9,052 research outputs found
Negative-energy perturbations in cylindrical equilibria with a radial electric field
The impact of an equilibrium radial electric field on negative-energy
perturbations (NEPs) (which are potentially dangerous because they can lead to
either linear or nonlinear explosive instabilities) in cylindrical equilibria
of magnetically confined plasmas is investigated within the framework of
Maxwell-drift kinetic theory. It turns out that for wave vectors with a
non-vanishing component parallel to the magnetic field the conditions for the
existence of NEPs in equilibria with E=0 [G. N. Throumoulopoulos and D.
Pfirsch, Phys. Rev. E 53, 2767 (1996)] remain valid, while the condition for
the existence of perpendicular NEPs, which are found to be the most important
perturbations, is modified. For ( is the
electrostatic potential) and ( is
the total plasma pressure), a case which is of operational interest in magnetic
confinement systems, the existence of perpendicular NEPs depends on ,
where is the charge of the particle species . In this case the
electric field can reduce the NEPs activity in the edge region of tokamaklike
and stellaratorlike equilibria with identical parabolic pressure profiles, the
reduction of electron NEPs being more pronounced than that of ion NEPs.Comment: 30 pages, late
Analytical Multi-kinks in smooth potentials
In this work we present an approach which can be systematically used to
construct nonlinear systems possessing analytical multi-kink profile
configurations. In contrast with previous approaches to the problem, we are
able to do it by using field potentials which are considerably smoother than
the ones of Doubly Quadratic family of potentials. This is done without losing
the capacity of writing exact analytical solutions. The resulting field
configurations can be applied to the study of problems from condensed matter to
brane world scenarios
Welfare guarantees for proportional allocations
According to the proportional allocation mechanism from the network
optimization literature, users compete for a divisible resource -- such as
bandwidth -- by submitting bids. The mechanism allocates to each user a
fraction of the resource that is proportional to her bid and collects an amount
equal to her bid as payment. Since users act as utility-maximizers, this
naturally defines a proportional allocation game. Recently, Syrgkanis and
Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with
respect to the social welfare and presented a lower bound of 26.8% on the price
of anarchy over coarse-correlated and Bayes-Nash equilibria in the full and
incomplete information settings, respectively. In this paper, we improve this
bound to 50% over both equilibrium concepts. Our analysis is simpler and,
furthermore, we argue that it cannot be improved by arguments that do not take
the equilibrium structure into account. We also extend it to settings with
budget constraints where we show the first constant bound (between 36% and 50%)
on the price of anarchy of the corresponding game with respect to an effective
welfare benchmark that takes budgets into account.Comment: 15 page
Negative-Energy Perturbations in Circularly Cylindrical Equilibria within the Framework of Maxwell-Drift Kinetic Theory
The conditions for the existence of negative-energy perturbations (which
could be nonlinearly unstable and cause anomalous transport) are investigated
in the framework of linearized collisionless Maxwell-drift kinetic theory for
the case of equilibria of magnetically confined, circularly cylindrical plasmas
and vanishing initial field perturbations. For wave vectors with a
non-vanishing component parallel to the magnetic field, the plane equilibrium
conditions (derived by Throumoulopoulos and Pfirsch [Phys Rev. E {\bf 49}, 3290
(1994)]) are shown to remain valid, while the condition for perpendicular
perturbations (which are found to be the most important modes) is modified.
Consequently, besides the tokamak equilibrium regime in which the existence of
negative-energy perturbations is related to the threshold value of 2/3 of the
quantity , a new
regime appears, not present in plane equilibria, in which negative-energy
perturbations exist for {\em any} value of . For various analytic
cold-ion tokamak equilibria a substantial fraction of thermal electrons are
associated with negative-energy perturbations (active particles). In
particular, for linearly stable equilibria of a paramagnetic plasma with flat
electron temperature profile (), the entire velocity space is
occupied by active electrons. The part of the velocity space occupied by active
particles increases from the center to the plasma edge and is larger in a
paramagnetic plasma than in a diamagnetic plasma with the same pressure
profile. It is also shown that, unlike in plane equilibria, negative-energy
perturbations exist in force-free reversed-field pinch equilibria with a
substantial fraction of active particles.Comment: 31 pages, late
Practical quantum metrology in noisy environments
This is the final version. Available from American Physical Society via the DOI in this recordThe problem of estimating an unknown phase
φ
using two-level probes in the presence of unital phase-covariant noise and using finite resources is investigated. We introduce a simple model in which the phase-imprinting operation on the probes is realized by a unitary transformation with a randomly sampled generator. We determine the optimal phase sensitivity in a sequential estimation protocol and derive a general (tight-fitting) lower bound. The sensitivity grows quadratically with the number of applications
N
of the phase-imprinting operation, then attains a maximum at some
N
opt
, and eventually decays to zero. We provide an estimate of
N
opt
in terms of accessible geometric properties of the noise and illustrate its usefulness as a guideline for optimizing the estimation protocol. The use of passive ancillas and of entangled probes in parallel to improve the phase sensitivity is also considered. We find that multiprobe entanglement may offer no practical advantage over single-probe coherence if the interrogation at the output is restricted to measuring local observables.European Research CouncilRoyal Societ
Asymptotic Bethe equations for open boundaries in planar AdS/CFT
We solve, by means of a nested coordinate Bethe ansatz, the open-boundaries
scattering theory describing the excitations of a free open string propagating
in , carrying large angular momentum , and ending on
a maximal giant graviton whose angular momentum is in the same plane. We thus
obtain the all-loop Bethe equations describing the spectrum, for finite but
large, of the energies of such strings, or equivalently, on the gauge side of
the AdS/CFT correspondence, the anomalous dimensions of certain operators built
using the epsilon tensor of SU(N). We also give the Bethe equations for strings
ending on a probe D7-brane, corresponding to meson-like operators in an
gauge theory with fundamental matter.Comment: 30 pages. v2: minor changes and discussion section added, J.Phys.A
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