Scientific Series

I shall discuss entanglement - assisted invariance (symmetry exhibited by correlated quantum states) and describe how it can be used to understand the nature of ignorance, and, hence, the origin of probabilities in quantum physics. WHZ, Phys. Rev. Lett. 90, 120404 (2003); Rev. Mod. Phys. 75, 715 (2003); Phys. Rev. 71, 052105 (2005) (quant-ph/0405161).

Highest energy cosmic rays reach {\it macroscopic} energies $> 10^{20}$ eV ($\sim 10$ joules; corresponding linear momentum in one proton is similar to a slapshot hockey puck's). Such protons can either be accelerated by nearby astrophysical sources or be by-products of decay of unknown superheavy fundamental particles. After reviewing phenomenology of cosmic rays, I will discuss a novel {\it non-stochastic} acceleration mechanism in jets of powerful active galactic nuclei. The mystery of ultra high energy cosmic rays is likely soon to be resolved by Pierre Auger observatory.

We show that the entropy resulting from the counting of microstates of non extremal black holes using field theory duals of string theories can be interpreted as arising from entanglement. The conditions for making such an interpretation consistent are discussed. First, we interpret the entropy (and thermodynamics) of spacetimes with non degenerate, bifurcating Killing horizons as arising from entanglement. We use a path integral method to define the Hartle-Hawking vacuum state in such spacetimes and discuss explicitly its entangled nature and its relation to the geometry. If string theory on such spacetimes has a field theory dual, then, in the low-energy, weak coupling limit, the field theory state that is dual to the Hartle-Hawking state is a thermofield double state. This allows the comparison of the entanglement entropy with the entropy of the field theory dual, and thus, with the Bekenstein-Hawking entropy of the black hole. As an example, we discuss in detail the case of the five dimensional anti-de Sitter, black hole spacetime.

The problem of vacuum energy is reviewed. The observational evidence in favor of a non-zero cosmological constant is described. I then discuss several possible explanations for how a theoretically natural huge value of vacuum energy could be adjusted down to the unnaturally tiny but observed value.

Synchronization phenomena are abundant in nature, science, engineering and social life. Synchronization was first recognized by Christiaan Huygens in 1665 for coupled pendulum clocks; this was the beginning of nonlinear sciences. First, several examples of synchronization in complex systems are presented, such as in organ pipes, fireflies, epilepsy and even in the (in)stability of large mechanical systems as bridges. These examples illustrate that, literally speaking, subsystems are able to synchronize due to interaction if they are able to communicate. Second, general physical mechanisms for synchronization and de-synchronization phenomena in coupled complex systems are presented and conditions for synchronizability are discussed. It is explained that diffusion properties give a crucial insight into this problem. I will show that the general concepts of curvature and recurrence are helpful to uncover complex synchronization. Third, applications of these new techniques are given. They range from El Nino – Monsoon interactions via electrochemical oscillators and lasers to cognitive processes during reading and to neuroscience.