This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Conventional wisdom holds that the majority of high energy atomic nuclei ("cosmic rays") that continually rain upon the Earth originate in galactic supernova shock waves, although some different (likely extragalactic) origin must be invoked to explain the highest energy particles. Despite many decades of intensive research on the subject, only indirect clues to these ideas exist at present. Direct measurements of the spectrum and mass composition of high energy cosmic rays are needed to validate these notions, but are hampered by rapidly dwindling fluxes with energy.
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, I'll show that "for most practical purposes" one can learn a quantum state using a number of measurements that grows only linearly with n. I'll discuss applications of this result in experimental physics and quantum computing theory, as well as possible implications for the foundations of quantum mechanics. quant-ph/0608142
I will first argue that the notion of black hole entropy extends universally to causal horizons. Then I will deduce the causal dynamics of spacetime from the equilibrium thermodynamics of causal horizons. Specifically, it will be shown how the Clausius relation dS = dQ/T between entropy change, energy flux, and acceleration temperature for all local causal horizons implies the Einstein equation, with Newton's constant determined by the universal horizon entropy density. Implications, non-equilibrium processes, and relations to AdS/CFT duality will also be discussed.
How should we think about quantum computing? The usual answer to this question is based on ideas inspired by computer science, such as qubits, quantum gates, and quantum circuits. In this talk I will explain an alternate geometric approach to quantum computation. In the geometric approach, an optimal quantum computation corresponds to "free falling" along the minimal geodesics of a certain Riemannian manifold.
Not only general relativity but also quantum theory plays important roles in current cosmology. Quantum fluctuations of matter fields are supposed to have provided the initial seeds of all the structure of the current universe, and quantum gravity is assumed to have been essential in the earliest stages. Both issues are not fully understood, although several heuristic effects have been discussed. In this talk, implications of an effective framework taking into account the coupling of matter and gravity are discussed.
At low energy and small curvature, general relativity has the form of an effective field theory. I will describe the structure of the effective field theory, and show how it can be used to calculate low energy quantum effects.
Category theory is a general language for describing things and processes - called "objects" and "morphisms". In this language, many counterintuitive features of quantum theory turn out to be properties shared by the category of Hilbert spaces and the category of cobordisms, in which objects are choices of "space" and emorphisms are choices of "spacetime". This striking fact suggests that "n-categories with duals" are a promising language for a quantum theory of spacetime.
Nanostructured materials continue to be the focus of intense research due to their promise of innumerable practical applications as well as advancing the fundamental understanding of these intriguing materials. From physics, to chemistry, to biology, to computer science, across the engineering disciplines and into the imagination of the general event, nanotechnology has become an extremely popular buzzword that represents both hope and hype to many people.
A variety of physical phenomena involve multiple length and time scales. Some interesting examples of multiple-scale phenomena are: (a) the mechanical behavior of crystals and in particular the interplay of chemistry and mechanical stress in determining the macroscopic brittle or ductile response of solids; (b) the molecular-scale forces at interfaces and their effect in macroscopic phenomena like wetting and friction; (c) the alteration of the structure and electronic properties of macromolecular systems due to external forces, as in stretched DNA nanowires or carbon nanotubes.