1,600 research outputs found
A Geometrical Derivation of a Family of Quantum Speed Limit Results
We derive a family of quantum speed limit results in time independent systems
with pure states and a finite dimensional state space, by using a geometric
method based on right invariant action functionals on SU(N). The method relates
speed limits for implementing quantum gates to bounds on orthogonality times.
We reproduce the known result of the Margolus-Levitin theorem, and a known
generalisation of the Margolis-Levitin theorem, as special cases of our method,
which produces a rich family of other similar speed limit formulas
corresponding to positive homogeneous functions on su(n). We discuss the
general relationship between speed limits for controlling a quantum state and a
system's time evolution operator.Comment: 12 page
A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds
The Newton iteration is a popular method for minimising a cost function on
Euclidean space. Various generalisations to cost functions defined on manifolds
appear in the literature. In each case, the convergence rate of the generalised
Newton iteration needed establishing from first principles. The present paper
presents a framework for generalising iterative methods from Euclidean space to
manifolds that ensures local convergence rates are preserved. It applies to any
(memoryless) iterative method computing a coordinate independent property of a
function (such as a zero or a local minimum). All possible Newton methods on
manifolds are believed to come under this framework. Changes of coordinates,
and not any Riemannian structure, are shown to play a natural role in lifting
the Newton method to a manifold. The framework also gives new insight into the
design of Newton methods in general.Comment: 36 page
Cusps on cosmic superstrings with junctions
The existence of cusps on non-periodic strings ending on D-branes is
demonstrated and the conditions, for which such cusps are generic, are derived.
The dynamics of F-, D-string and FD-string junctions are investigated. It is
shown that pairs of FD-string junctions, such as would form after
intercommutations of F- and D-strings, generically contain cusps. This new
feature of cosmic superstrings opens up the possibility of extra channels of
energy loss from a string network. The phenomenology of cusps on such cosmic
superstring networks is compared to that of cusps formed on networks of their
field theory analogues, the standard cosmic strings.Comment: 22 pages, 5 figure
Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices
The time evolution of several interacting Ginzburg-Landau vortices according
to an equation of Schroedinger type is approximated by motion on a
finite-dimensional manifold. That manifold is defined as an unstable manifold
of an auxiliary dynamical system, namely the gradient flow of the
Ginzburg-Landau energy functional. For two vortices the relevant unstable
manifold is constructed numerically and the induced dynamics is computed. The
resulting model provides a complete picture of the vortex motion for arbitrary
vortex separation, including well-separated and nearly coincident vortices.Comment: 23 pages amslatex, 5 eps figures, minor typos correcte
Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations
In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the
smoothest invariant manifolds tangent to linear modal subspaces of an
equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the
classic backbone curves sought in experimental nonlinear model identification.
We develop here a methodology to compute analytically both the shape of SSMs
and their corresponding backbone curves from a data-assimilating model fitted
to experimental vibration signals. Using examples of both synthetic and real
experimental data, we demonstrate that this approach reproduces backbone curves
with high accuracy.Comment: 32 pages, 4 figure
Relativistic Constraints for a Naturalistic Metaphysics of Time
The traditional metaphysical debate between static and dynamic views in the
philosophy of time is examined in light of considerations concerning the nature
of time in physical theory. Adapting the formalism of Rovelli (1995, 2004), I
set out a precise framework in which to characterise the formal structure of
time that we find in physical theory. This framework is used to provide a new
perspective on the relationship between the metaphysics of time and the special
theory of relativity by emphasising the dual representations of time that we
find in special relativity. I extend this analysis to the general theory of
relativity with a view to prescribing the constraints that must be heeded for a
metaphysical theory of time to remain within the bounds of a naturalistic
metaphysics
Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
The spectral problem for the superstring and
its dual planar maximally supersymmetric Yang-Mills theory can be efficiently
solved through a set of functional equations known as the quantum spectral
curve. We discuss how the same concepts apply to the -deformed superstring, an integrable deformation of the superstring with quantum group symmetry. This model can
be viewed as a trigonometric version of the
superstring, like the relation between the XXZ and XXX spin chains, or the
sausage and the sigma models for instance. We derive the quantum
spectral curve for the -deformed string by reformulating the
corresponding ground-state thermodynamic Bethe ansatz equations as an analytic
system, and map this to an analytic system which upon suitable gauge
fixing leads to a system -- the quantum spectral curve. We
then discuss constraints on the asymptotics of this system to single out
particular excited states. At the spectral level the -deformed string and
its quantum spectral curve interpolate between the superstring and a superstring on "mirror" ,
reflecting a more general relationship between the spectral and thermodynamic
data of the -deformed string. In particular, the spectral problem of the
mirror string, and the thermodynamics of the
undeformed string, are described by a second
rational limit of our trigonometric quantum spectral curve, distinct from the
regular undeformed limit.Comment: 32+37 pages; 6 figures. v2: added reference
- …