20,517 research outputs found
Approximation of Feynman path integrals with non-smooth potentials
We study the convergence in of the time slicing approximation of
Feynman path integrals under low regularity assumptions on the potential.
Inspired by the custom in Physics and Chemistry, the approximate propagators
considered here arise from a series expansion of the action. The results are
ultimately based on function spaces, tools and strategies which are typical of
Harmonic and Time-frequency analysis.Comment: 18 page
On the pointwise convergence of the integral kernels in the Feynman-Trotter formula
We study path integrals in the Trotter-type form for the Schr\"odinger
equation, where the Hamiltonian is the Weyl quantization of a real-valued
quadratic form perturbed by a potential in a class encompassing that -
considered by Albeverio and It\^o in celebrated papers - of Fourier transforms
of complex measures. Essentially, is bounded and has the regularity of a
function whose Fourier transform is in . Whereas the strong convergence in
in the Trotter formula, as well as several related issues at the operator
norm level are well understood, the original Feynman's idea concerned the
subtler and widely open problem of the pointwise convergence of the
corresponding probability amplitudes, that are the integral kernels of the
approximation operators. We prove that, for the above class of potentials, such
a convergence at the level of the integral kernels in fact occurs, uniformly on
compact subsets and for every fixed time, except for certain exceptional time
values for which the kernels are in general just distributions. Actually,
theorems are stated for potentials in several function spaces arising in
Harmonic Analysis, with corresponding convergence results. Proofs rely on
Banach algebras techniques for pseudo-differential operators acting on such
function spaces.Comment: 26 page
Extruding the vortex lattice: two reacting populations of dislocations
A controllable soft solid is realised in vortex matter in a type II
superconductor. The two-dimensional unit cell area can be varied by a factor of
in the solid phase, without a change of crystal symmetry offering easy
exploration of extreme regimes compared to ordinary materials. The capacity to
confine two-dimensional vortex matter to mesoscopic regions provides an arena
for the largely unexplored metallurgy of plastic deformation at large density
gradients. Our simulations reveal a novel plastic flow mechanism in this driven
non-equilibrium system, utilising two distinct, but strongly interacting,
populations of dislocations. One population facilitates the relaxation of
density; a second aids the relaxation of shear stresses concentrated at the
boundaries. The disparity of the bulk and shear moduli in vortex matter ensures
the dislocation motion follows the overall continuum flow reflecting density
variation
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Social Security Reform: Legal Analysis of Social Security Benefit Entitlement Issues
[Excerpt] Calculations indicating that in the long run the Social Security program will not be financially sustainable under the present statutory scheme have fueled the current debate regarding Social Security reform. This report addresses selected legal issues which may be raised regarding entitlement to Social Security benefits as Congress considers possible changes to the Social Security program, and in view of projected long-range shortfalls in the Social Security Trust Funds
Importance Sampling Simulation of Population Overflow in Two-node Tandem Networks
In this paper we consider the application of importance sampling in simulations of Markovian tandem networks in order to estimate the probability of rare events, such as network population overflow. We propose a heuristic methodology to obtain a good approximation to the 'optimal' state-dependent change of measure (importance sampling distribution). Extensive experimental results on 2-node tandem networks are very encouraging, yielding asymptotically efficient estimates (with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient The methodology avoids the costly optimization involved in other recently proposed approaches to approximate the 'optimal' state-dependent change of measure. Moreover, the insight drawn from the heuristic promises its applicability to larger networks and more general topologies
Banking globalization, monetary transmission and the lending channel
The globalization of banking in the United States is influencing the monetary transmission mechanism both domestically and in foreign markets. Using quarterly information from all U.S. banks filing call reports between 1980 and 2005, we find evidence for the lending channel for monetary policy in large banks, but only those banks that are domestically-oriented and without international operations. We show that the large globally-oriented banks rely on internal capital markets with their foreign affiliates to help smooth domestic liquidity shocks. We also show that the existence of such internal capital markets contributes to an international propagation of domestic liquidity shocks to lending by affiliated banks abroad. While these results imply a substantially more active lending channel than documented in the seminal work of Kashyap and Stein (2000), the lending channel within the United States is declining in strength as banking becomes more globalized. --Lending channel,Bank,global,liquidity,transmission,internal capital markets
Information Gains from Cosmological Probes
In light of the growing number of cosmological observations, it is important
to develop versatile tools to quantify the constraining power and consistency
of cosmological probes. Originally motivated from information theory, we use
the relative entropy to compute the information gained by Bayesian updates in
units of bits. This measure quantifies both the improvement in precision and
the 'surprise', i.e. the tension arising from shifts in central values. Our
starting point is a WMAP9 prior which we update with observations of the
distance ladder, supernovae (SNe), baryon acoustic oscillations (BAO), and weak
lensing as well as the 2015 Planck release. We consider the parameters of the
flat CDM concordance model and some of its extensions which include
curvature and Dark Energy equation of state parameter . We find that,
relative to WMAP9 and within these model spaces, the probes that have provided
the greatest gains are Planck (10 bits), followed by BAO surveys (5.1 bits) and
SNe experiments (3.1 bits). The other cosmological probes, including weak
lensing (1.7 bits) and {} measures (1.7 bits), have contributed
information but at a lower level. Furthermore, we do not find any significant
surprise when updating the constraints of WMAP9 with any of the other
experiments, meaning that they are consistent with WMAP9. However, when we
choose Planck15 as the prior, we find that, accounting for the full
multi-dimensionality of the parameter space, the weak lensing measurements of
CFHTLenS produce a large surprise of 4.4 bits which is statistically
significant at the 8 level. We discuss how the relative entropy
provides a versatile and robust framework to compare cosmological probes in the
context of current and future surveys.Comment: 26 pages, 5 figure
Isotropic vs. Anisotropic components of BAO data: a tool for model selection
We conduct a selective analysis of the isotropic () and anisotropic
() components of the most recent Baryon Acoustic Oscillations (BAO) data.
We find that these components provide significantly different constraints and
could provide strong diagnostics for model selection, also in view of more
precise data to arrive. For instance, in the CDM model, we find a mild
tension of for the estimates obtained using
and separately. Considering both and as free parameters, we
find that the concordance model is in tension with the best-fit values provided
by the BAO data alone at 2.2. We complemented the BAO data with the
Supernova Ia (SNIa) and Observational \textit{Hubble} datasets to perform a
joint analysis on the CDM model and its standard extensions. By
assuming CDM scenario, we find that these data provide \text{km/s Mpc} as the best-fit value for the present expansion
rate. In the CDM scenario we find that the evidence for acceleration
using the BAO data alone is more than , which increases to in our joint analysis.Comment: Accepted for publication in JCAP. References update
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