices

We report the effect of symmetry-broken contacts on quantum transport in quasi-one-dimensional lattices. In contrast to 1D chains, transport in quasi-one-dimensional lattices, which are made up of a finite number of 1D chain layers, is strongly influenced by contacts. Contact symmetry depends on whether the contacts maintain or break the parity symmetry between the layers. With balanced on-site potential, a flat band can be detected by asymmetric contacts, but not by symmetric contacts. In the case of asymmetric contacts with imbalanced on-site potential, transmission is suppressed at certain energies. We elucidate these energies of transmission suppression related to antiresonance using reduced lattice models and Feynman paths. These results provide a nondestructive measurement of flat band energy which it is difficult to detect.Comment: 8 pages, 5 figure

Reconfiguration of quantum states in PT\mathcal PT-symmetric quasi-one dimensional lattices

We demonstrate mesoscopic transport through quantum states in quasi-1D lattices maintaining the combination of parity and time-reversal symmetries by controlling energy gain and loss. We investigate the phase diagram of the non-Hermitian system where transitions take place between unbroken and broken $\mathcal{PT}$-symmetric phases via exceptional points. Quantum transport in the lattice is measured only in the unbroken phases in the energy band-but not in the broken phases. The broken phase allows for spontaneous symmetry-broken states where the cross-stitch lattice is separated into two identical single lattices corresponding to conditionally degenerate eigenstates. These degeneracies show a lift-up in the complex energy plane, caused by the non-Hermiticity with $\mathcal{PT}$-symmetry.Comment: 12 pages, 7 figure

Quasiscarred modes and their branching behavior at an exceptional point

We study quasiscarring phenomenon and mode branching at an exceptional point (EP) in typically deformed microcavities. It is shown that quasiscarred (QS) modes are dominant in some mode group and their pattern can be understood by short-time ray dynamics near the critical line. As cavity deformation increases, high-Q and low-Q QS modes are branching in an opposite way, at an EP, into two robust mode types showing QS and diamond patterns, respectively. Similar branching behavior can be also found at another EP appearing at a higher deformation. This branching behavior of QS modes has its origin on the fact that an EP is a square-root branch point.Comment: 5 pages, 5 figure

Oscillation death in coupled counter-rotating identical nonlinear oscillators

We study oscillatory and oscillation suppressed phases in coupled counter-rotating nonlinear oscillators. We demonstrate the existence of limit cycle, amplitude death, and oscillation death, and also clarify the Hopf, pitchfork, and infinite period bifurcations between them. Especially, the oscillation death is a new type of oscillation suppressions of which the inhomogeneous steady states are neutrally stable. We discuss the robust neutral stability of the oscillation death in non-conservative systems via the anti-PT-symmetric phase transitions at exceptional points in terms of non-Hermitian systems.Comment: 7 pages, 4 figure

Building World-Class Universities in Developing Systems: The Success Case of the Indian Institutes of Technology

With a global shift towards knowledge-based economy,universities are required to produce knowledge and cutting-edge technologies to support their respective country’s economy. In response, many countries around the world seek to build their own world-class universities. Altbach (2010, p.1) argues that world-class universities‘demonstrate world class thinking and policy development in the sense that they employ state of the art solutions to pressing challenges of the twenty first century’.However, world-class universities are found only in a few wealthy Western countries. For instance, if one takes a quick glance at Global University Rankings (GUR), nearly every top university is situated in a high-income country. There are exceptions, such as the Indian Institutes of Technology (IIT), which are known to produce the world’s most creative engineers. The GUR of IIT steadily rose over the past few years, drawing much attention from the industry for its unprecedented success. This research aims to trace the successful path of IIT to identify its success factors which may serve as reference points for other developing systems that aim to build world-class universities of their own. The study takes the two most prominent IIT, namely IIT Delhi and IIT Bombay.It also hypothesises and investigates whether the considerable amount of international co-operation activities IIT engaged in at the establishments have played a significant role in its success. The findings of the study showed that IIT’s limited financial resources were complemented by a highly concentrated pool of talented and motivated students,as well as professors who have abundant experiences in top-tier research and technical firms aboard. Another major factor was the government’s dedication. The government focused on creating a favourable environment for the institution and also prioritised IIT in its allocation of financial resources. Meanwhile, the study was unsuccessful in illustrating the role of international cooperation as the two sets of the collected data were contradictive