Spontaneous Breaking of Classical PT Symmetry

The classical trajectories of the family of complex PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric). The periods of these orbits exhibit an unusual dependence on the parameter $\epsilon$. There are regions in $\epsilon$ of smooth behavior interspersed with regions of rapid variation. It is demonstrated that the onset of rapid variation is associated with strange new kinds of classical trajectories that have never been seen previously. These rare kinds of trajectories are not PT symmetric and occur only for special rational values of $\epsilon$.Comment: 16 pages, 17 figures, accepted for publication in the Journal of Mathematical Physic

Classical Trajectories for Complex Hamiltonians

It has been found that complex non-Hermitian quantum-mechanical Hamiltonians may have entirely real spectra and generate unitary time evolution if they possess an unbroken \cP\cT symmetry. A well-studied class of such Hamiltonians is $H= p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$). This paper examines the underlying classical theory. Specifically, it explores the possible trajectories of a classical particle that is governed by this class of Hamiltonians. These trajectories exhibit an extraordinarily rich and elaborate structure that depends sensitively on the value of the parameter $\epsilon$ and on the initial conditions. A system for classifying complex orbits is presented.Comment: 24 pages, 34 figure

Complex trajectories of a simple pendulum

Accepted versio

Galaxy Zoo: CANDELS barred discs and bar fractions

The formation of bars in disc galaxies is a tracer of the dynamical maturity of the population. Previous studies have found that the incidence of bars in discs decreases from the local Universe to z ~ 1, and by z > 1 simulations predict that bar features in dynamically mature discs should be extremely rare. Here, we report the discovery of strong barred structures in massive disc galaxies at z ~ 1.5 in deep rest-frame optical images from the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey. From within a sample of 876 disc galaxies identified by visual classification in Galaxy Zoo, we identify 123 barred galaxies. Selecting a subsample within the same region of the evolving galaxy luminosity function (brighter than L*), we find that the bar fraction across the redshift range 0.5 ≤ z ≤ 2 (fbar = 10.7+6.3 -3.5 per cent after correcting for incompleteness) does not significantly evolve.We discuss the implications of this discovery in the context of existing simulations and our current understanding of the way disc galaxies have evolved over the last 11 billion yearsPeer reviewedFinal Accepted Versio

Pattern Recognition in Astrophysics and the Anthropic Principle

The role of the Anthropic Principle in astrophysics and cosmology is examined in two principal parts. The first (minor) part takes a chiefly philosophical perspective and examines the manner in which human cognition features into discussions on cosmic origins. It is shown that the philosophical questions raised by the Anthropic Principle and ‘fine-tuning of life’ bear resemblances to problems within the philosophy of mind and we seek a common origin for this surprising parallel. A form of ‘epistemic structural realism’ is defended and used to critique the physicalist identity thesis. It is argued that equating ‘reality’ with mathematical structures, which is the basis of the identity thesis, leads to incoherent conclusions. Similar reasoning is used to critique infinite Multiverse theories. In the second (major) part, we gradually transition into mainstream astrophysics, first presenting a new line of research to explore counterfactual universes using semi-analytic models (SAMs) and offering a preliminary study wherein the cosmological constant is varied and the effects on ‘advanced civilisations’ are examined. The importance of galaxy mergers is highlighted and leads to their study. We first try solving the pattern-recognition problem of locating mergers using the Galaxy Zoo database and produce the largest homogenous merger catalogue to date. We examine their properties and compare them with the SAMs of the Millennium Simulation finding good general agreement. We develop the Galaxy Zoo approach with a new visual-interface design and double the size of the merger catalogue of SDSS mergers in the local Universe

Pattern recognition in astrophysics and the anthropic principle

The role of the Anthropic Principle in astrophysics and cosmology is examined in two principal parts. The first (minor) part takes a chiefly philosophical perspective and examines the manner in which human cognition features into discussions on cosmic origins. It is shown that the philosophical questions raised by the Anthropic Principle and ‘fine-tuning of life’ bear resemblances to problems within the philosophy of mind and we seek a common origin for this surprising parallel. A form of ‘epistemic structural realism’ is defended and used to critique the physicalist identity thesis. It is argued that equating ‘reality’ with mathematical structures, which is the basis of the identity thesis, leads to incoherent conclusions. Similar reasoning is used to critique infinite Multiverse theories. In the second (major) part, we gradually transition into mainstream astrophysics, first presenting a new line of research to explore counterfactual universes using semi-analytic models (SAMs) and offering a preliminary study wherein the cosmological constant is varied and the effects on ‘advanced civilisations’ are examined. The importance of galaxy mergers is highlighted and leads to their study. We first try solving the pattern-recognition problem of locating mergers using the Galaxy Zoo database and produce the largest homogenous merger catalogue to date. We examine their properties and compare them with the SAMs of the Millennium Simulation finding good general agreement. We develop the Galaxy Zoo approach with a new visual-interface design and double the size of the merger catalogue of SDSS mergers in the local Universe.EThOS - Electronic Theses Online ServiceGBUnited Kingdo