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Anderson E.,DAMTP | Anderson E.,Autonomous University of Madrid
General Relativity and Gravitation | Year: 2011

With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i. e. scale-free) triangle formed by 3 particles in 2-d. I do so by importing techniques to the triangle model from the corresponding 4 particles in 1-d model, using the fact that both have 2-spheres for shape spaces, though the latter has a trivial realization whilst the former has a more involved Hopf (or Dragt) type realization. I furthermore interpret the ensuing Dragt-type coordinates as shape quantities: a measure of anisoscelesness, the ellipticity of the base and apex's moments of inertia, and a quantity proportional to the area of the triangle. I promote these quantities at the quantum level to operators whose expectation and spread are then useful in understanding the quantum states of the system. Additionally, I tessellate the 2-sphere by its physical interpretation as the shape space of triangles, and then use this as a back-cloth from which to read off the interpretation of dynamical trajectories, potentials and wavefunctions. I include applications to timeless approaches to the problem of time and to the role of uniform states in quantum cosmological modelling. © 2011 Springer Science+Business Media, LLC.


Dolan F.A.H.,DAMTP | Spiridonov V.P.,Joint Institute for Nuclear Research | Vartanov G.S.,Max Planck Institute For Gravitationsphysik
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2011

An exact formula for partition functions in 3. d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific q-hypergeometric integrals whose key building block is the double sine function (or the hyperbolic gamma function). Elliptic hypergeometric integrals, discovered by the second author, define 4. d superconformal indices. Using their reduction to the hyperbolic level, we describe a general scheme of reducing 4. d superconformal indices to 3. d partition functions which imply an efficient way of getting 3. d N=2 supersymmetric dualities for both SYM and CS theories from the "parent" 4. d N=1 dualities for SYM theories. As an example, we consider explicitly the duality pattern for 3. d N=2 SYM and CS theories with SP(2N) gauge group with the antisymmetric tensor matter. © 2011 Elsevier B.V.


Hartle J.,University of California at Santa Barbara | Hawking S.W.,DAMTP | Hertog T.,University Paris Diderot | Hertog T.,Solvay Group
Physical Review Letters | Year: 2011

We consider landscape models that admit several regions where the conditions for eternal inflation hold. It is shown that one can use the no-boundary wave function to calculate small departures from homogeneity within our past light cone despite the possibility of much larger fluctuations on super horizon scales. The dominant contribution comes from the history exiting eternal inflation at the lowest value of the potential. In a class of landscape models this predicts a tensor to scalar ratio of about 10%. In this way the no-boundary wave function defines a measure for the prediction of local cosmological observations. © 2011 American Physical Society.


Anderson E.,DAMTP
Classical and Quantum Gravity | Year: 2011

Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1D to include a notion of scale. This is useful as regards forming a tight analogy with quantum cosmology and the emergent semiclassical time and hidden time approaches to the problem of time. This paper shows furthermore that the correspondence between relational particle models and classical and quantum cosmology can be strengthened using judicious choices of the mechanical potential. This gives relational particle mechanics models with analogues of spatial curvature, cosmological constant, dust and radiation terms. A number of these models are then tractable at the quantum level. These models can be used to study important issues (1) in canonical quantum gravity: the problem of time, the semiclassical approach to it and timeless approaches to it (such as the naive Schrödinger interpretation and records theory) and (2) in quantum cosmology, such as in the investigation of uniform states, robustness and the qualitative understanding of the origin of structure formation. © 2011 IOP Publishing Ltd.


Paardekooper S.-J.,DAMTP | Leinhardt Z.M.,University of Bristol | Thebault P.,Observatoire de Paris | Baruteau C.,DAMTP
Astrophysical Journal Letters | Year: 2012

We study planetesimal evolution in circumbinary disks, focusing on the three systems Kepler 16, 34, and 35 where planets have been discovered recently. We show that for circumbinary planetesimals, in addition to secular forcing, eccentricities evolve on a dynamical timescale, which leads to orbital crossings even in the presence of gas drag. This makes the current locations of the circumbinary Kepler planets hostile to planetesimal accretion. We then present results from simulations including planetesimal formation and dust accretion, and show that even in the most favorable case of 100% efficient dust accretion, in situ growth starting from planetesimals smaller than 10 km is difficult for Kepler 16b, Kepler 34b, and Kepler 35b. These planets were likely assembled further out in the disk, and migrated inward to their current location. © 2012. The American Astronomical Society. All rights reserved.


Anderson E.,DAMTP
General Relativity and Gravitation | Year: 2013

A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner-Nordström and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr-Newman case's 3 by 3 thermodynamical state space metric. © 2013 Springer Science+Business Media New York.


Anderson E.,DAMTP
Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics | Year: 2015

I previously showed that Kendall's work on shape geometry is in fact also the geometrical description of Barbour's relational mechanics' reduced configuration spaces (alias shape spaces). I now describe the extent to which Kendall's subsequent statistical application to e.g. the 'standing stones problem' realizes further ideas along the lines of Barbour-type timeless records theories, albeit just at the classical level. © 2015 Elsevier Ltd.


Mezincescu L.,University of Miami | Routh A.J.,DAMTP | Townsend P.K.,DAMTP
Annals of Physics | Year: 2014

In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a "spin-shell" constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with N-extended space-time supersymmetry) in three and four space-time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N = 1 and BPS-saturated N = 2 superparticle actions. We also find the supertwistor form of the action for "spinning particles" with N-extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N = 2 case. © 2014.


Paardekooper S.-J.,DAMTP | Lesur G.,DAMTP | Papaloizou J.C.B.,DAMTP
Astrophysical Journal | Year: 2010

We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulting spiral wave pattern is reminiscent of an embedded planet. There are two main causes for asymmetries in these wakes: geometrical effects tend to favor the outer wave, while a radial vortensity gradient leads to an asymmetric vortex core, which favors the wave at the side that has the lowest density. In the case of asymmetric waves, which we always find except for a disk of constant pressure, there is a net exchange of angular momentum between the vortex and the surrounding disk, which leads to orbital migration of the vortex. Numerical hydrodynamical simulations show that this migration can be very rapid, on a timescale of a few thousand orbits, for vortices with a size comparable to the scale height of the disk. We discuss the possible effects of vortex migration on planet formation scenarios. © 2010. The American Astronomical Society.


Liu R.G.,Cambridge College | Williams R.M.,DAMTP | Williams R.M.,Cambridge College
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2016

This paper examines the behavior of closed "lattice universes" wherein masses are distributed in a regular lattice on the Cauchy surfaces of closed vacuum universes. Such universes are approximated using a form of Regge calculus originally developed by Collins and Williams to model closed Friedmann-Lemaître-Robertson-Walker universes. We consider two types of lattice universes, one where all masses are identical to each other and another where one mass gets perturbed in magnitude. In the unperturbed universe, we consider the possible arrangements of the masses in the Regge Cauchy surfaces and demonstrate that the model will only be stable if each mass lies within some spherical region of convergence. We also briefly discuss the existence of Regge models that are dual to the ones we have considered. We then model a perturbed lattice universe and demonstrate that the model's evolution is well behaved, with the expansion increasing in magnitude as the perturbation is increased. © 2016 American Physical Society.

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