This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
In this expository talk, I describe how "chaotic behavior" not only was discovered in the study of the Newtonian N-body problem, but also is responsible for several strange appearing motions. Then, a mathematical outline of the general evolution of the universe, under Newton's laws, is provided. No prior background in dynamics or the mathematics of the N-body problem is needed to follow this lecture
Strongly correlated many-body systems are often formulated as gauge theories where gauge field plays a role of Lagrangian multiplier and fundamental matter field represents a fractional degree of freedom which carries only a fractional quantum number of microscopic particle. Although the fractional particles are prone to be confined at high energy owing to an infinite bare gauge coupling, they can emerge as deconfined degrees of freedom at low/intermediate energy scales as the gauge coupling is renormalized to a finite value by fluctuating matter fields.
Kilometer-scale neutrino detectors such as IceCube are discovery instruments covering nuclear and particle physics, cosmology and astronomy. Examples of their multidisciplinary missions include the search for the particle nature of dark matter and for additional small dimensions of space. In the end, their conceptual design is very much anchored to the observational fact that Nature produces protons and photons with energies in excess of 1020 and1013 electronvolts, respectively. The cosmic ray connection sets the scale of cosmic neutrino fluxes.
The TeV energy range is a privileged part of the EM spectrum for astrophysical observations, allowing a view of some of the most energetic processes in the Universe, in objects as diverse as supernova remnants and black-hole driven Active Galactic Nuclei. Driven by new instruments, TeV gamma-rays astrophysics has made enormous strides in recent years with the discovery of many new sources, including new classes of sources such as galactic micro-quasars.
I look at the information-processing involved in a quantum computation, in terms of the difference between the Boolean logic underlying a classical computation and the non-Boolean logic represented by the projective geometry of Hilbert space, in which the subspace structure of Hilbert space replaces the set-theoretic structure of classical logic. I show that the original Deutsch XOR algorithm, Simon's algorithm, and Shor's algorithm all involve a similar geometric formulation.
It is shown that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow the existence of vacuum states with non-standard field fluctuations (quantum non-equilibrium). It is shown that such non-equilibrium vacua lead to statistical anomalies, such as a breaking of scale invariance for the primordial power spectrum. The results depend only weakly on the details of the de Broglie-Bohm dynamics.
Up to 90% of matter in the Universe could be composed of heavy particles, which were non-relativistic, or 'cold', when they froze-out from the primordial soup. I will review current searches for these hypothetical particles, both via elastic scattering from nuclei in deep underground detectors, and via the observation of their annihilation products in the Sun, galactic halo and galactic center. The emphasis will be on most recent results, and on comparison with reaches of future particle colliders, such as the LHC and ILC.
The origin of the chemical elements that make up our world is one of the oldest most fundamental scientific questions. The universe after the Big Bang consisted only of hydrogen and helium with traces of lithium. All the other elements, including the carbon in our bodies, the iron, silicon, and oxygen that makes up most of our earth, have been created later by nuclear reactions in stars. However, the origin of many elements beyond iron, including gold and uranium, is still a mystery.
In the standard cosmological model, galaxies and large-scale structure grew by a process of gravitational instability from initial perturbations which were of the simplest statistical form imaginable: a statistically homogeneous and isotropic Gaussian random field. One of the properties of such a field is that its Fourier transform has real and imaginary parts which are independently Gaussian and consequently the phases are uniformly random.