2,751 research outputs found
On certain finiteness questions in the arithmetic of modular forms
We investigate certain finiteness questions that arise naturally when
studying approximations modulo prime powers of p-adic Galois representations
coming from modular forms. We link these finiteness statements with a question
by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms.
Specifically, we conjecture that for fixed N, m, and prime p with p not
dividing N, there is only a finite number of reductions modulo p^m of
normalized eigenforms on \Gamma_1(N). We consider various variants of our basic
finiteness conjecture, prove a weak version of it, and give some numerical
evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3:
restructered parts of the article; v4: minor corrections and change
Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model
We obtain an exact solution for the motion of a particle driven by a spring
in a Brownian random-force landscape, the Alessandro-Beatrice-Bertotti-Montorsi
(ABBM) model. Many experiments on quasi-static driving of elastic interfaces
(Barkhausen noise in magnets, earthquake statistics, shear dynamics of granular
matter) exhibit the same universal behavior as this model. It also appears as a
limit in the field theory of elastic manifolds. Here we discuss predictions of
the ABBM model for monotonous, but otherwise arbitrary, time-dependent driving.
Our main result is an explicit formula for the generating functional of
particle velocities and positions. We apply this to derive the
particle-velocity distribution following a quench in the driving velocity. We
also obtain the joint avalanche size and duration distribution and the mean
avalanche shape following a jump in the position of the confining spring. Such
non-stationary driving is easy to realize in experiments, and provides a way to
test the ABBM model beyond the stationary, quasi-static regime. We study
extensions to two elastically coupled layers, and to an elastic interface of
internal dimension d, in the Brownian force landscape. The effective action of
the field theory is equal to the action, up to 1-loop corrections obtained
exactly from a functional determinant. This provides a connection to
renormalization-group methods.Comment: 18 pages, 3 figure
Magnetic properties of antiferromagnetically coupled CoFeB/Ru/CoFeB
This work reports on the thermal stability of two amorphous CoFeB layers
coupled antiferromagnetically via a thin Ru interlayer. The saturation field of
the artificial ferrimagnet which is determined by the coupling, J, is almost
independent on the annealing temperature up to more than 300 degree C. An
annealing at more than 325 degree C significantly increases the coercivity, Hc,
indicating the onset of crystallization.Comment: 4 pages, 3 figure
Interacting crumpled manifolds
In this article we study the effect of a delta-interaction on a polymerized
membrane of arbitrary internal dimension D. Depending on the dimensionality of
membrane and embedding space, different physical scenarios are observed. We
emphasize on the difference of polymers from membranes. For the latter,
non-trivial contributions appear at the 2-loop level. We also exploit a
``massive scheme'' inspired by calculations in fixed dimensions for scalar
field theories. Despite the fact that these calculations are only amenable
numerically, we found that in the limit of D to 2 each diagram can be evaluated
analytically. This property extends in fact to any order in perturbation
theory, allowing for a summation of all orders. This is a novel and quite
surprising result. Finally, an attempt to go beyond D=2 is presented.
Applications to the case of self-avoiding membranes are mentioned
Antiferromagnetically coupled CoFeB/Ru/CoFeB trilayers
This work reports on the magnetic interlayer coupling between two amorphous
CoFeB layers, separated by a thin Ru spacer. We observe an antiferromagnetic
coupling which oscillates as a function of the Ru thickness x, with the second
antiferromagnetic maximum found for x=1.0 to 1.1 nm. We have studied the
switching of a CoFeB/Ru/CoFeB trilayer for a Ru thickness of 1.1 nm and found
that the coercivity depends on the net magnetic moment, i.e. the thickness
difference of the two CoFeB layers. The antiferromagnetic coupling is almost
independent on the annealing temperatures up to 300 degree C while an annealing
at 350 degree C reduces the coupling and increases the coercivity, indicating
the onset of crystallization. Used as a soft electrode in a magnetic tunnel
junction, a high tunneling magnetoresistance of about 50%, a well defined
plateau and a rectangular switching behavior is achieved.Comment: 3 pages, 3 figure
THE PERIOD-DECLINE-RATE RELATION FOR PULSATING STARS
The relationships between the periods and the rate of decline in V and R for pulsating stars are investigated. It is shown that these relationships are useful for making preliminary estimates of periods for stars with little data. These estimates can then be used to optimize times of further observations
O(N) Models with Topological Lattice Actions
A variety of lattice discretisations of continuum actions has been
considered, usually requiring the correct classical continuum limit. Here we
discuss "weird" lattice formulations without that property, namely lattice
actions that are invariant under most continuous deformations of the field
configuration, in one version even without any coupling constants. It turns out
that universality is powerful enough to still provide the correct quantum
continuum limit, despite the absence of a classical limit, or a perturbative
expansion. We demonstrate this for a set of O(N) models (or non-linear
-models). Amazingly, such "weird" lattice actions are not only in the
right universality class, but some of them even have practical benefits, in
particular an excellent scaling behaviour.Comment: 7 pages, LaTex, 4 figures, 1 table, talk presented at the 31st
Symposium on Lattice Field Theor
Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows
We use renormalization group methods to derive equations of motion for large
scale variables in fluid dynamics. The large scale variables are averages of
the underlying continuum variables over cubic volumes, and naturally live on a
lattice. The resulting lattice dynamics represents a perfect discretization of
continuum physics, i.e. grid artifacts are completely eliminated. Perfect
equations of motion are derived for static, slow flows of incompressible,
viscous fluids. For Hagen-Poiseuille flow in a channel with square cross
section the equations reduce to a perfect discretization of the Poisson
equation for the velocity field with Dirichlet boundary conditions. The perfect
large scale Poisson equation is used in a numerical simulation, and is shown to
represent the continuum flow exactly. For non-square cross sections we use a
numerical iterative procedure to derive flow equations that are approximately
perfect.Comment: 25 pages, tex., using epsfig, minor changes, refernces adde
The nucleon spin and momentum decomposition using lattice QCD simulations
We determine within lattice QCD, the nucleon spin carried by valence and sea
quarks, and gluons. The calculation is performed using an ensemble of gauge
configurations with two degenerate light quarks with mass fixed to
approximately reproduce the physical pion mass. We find that the total angular
momentum carried by the quarks in the nucleon is and the gluon contribution is giving a total of consistent with the spin sum. For the quark intrinsic spin contribution
we obtain . All quantities are given in the scheme at
2~GeV. The quark and gluon momentum fractions are also computed and add up to
satisfying the momentum sum.Comment: Version published in PR
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