Time-optimal navigation through quantum wind

The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the required task, we are able to deduce the form of the solution to the problem by deriving a universal quantum speed limit. The expression thus obtained indicates that further simplifications of this apparently difficult problem are possible if we switch to the interaction picture of quantum mechanics. A complete solution to the navigation problem for an arbitrary quantum system is then obtained, and the behaviour of the solution is illustrated in the case of a two-level system

Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

Maximum tension: With and without a cosmological constant

We discuss various examples and ramifications of the conjecture that there exists a maximum force (or tension) in general relativistic systems. We contrast this situation with that in Newtonian gravity, where no maximum force exists, and relate it to the existence of natural units defined by constants of Nature and the fact that the Planck units of force and power do not depend on Planck's constant. We discuss how these results change in higher dimensions where the Planck units of force are no longer non-quantum. We discuss the changes that might occur to the conjecture if a positive cosmological constant exists and derive a maximum force bound using the Kottler-Schwarzschildde Sitter black hole

Aspherical photon and anti-photon surfaces

© 2016 The Authors In this note we identify photon surfaces and anti-photon surfaces in some physically interesting spacetimes, which are not spherically symmetric. All of our examples solve physically reasonable field equations, including for some cases the vacuum Einstein equations, albeit they are not asymptotically flat. Our examples include the vacuum C-metric, the Melvin solution of Einstein–Maxwell theory and generalisations including dilaton fields. The (anti-)photon surfaces are not round spheres, and the lapse function is not always constant

Gravitational lensing in the Kerr-Randers optical geometry

A new geometric method to determine the deflection of light in the equatorial plane of the Kerr solution is presented, whose optical geometry is a surface with a Finsler metric of Randers type. Applying the Gauss-Bonnet theorem to a suitable osculating Riemannian manifold, adapted from a construction by Naz\i m, it is shown explicitly how the two leading terms of the asymptotic deflection angle of gravitational lensing can be found in this way.Comment: 7 pages, 1 figure. Accepted by Gen. Rel. Grav. Version 2: change of notation in sec.

An instability of higher-dimensional rotating black holes

We present the first example of a linearized gravitational instability of an asymptotically flat vacuum black hole. We study perturbations of a Myers-Perry black hole with equal angular momenta in an odd number of dimensions. We find no evidence of any instability in five or seven dimensions, but in nine dimensions, for sufficiently rapid rotation, we find perturbations that grow exponentially in time. The onset of instability is associated with the appearance of time-independent perturbations which generically break all but one of the rotational symmetries. This is interpreted as evidence for the existence of a new 70-parameter family of black hole solutions with only a single rotational symmetry. We also present results for the Gregory-Laflamme instability of rotating black strings, demonstrating that rotation makes black strings more unstable.Comment: 38 pages, 13 figure

SIM(2) and supergraphs

We construct Feynman rules and Supergraphs in SIM(2) superspace. To test our methods we perform a one-loop calculation of the effective action of the SIM(2) supersymmetric Wess-Zumino model including a term which explicitly breaks Lorentz invariance. The renormalization of the model is also discussed.Comment: 28 page

Maximum magnetic moment to angular momentum conjecture

Conjectures play a central role in theoretical physics, especially those that assert an upper bound to some dimensionless ratio of physical quantities. In this paper we introduce a new such conjecture bounding the ratio of the magnetic moment to angular momentum in nature. We also discuss the current status of some old bounds on dimensionless and dimensional quantities in arbitrary spatial dimension. Our new conjecture is that the dimensionless Schuster-Wilson-Blackett number, cμ/$\textit{JG}\frac{1}{2}$, where μ is the magnetic moment and $\textit{J}$ is the angular momentum, is bounded above by a number of order unity. We verify that such a bound holds for charged rotating black holes in those theories for which exact solutions are available, including the Einstein-Maxwell theory, Kaluza-Klein theory, the Kerr-Sen black hole, and the so-called STU family of charged rotating supergravity black holes. We also discuss the current status of the maximum tension conjecture, the Dyson luminosity bound, and Thorne’s hoop conjecture.The authors are supported by the Science and Technology Facilities Council (STFC) of the United Kingdom

Fast Scramblers Of Small Size

We investigate various geometrical aspects of the notion of `optical depth' in the thermal atmosphere of black hole horizons. Optical depth has been proposed as a measure of fast-crambling times in such black hole systems, and the associated optical metric suggests that classical chaos plays a leading role in the actual scrambling mechanism. We study the behavior of the optical depth with the size of the system and find that AdS/CFT phase transitions with topology change occur naturally as the scrambler becomes smaller than its thermal length. In the context of detailed AdS/CFT models based on D-branes, T-duality implies that small scramblers are described in terms of matrix quantum mechanics.Comment: 14 pages, 3 figures. Added reference

Spacetime diffeomorphisms and the geodesic approximation

We present a spacetime diffeomorphism invariant formulation of the geodesic approximation to soliton dynamics