# Research

Synthesizing the flow of light using Parity-Time Symmetry
Synthetic Parity-Time symmetric materials simultaneously exploit loss, gain and index of refraction. They produce novel space-time reflections that allow for spatial guiding and selection of propagating radiation and hold promises for a new generation of sophisticated integrated photonic devices. [Read more]

Bose-Einstein Condensates in Optical Lattices
While the physics of the last century was mainly characterized by great advances in understanding the properties of one-particle systems, recent experimental developments have put the effects of interacting bosons at the top of the research agenda. In fact, the growing theoretical interest was further enhanced by recent experimental achievements. The most fascinating of these was the realization of Bose-Einstein condensation (BEC) of ultra-cold atoms in periodic optical lattices, which allows for novel concrete applications of quantum mechanics such as atom interferometers and atom lasers. [Read more]

Quantum Graphs as Models of Mesoscopic Physics and Quantum Chaos
In quantum chaos one tries to understand the implications of a chaotic classical limit for a quantum system. Despite the large variety of such systems, they have a number of universal physical properties in common. For example, a statistical analysis of the energy levels invariably shows striking similarities with the “energies” obtained from the diagonalization of random matrices. In the semiclassical approach to this problem the quantum density of states is expressed as a sum over classical periodic orbits by Gutzwiller’s trace formula. One can then describe fluctuations in quantum spectra on the basis of information about the classical dynamics (sum rules and action correlations of periodic orbits). In most cases, only the semi-classical approximation for the trace formulae are known and their application is not only hampered by the intrinsic complexity of the set of periodic orbits, but also by doubts about the ability of the semi-classical trace formulae to provide an accurate enough basis for further developments. [Read more]

Wavepacket Dynamics, Quantum Irreversibility and the Applicability of RMT
The past mesoscopic physics/quantum chaos literature was strongly focused on understanding the interplay between universal (RMT-like) and non-universal (semiclassical) features as far as spectral properties are concerned. However, the study of spectral statistics is just the lower level in the hierarchy of challenges to understand quantum systems. The two other levels are: studies of the shape of the eigenstates, and studies of the generated dynamics. The latter two aspects had been barely treated prior to our studies. [Read more]

Parametric Evolution of Wavefunctions (LDoS)
The analysis of the structural changes that the eigenstates of a mesoscopic/chaotic system exhibit as one varies a parameter $x$ of the Hamiltonian ${\cal H}(x)$ has sparked a great deal of research activity for many years. Physically the change of $x$ may represent the effect of some externally controlled field (like electric field, magnetic flux, gate voltage) or a change of an effective-interaction (as in molecular dynamics). Thus, these studies are relevant for diverse areas of physics ranging from nuclear and atomic physics to quantum chaos and mesoscopics. [Read more]

Driven Mesoscopic Systems
Driven systems are described by Hamiltonian H(Q,P,x(t)), where x(t) is a time dependent parameter and Q,P is a set of canonical co-ordinates. Such systems are of interest in mesoscopic physics (quantum dots), as well as in nuclear, atomic and molecular physics. The time dependent parameter x(t) may have the significance of an external electric field or magnetic flux or gate voltage. Due to the time dependence of x(t), the energy of the system is not a constant of motion. Rather the system makes “transitions” between energy levels, and therefore the energy distribution evolves with time. The aim of these studies is to develop a general theory for this evolution. The possibility to present a general quantum mechanical theory follows from the simple fact that chaos leads to universality. This universality is captured to some extend by RMT. [Read more]

Transport Properties of Random Media
Descriptions and pictures [Read more]

Control of Chaos and Pattern Formation by Impurities
Coupled arrays of oscillators are studied extensively in many fields of science because of their prevalence in nature. They are used as models for coupled arrays of neurons, chemical reactions, coupled lasers or Josephson junctions, charge-density wave conductors, crystal dislocations in metals, and proton conductivity in hydrogen-bonded chains. Various models and coupling schemes have been proposed and analyzed previously. A particular class are arrays of coupled oscillators, which exhibit chaotic motion when uncoupled. This class includes the forced Frenkel-Kontorova model, which finds a straightforward physical realization in an array of diffusively coupled Josephson junctions, in which the applied current of each junction is modulated by a common frequency. Motivated by ideas that emerged in the theory of disordered systems, we have studied the appearance of synchronized motion in one and two-dimensional arrays of coupled chaotic pendula, due to the presence of a single impurity. [Read more]

Photonically Inspired Electronics
Among the many recent developments in PT systems, the application of pseudo-
Hermitian ideas into the realm of electronic circuitry not only promises a new generation
of electronic structures and devices, but also provides a platform for detailed scrutiny of
many new concepts within a framework of easily accessible experimental conﬁgurations.[Read more]