Scientific Series

We propose an extended quantum theory, in which the number of degrees of freedom K behaves as FOURTH power the number N of distinguishable states. As the simplex of classical N--point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory is shown to be a non-trivial generalisation of the standard quantum theory for which K=N^2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. We discuss the question, how the theory of information processing looks like in the framework of the generalised quantum theory. In particular we propose a scheme of extended dense coding, in which one transmits two qubits by sending one extended bit, provided it was initially entangled with the extended bit of the receiver.

Neural circuits exhibit complex patterns of spontaneous activity. I will discuss how neural network models can reproduce this activity and how it interacts with responses evoked by sensory stimuli. This work involves analytic, mean-field and computer analyses of large systems of nonlinear differential equations with random parameters.

The general relativity has been tested from mm scales to solar system scales. The discovery of cosmic acceleration motivates the study of infrared modification of gravity at horizon scales. The cosmic expansion can be accelerated by dark energy without any correction to GR, but alternatively it can be explained by the modified gravity at large scales without introducing the unknown exotic energy. We introduce the linear structure formation theory of DGP and f(R) gravity, and present what it the strategy to test general relativity at cosmological scales.

Experimentalists at the Relativistic Heavy Ion Collider create exploding droplets of quark-gluon plasma, the stuff which filled the universe for the first microseconds after the big bang. I'll give one theorist's perspective on what we are learning about the properties of quark-gluon plasma from these experiments, including the conclusion that it is closer to an ideal liquid than to an ideal gas and the observation that it "quenches" high energy quarks ("jets") trying to plow through it. The static properties of quark-gluon plasma can be calculated from first principles, but we have no rigorous calculations of what QCD predicts for the viscosity and jet quenching ability of the evidently very strongly interacting quark-gluon plasma that RHIC has discovered. In desperation, theorists are resorting to calculating the properties of quark-gluon plasma in theories other than QCD, wherein difficult dynamical questions like how does a strongly interacting plasma quench jets can be answered by doing easy string theory calculations. I will discuss two examples where such calculations have been compared quantitatively to inferences drawn from existing RHIC data, and close with one prediction for data to come.

Light-cone superstring field theory (LCSFT) and matrix string theory (MST) are closely related. Both theories at the tree level are the Green-Schwarz superstring theory in the light-cone gauge. At the interaction level, the twist fields and the spin fields in MST correspond to the string interaction vertices in LCSFT. Since the CFT fields in MST are characterized by their OPEs, we would like to realize the OPEs by the interaction vertices in LCSFT to see the correspondence. In this talk I will begin with reviews of both theories and proceed to the correspondence between them.

Current measurements from WMAP and other cosmological probes are consistent with a simple inflationary model. Such models predict a background of gravitational waves which may soon be observable in the polarized component of the Cosmic Microwave Background. However, WMAP has observed significant levels of polarized radiation from our galaxy, due to both synchrotron radiation and thermal dust emission. A better understanding of this radiation will be vital if we are to correctly remove it and confidently detect an inflationary signal. As well as discussing the observational case for inflation, I will review the physical origins of the polarized galactic emission, present a simple model for the galactic magnetic field, and discuss current and future directions for improving upon our galactic models.

Soon after Quantum Chromodynamics (QCD) was shown to exhibit asymptotic freedom at short distances, it was realized that it might be possible to create a new form of matter at high temperatures (T „d 150 MeV) in which hadrons dissolve and quarks and gluons become locally deconfined. Experiments have been carried out for the last two decades attempting to create this new form of matter, called ¡§quark-gluon plasma¡¨ (QGP), via high-energy collisions of large nuclei. In 2000, the Relativistic Heavy Ion Collider (RHIC) started operation at Brookhaven National Laboratory in the US and results obtained from the first five years of RHIC operation provide the first convincing evidence for creation of the quark-gluon plasma in the laboratory. Measurements at RHIC show that the QGP is opaque to the passage of high-energy quarks and gluons and that interactions between the quarks and gluons in the QGP appears to be much stronger than initially expected. The estimated viscosity to entropy ratio of the QGP has been interpreted as showing that the QGP produced at RHIC is the most perfect fluid ever observed in the laboratory. Measurements from RHIC also suggest that the strong, coherent gluon fields in the incident nuclei play a significant role in the initial particle production and early evolution of the quark gluon plasma. Within the next few years, the large hadron collider will provide Pb+Pb collisions at a nucleon-nucleon center of mass energy of 5.5 TeV, thus opening a new frontier in the study of the QGP. I will provide a summary of the key experimental observables at RHIC, a discussion of their canonical interpretation and then discuss how measurements at the LHC can be used to test these interpretations.

The duality between theories of quantum strings and Yang-Mills gauge theories, in particular the AdS/CFT conjecture, has over the years given rise to many important physical insights. Recently, the realization that both sides of the duality, in certain limits, can be be described by integrable systems has lead to a good deal of progress. In this talk we will review the construction of these integrable structures and their usefulness in understanding strings in curved backgrounds/strongly coupled gauge theories. We will discuss how the asymptotic S-matrix that enters the Bethe equations for gauge theory anomalous dimensions provides a very convenient description of the system and how it can be reproduced from the classical string theory. Further, we will outline some partial attempts to extend this equivalence, and the corresponding integrable structures, to include world-sheet quantum loop effects.

I first summarize how the recent avalanche of precision measurements involving the cosmic microwave background, galaxy clustering, the Lyman alpha forest, gravitational lensing, supernovae Ia and other tools probes has transformed our understanding of our universe. I then discuss key open problems such as the nature of dark matter, dark energy and the early universe.

With a cosmic flight simulator, we'll take a scenic journey through space and time. After exploring our local Galactic neighborhood, we'll travel back 13.7 billion years to explore the Big Bang itself and how state-of-the-art measurements are transforming our understanding of our cosmic origin and ultimate fate. We then turn to the question of whether this can all be described purely mathematically, and discuss implications ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like parallel universes, simulations and and Goedel incompleteness.