22,805 research outputs found
Projections and Dyadic Parseval Frame MRA Wavelets
A classical theorem attributed to Naimark states that, given a Parseval frame
in a Hilbert space , one can embed in
a larger Hilbert space so that the image of is the
projection of an orthonormal basis for . In the present work, we
revisit the notion of Parseval frame MRA wavelets from two papers of
Paluszy\'nski, \v{S}iki\'c, Weiss, and Xiao (PSWX) and produce an analog of
Naimark's theorem for these wavelets at the level of their scaling functions.
We aim to make this discussion as self-contained as possible and provide a
different point of view on Parseval frame MRA wavelets than that of PSWX.Comment: 19 page
Ground state energy of a homogeneous Bose-Einstein condensate beyond Bogoliubov
The standard calculations of the ground-state energy of a homogeneous Bose
gas rely on approximations which are physically reasonable but difficult to
control. Lieb and Yngvason [Phys. Rev. Lett. 80, 2504 (1998)] have proved
rigorously that the commonly accepted leading order term of the ground state
energy is correct in the zero-density-limit. Here, strong indications are given
that also the next to leading term is correct. It is shown that the first terms
obtained in a perturbative treatment provide contributions which are lost in
the Bogoliubov approach.Comment: 6 pages, accepted for publication in Europhys. Lett.
http://www.epletters.ch
Magnetic buoyancy instabilities in the presence of magnetic flux pumping at the base of the solar convection zone
We perform idealized numerical simulations of magnetic buoyancy instabilities in three dimensions, solving the equations of compressible magnetohydrodynamics in a model of the solar tachocline. In particular, we study the effects of including a highly simplified model of magnetic flux pumping in an upper layer (‘the convection zone’) on magnetic buoyancy instabilities in a lower layer (‘the upper parts of the radiative interior – including the tachocline’), to study these competing flux transport mechanisms at the base of the convection zone. The results of the inclusion of this effect in numerical simulations of the buoyancy instability of both a preconceived magnetic slab and a shear-generated magnetic layer are presented. In the former, we find that if we are in the regime that the downward pumping velocity is comparable with the Alfvén speed of the magnetic layer, magnetic flux pumping is able to hold back the bulk of the magnetic field, with only small pockets of strong field able to rise into the upper layer.
In simulations in which the magnetic layer is generated by shear, we find that the shear velocity is not necessarily required to exceed that of the pumping (therefore the kinetic energy of the shear is not required to exceed that of the overlying convection) for strong localized pockets of magnetic field to be produced which can rise into the upper layer. This is because magnetic flux pumping acts to store the field below the interface, allowing it to be amplified both by the shear and by vortical fluid motions, until pockets of field can achieve sufficient strength to rise into the upper layer. In addition, we find that the interface between the two layers is a natural location for the production of strong vertical gradients in the magnetic field. If these gradients are sufficiently strong to allow the development of magnetic buoyancy instabilities, strong shear is not necessarily required to drive them (cf. previous work by Vasil & Brummell). We find that the addition of magnetic flux pumping appears to be able to assist shear-driven magnetic buoyancy in producing strong flux concentrations that can rise up into the convection zone from the radiative interior
Spintronics of a Nanoelectromechanical Shuttle
We consider effects of the spin degree of freedom on the nanomechanics of a
single-electron transistor (SET) containing a nanometer-sized metallic cluster
suspended between two magnetic leads. It is shown that in such a
nanoelectromechanical SET(NEM-SET) the onset of an electromechanical
instability leading to cluster vibrations and "shuttle" transport of electrons
between the leads can be controlled by an external magnetic field. Different
stable regimes of this spintronic NEM-SET operation are analyzed. Two different
scenarios for the onset of shuttle vibrations are found.Comment: 4 pages, 3 figure
Deformation of grain boundaries in polar ice
The ice microstructure (grain boundaries) is a key feature used to study ice
evolution and to investigate past climatic changes. We studied a deep ice core,
in Dome Concordia, Antarctica, which records past mechanical deformations. We
measured a "texture tensor" which characterizes the pattern geometry and
reveals local heterogeneities of deformation along the core. These results
question key assumptions of the current models used for dating
Finite Density Algorithm in Lattice QCD -- a Canonical Ensemble Approach
I will review the finite density algorithm for lattice QCD based on finite
chemical potential and summarize the associated difficulties. I will propose a
canonical ensemble approach which projects out the finite baryon number sector
from the fermion determinant. For this algorithm to work, it requires an
efficient method for calculating the fermion determinant and a Monte Carlo
algorithm which accommodates unbiased estimate of the probability. I shall
report on the progress made along this direction with the Pad\'{e} - Z
estimator of the determinant and its implementation in the newly developed
Noisy Monte Carlo algorithm.Comment: Invited talk at Nankai Symposium on Mathematical Physics, Tianjin,
Oct. 2001, 18 pages, 3 figures; expanded and references adde
Quantum Shuttle Phenomena in a Nanoelectromechanical Single-Electron Transistor
An analytical analysis of quantum shuttle phenomena in a
nanoelectromechanical single-electron transistor has been performed in the
realistic case, when the electron tunnelling length is much greater than the
amplitude of the zero point oscillations of the central island. It is shown
that when the dissipation is below a certain threshold value, the vibrational
ground state of the central island is unstable. The steady-state into which
this instability develops is studied. It is found that if the electric field
between the leads is much greater than a characteristic value , the quasiclassical shuttle picture is recovered, while if a new quantum regime of shuttle vibrations occurs. We show
that in the latter regime small quantum fluctuations result in large (i.e.
finite in the limit ) shuttle vibrations.Comment: 5 pages, 1 figur
Landau functions for non-interacting bosons
We discuss the statistics of Bose-Einstein condensation (BEC) in a canonical
ensemble of N non-interacting bosons in terms of a Landau function L_N^{BEC}
(q) defined by the logarithm of the probability distribution of the order
parameter q for BEC. We also discuss the corresponding Landau function for
spontaneous symmetry breaking (SSB), which for finite N should be distinguished
from L_N^{BEC}. Only for intinite N BEC and SSB can be described by the same
Landau function which depends on the dimensionality and on the form of the
external potential in a surprisingly complex manner. For bosons confined by a
three-dimensional harmonic trap the Landau function exhibits the usual behavior
expected for continuous phase transitions.Comment: 4 pages, 4 figures; final version to appear as a rapid communication
in Physical Review A. Abstract modified and typos correcte
Complete High Temperature Expansions for One-Loop Finite Temperature Effects
We develop exact, simple closed form expressions for partition functions
associated with relativistic bosons and fermions in odd spatial dimensions.
These expressions, valid at high temperature, include the effects of a
non-trivial Polyakov loop and generalize well-known high temperature
expansions. The key technical point is the proof of a set of Bessel function
identities which resum low temperature expansions into high temperature
expansions. The complete expressions for these partition functions can be used
to obtain one-loop finite temperature contributions to effective potentials,
and thus free energies and pressures.Comment: 9 pages, RevTeX, no figures. To be published in Phys. Rev D. v2 has
revised introduction and conclusions, plus a few typographical errors are
corrected; v3 corrects one typ
Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
The main result of this paper concerns the behavior of a free boundary
arising from a minimization problem, close to the fixed boundary in two
dimensions
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