759 research outputs found
An example of optimal field cut in lattice gauge perturbation theory
We discuss the weak coupling expansion of a one plaquette SU(2) lattice gauge
theory. We show that the conventional perturbative series for the partition
function has a zero radius of convergence and is asymptotic. The average
plaquette is discontinuous at g^2=0. However, the fact that SU(2) is compact
provides a perturbative sum that converges toward the correct answer for
positive g^2. This alternate methods amounts to introducing a specific coupling
dependent field cut, that turns the coefficients into g-dependent quantities.
Generalizing to an arbitrary field cut, we obtain a regular power series with a
finite radius of convergence. At any order in the modified perturbative
procedure, and for a given coupling, it is possible to find at least one (and
sometimes two) values of the field cut that provide the exact answer. This
optimal field cut can be determined approximately using the strong coupling
expansion. This allows us to interpolate accurately between the weak and strong
coupling regions. We discuss the extension of the method to lattice gauge
theory on a D-dimensional cubic lattice.Comment: 9 pages, 11 figs., uses revtex4, modified presentatio
A New Phase Time Formula for Opaque Barrier Tunneling
After a brief review of the derivation of the standard phase time formula,
based on the use of the stationary phase method, we propose, in the opaque
limit, an alternative method to calculate the phase time. The new formula for
the phase time is in excellent agreement with the numerical simulations and
shows that for wave packets whose upper limit of the momentum distribution is
very close to the barrier height, the transit time is proportional to the
barrier width.Comment: 9 pages, 2 figure
Effect of speed on economy of airship traffic
The economic costs and benefits of speed on airship traffic are calculated and different factors are considered
Molecular Feshbach dissociation as a source for motionally entangled atoms
We describe the dissociation of a diatomic Feshbach molecule due to a
time-varying external magnetic field in a realistic trap and guide setting. An
analytic expression for the asymptotic state of the two ultracold atoms is
derived, which can serve as a basis for the analysis of dissociation protocols
to generate motionally entangled states. For instance, the gradual dissociation
by sequences of magnetic field pulses may delocalize the atoms into
macroscopically distinct wave packets, whose motional entanglement can be
addressed interferometrically. The established relation between the applied
magnetic field pulse and the generated dissociation state reveals that
square-shaped magnetic field pulses minimize the momentum spread of the atoms.
This is required to control the detrimental influence of dispersion in a
recently proposed experiment to perform a Bell test in the motion of the two
atoms [C. Gneiting and K. Hornberger, Phys. Rev. Lett. 101, 260503 (2008)].Comment: 12 pages, 3 figures; corresponds to published versio
On the Generalization Capacities of Neural Controlled Differential Equations
We consider a supervised learning setup in which the goal is to predicts an
outcome from a sample of irregularly sampled time series using Neural
Controlled Differential Equations (Kidger, Morrill, et al. 2020). In our
framework, the time series is a discretization of an unobserved continuous
path, and the outcome depends on this path through a controlled differential
equation with unknown vector field. Learning with discrete data thus induces a
discretization bias, which we precisely quantify. Using theoretical results on
the continuity of the flow of controlled differential equations, we show that
the approximation bias is directly related to the approximation error of a
Lipschitz function defining the generative model by a shallow neural network.
By combining these result with recent work linking the Lipschitz constant of
neural networks to their generalization capacities, we upper bound the
generalization gap between the expected loss attained by the empirical risk
minimizer and the expected loss of the true predictor.Comment: Edited typo
Echolocation by Quasiparticles
It is shown that the local density of states (LDOS), measured in an Scanning
Tunneling Microscopy (STM) experiment, at a single tip position contains
oscillations as a function of Energy, due to quasiparticle interference, which
is related to the positions of nearby scatterers. We propose a method of STM
data analysis based on this idea, which can be used to locate the scatterers.
In the case of a superconductor, the method can potentially distinguish the
nature of the scattering by a particular impurity.Comment: 4+ page
The effect of dressing on high-order harmonic generation in vibrating H molecules
We develop the strong-field approximation for high-order harmonic generation
in hydrogen molecules, including the vibrational motion and the laser-induced
coupling of the lowest two Born-Oppenheimer states in the molecular ion that is
created by the initial ionization of the molecule. We show that the field
dressing becomes important at long laser wavelengths (m),
leading to an overall reduction of harmonic generation and modifying the ratio
of harmonic signals from different isotopes.Comment: 23 pages, 11 figures, submitted to PR
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