152,425 research outputs found
On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system
Using Lax-Sato formulation of Manakov-Santini hierarchy, we introduce a class
of reductions, such that zero order reduction of this class corresponds to dKP
hierarchy, and the first order reduction gives the hierarchy associated with
the interpolating system introduced by Dunajski. We present Lax-Sato form of
reduced hierarchy for the interpolating system and also for the reduction of
arbitrary order. Similar to dKP hierarchy, Lax-Sato equations for (Lax
fuction) due to the reduction split from Lax-Sato equations for (Orlov
function), and the reduced hierarchy for arbitrary order of reduction is
defined by Lax-Sato equations for only. Characterization of the class of
reductions in terms of the dressing data is given. We also consider a waterbag
reduction of the interpolating system hierarchy, which defines
(1+1)-dimensional systems of hydrodynamic type.Comment: 15 pages, revised and extended, characterization of the class of
reductions in terms of the dressing data is give
Classification of -dimensional metric -Lie algebras
In this paper, we focus on -dimensional metric -Lie algebras. To
begin with, we give some properties on -dimensional -Lie algebras.
Then based on the properties, we obtain the classification of
-dimensional metric -Lie algebras
Permissive Controller Synthesis for Probabilistic Systems
We propose novel controller synthesis techniques for probabilistic systems
modelled using stochastic two-player games: one player acts as a controller,
the second represents its environment, and probability is used to capture
uncertainty arising due to, for example, unreliable sensors or faulty system
components. Our aim is to generate robust controllers that are resilient to
unexpected system changes at runtime, and flexible enough to be adapted if
additional constraints need to be imposed. We develop a permissive controller
synthesis framework, which generates multi-strategies for the controller,
offering a choice of control actions to take at each time step. We formalise
the notion of permissivity using penalties, which are incurred each time a
possible control action is disallowed by a multi-strategy. Permissive
controller synthesis aims to generate a multi-strategy that minimises these
penalties, whilst guaranteeing the satisfaction of a specified system property.
We establish several key results about the optimality of multi-strategies and
the complexity of synthesising them. Then, we develop methods to perform
permissive controller synthesis using mixed integer linear programming and
illustrate their effectiveness on a selection of case studies
Non-analyticity of the groud state energy of the Hamiltonian for Hydrogen atom in non-relativistic QED
We derive the ground state energy up to the fourth order in the fine
structure constant for the translation invariant Pauli-Fierz
Hamiltonian for a spinless electron coupled to the quantized radiation field.
As a consequence, we obtain the non-analyticity of the ground state energy of
the Pauli-Fierz operator for a single particle in the Coulomb field of a
nucleus
Renormalized Electron Mass in Nonrelativistic QED
Within the framework of nonrelativistic QED, we prove that, for small values
of the coupling constant, the energy function, E_|P|, of a dressed electron is
twice differentiable in the momentum P in a neighborhood of P = 0. Furthermore,
(E_|P|)" is bounded from below by a constant larger than zero. Our results are
proven with the help of iterative analytic perturbation theory
Quantum criticality in a Mott pn-junction in an armchair carbon nanotube
In an armchair carbon nanotube pn junction the p- and n- regions are
separated by a region of a Mott insulator, which can backscatter electrons only
in pairs. We predict a quantum-critical behavior in such a pn junction.
Depending on the junction's built-in electric field E, its conductance G scales
either to zero or to the ideal value G=4e^2/h as the temperature T is lowered.
The two types of the G(T) dependence indicate the existence, at some special
value of E, of an intermediate quantum critical point with a finite conductance
G<4e^2/h. This makes the pn junction drastically different from a simple
barrier in a Luttinger liquid.Comment: 5 pages, 1 figur
Recommended from our members
Advances in test and measurement of the interface adhesion and bond strengths in coating-substrate systems, emphasising blister and bulk techniques
In this paper, recent advances in the minimum-destructive testing of the adhesion of coating-substrate systems are reviewed, focusing on key techniques such as micro- and nano-scale levels of indentation, scratching, laser-induced wave shock, as well as the blister and buckle approach. Along with adhesion failure tests, the latest and most extensive applications of the adhesion test methods in nano-, micro- and bulk-coating technology and the associated techniques to determine the minimum damage defects left on the coatings are discussed and their use reviewed
Applications of hidden symmetries to black hole physics
This work is a brief review of applications of hidden symmetries to black
hole physics. Symmetry is one of the most important concepts of the science. In
physics and mathematics the symmetry allows one to simplify a problem, and
often to make it solvable. According to the Noether theorem symmetries are
responsible for conservation laws. Besides evident (explicit) spacetime
symmetries, responsible for conservation of energy, momentum, and angular
momentum of a system, there also exist what is called hidden symmetries, which
are connected with higher order in momentum integrals of motion. A remarkable
fact is that black holes in four and higher dimensions always possess a set
(`tower') of explicit and hidden symmetries which make the equations of motion
of particles and light completely integrable. The paper gives a general review
of the recently obtained results. The main focus is on understanding why at all
black holes have something (symmetry) to hide.Comment: This is an extended version of the talks at NEB-14 conference
(June,Ioannina,Greece) and JGRG20 meeting (September, Kyoto, Japan
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