806 research outputs found
Vertex corrections in gauge theories for two-dimensional condensed matter systems
We calculate the self-energy of two-dimensional fermions that are coupled to
transverse gauge fields, taking two-loop corrections into account. Given a bare
gauge field propagator that diverges for small momentum transfers q as 1 /
q^{eta}, 1 < eta < 2, the fermionic self-energy without vertex corrections
vanishes for small frequencies omega as Sigma (omega) propto omega^{gamma with
gamma = {frac{2}{1 + eta}} < 1. We show that inclusion of the leading radiative
correction to the fermion - gauge field vertex leads to
Sigma (omega) propto omega^{gamma} [ 1 - a_{eta} ln (omega_0 / omega) ],
where a_{\eta} is a positive numerical constant and omega_0 is some finite
energy scale. The negative logarithmic correction is consistent with the
scenario that higher order vertex corrections push the exponent gamma to larger
values.Comment: 6 figure
Hydrodynamic object recognition using pressure sensing
Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing
Absolute instabilities of travelling wave solutions in a Keller-Segel model
We investigate the spectral stability of travelling wave solutions in a
Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity
function and a constant, sublinear, and linear consumption rate. Linearising
around the travelling wave solutions, we locate the essential and absolute
spectrum of the associated linear operators and find that all travelling wave
solutions have essential spectrum in the right half plane. However, we show
that in the case of constant or sublinear consumption there exists a range of
parameters such that the absolute spectrum is contained in the open left half
plane and the essential spectrum can thus be weighted into the open left half
plane. For the constant and sublinear consumption rate models we also determine
critical parameter values for which the absolute spectrum crosses into the
right half plane, indicating the onset of an absolute instability of the
travelling wave solution. We observe that this crossing always occurs off of
the real axis
Nekhoroshev theorem for the periodic Toda lattice
The periodic Toda lattice with sites is globally symplectomorphic to a
two parameter family of coupled harmonic oscillators. The action
variables fill out the whole positive quadrant of . We prove that in
the interior of the positive quadrant as well as in a neighborhood of the
origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's
theorem applies on (almost) all parts of phase space.Comment: 28 page
Foundations for Cooperating with Control Noise in the Manipulation of Quantum Dynamics
This paper develops the theoretical foundations for the ability of a control
field to cooperate with noise in the manipulation of quantum dynamics. The
noise enters as run-to-run variations in the control amplitudes, phases and
frequencies with the observation being an ensemble average over many runs as is
commonly done in the laboratory. Weak field perturbation theory is developed to
show that noise in the amplitude and frequency components of the control field
can enhance the process of population transfer in a multilevel ladder system.
The analytical results in this paper support the point that under suitable
conditions an optimal field can cooperate with noise to improve the control
outcome.Comment: submitted to Phys. Rev.
The Laplace equation for the exterior of the Hankel contour and novel identities for hypergeometric functions
By employing conformal mappings, it is possible to express the solution of
certain boundary value problems for the Laplace equation in terms of a single
integral involving the given boundary data. We show that such explicit formulae
can be used to obtain novel identities for special functions. A convenient tool
for deriving this type of identities is the so-called \emph{global relation},
which has appeared recently in a wide range of boundary value problems. As a
concrete application, we analyze the Neumann boundary value problem for the
Laplace equation in the exterior of the so-called Hankel contour, which is the
contour that appears in the definition of both the gamma and the Riemann zeta
functions. By utilizing the explicit solution of this problem, we derive a
plethora of novel identities involving the hypergeometric function
Hydromagnetic Instability in plane Couette Flow
We study the stability of a compressible magnetic plane Couette flow and show
that compressibility profoundly alters the stability properties if the magnetic
field has a component perpendicular to the direction of flow. The necessary
condition of a newly found instability can be satisfied in a wide variety of
flows in laboratory and astrophysical conditions. The instability can operate
even in a very strong magnetic field which entirely suppresses other MHD
instabilities. The growth time of this instability can be rather short and
reach shear timescales.Comment: 6 pages, 5 figures. To appear on PR
String equations in Whitham hierarchies: tau-functions and Virasoro constraints
A scheme for solving Whitham hierarchies satisfying a special class of string
equations is presented. The tau-function of the corresponding solutions is
obtained and the differential expressions of the underlying Virasoro
constraints are characterized. Illustrative examples of exact solutions of
Whitham hierarchies are derived and applications to conformal maps dynamics are
indicated.Comment: 26 pages, 2 figure
Variable-delay feedback control of unstable steady states in retarded time-delayed systems
We study the stability of unstable steady states in scalar retarded
time-delayed systems subjected to a variable-delay feedback control. The
important aspect of such a control problem is that time-delayed systems are
already infinite-dimensional before the delayed feedback control is turned on.
When the frequency of the modulation is large compared to the system's
dynamics, the analytic approach consists of relating the stability properties
of the resulting variable-delay system with those of an analogous distributed
delay system. Otherwise, the stability domains are obtained by a numerical
integration of the linearized variable-delay system. The analysis shows that
the control domains are significantly larger than those in the usual
time-delayed feedback control, and that the complexity of the domain structure
depends on the form and the frequency of the delay modulation.Comment: 13 pages, 8 figures, RevTeX, accepted for publication in Physical
Review
Mapping the phase diagram of strongly interacting matter
We employ a conformal mapping to explore the thermodynamics of strongly
interacting matter at finite values of the baryon chemical potential .
This method allows us to identify the singularity corresponding to the critical
point of a second-order phase transition at finite , given information
only at . The scheme is potentially useful for computing thermodynamic
properties of strongly interacting hot and dense matter in lattice gauge
theory. The technique is illustrated by an application to a chiral effective
model.Comment: 5 pages, 3 figures; published versio
- …