7,001 research outputs found
Causality and dispersion relations and the role of the S-matrix in the ongoing research
The adaptation of the Kramers-Kronig dispersion relations to the causal
localization structure of QFT led to an important project in particle physics,
the only one with a successful closure. The same cannot be said about the
subsequent attempts to formulate particle physics as a pure S-matrix project.
The feasibility of a pure S-matrix approach are critically analyzed and their
serious shortcomings are highlighted. Whereas the conceptual/mathematical
demands of renormalized perturbation theory are modest and misunderstandings
could easily be corrected, the correct understanding about the origin of the
crossing property requires the use of the mathematical theory of modular
localization and its relation to the thermal KMS condition. These new concepts,
which combine localization, vacuum polarization and thermal properties under
the roof of modular theory, will be explained and their potential use in a new
constructive (nonperturbative) approach to QFT will be indicated. The S-matrix
still plays a predominant role but, different from Heisenberg's and
Mandelstam's proposals, the new project is not a pure S-matrix approach. The
S-matrix plays a new role as a "relative modular invariant"..Comment: 47 pages expansion of arguments and addition of references,
corrections of misprints and bad formulation
Grid-free compressive beamforming
The direction-of-arrival (DOA) estimation problem involves the localization
of a few sources from a limited number of observations on an array of sensors,
thus it can be formulated as a sparse signal reconstruction problem and solved
efficiently with compressive sensing (CS) to achieve high-resolution imaging.
On a discrete angular grid, the CS reconstruction degrades due to basis
mismatch when the DOAs do not coincide with the angular directions on the grid.
To overcome this limitation, a continuous formulation of the DOA problem is
employed and an optimization procedure is introduced, which promotes sparsity
on a continuous optimization variable. The DOA estimation problem with
infinitely many unknowns, i.e., source locations and amplitudes, is solved over
a few optimization variables with semidefinite programming. The grid-free CS
reconstruction provides high-resolution imaging even with non-uniform arrays,
single-snapshot data and under noisy conditions as demonstrated on experimental
towed array data.Comment: 14 pages, 8 figures, journal pape
A Distributed Asynchronous Method of Multipliers for Constrained Nonconvex Optimization
This paper presents a fully asynchronous and distributed approach for
tackling optimization problems in which both the objective function and the
constraints may be nonconvex. In the considered network setting each node is
active upon triggering of a local timer and has access only to a portion of the
objective function and to a subset of the constraints. In the proposed
technique, based on the method of multipliers, each node performs, when it
wakes up, either a descent step on a local augmented Lagrangian or an ascent
step on the local multiplier vector. Nodes realize when to switch from the
descent step to the ascent one through an asynchronous distributed logic-AND,
which detects when all the nodes have reached a predefined tolerance in the
minimization of the augmented Lagrangian. It is shown that the resulting
distributed algorithm is equivalent to a block coordinate descent for the
minimization of the global augmented Lagrangian. This allows one to extend the
properties of the centralized method of multipliers to the considered
distributed framework. Two application examples are presented to validate the
proposed approach: a distributed source localization problem and the parameter
estimation of a neural network.Comment: arXiv admin note: substantial text overlap with arXiv:1803.0648
Holography with Schroedinger Potentials
We examine the analogue one-dimensional quantum mechanics problem associated
with bulk scalars and fermions in a slice of AdS_5. The ``Schroedinger''
potential can take on different qualitative shapes depending on the values of
the mass parameters in the bulk theory. Several interesting correlations
between the shape of the Schroedinger potential and the holographic theory
exist. We show that the quantum mechanical picture is a useful guide to the
holographic theory by examining applications from phenomenology.Comment: 22 pages, 4 figure
Dual approach to circuit quantization using loop charges
The conventional approach to circuit quantization is based on node fluxes and
traces the motion of node charges on the islands of the circuit. However, for
some devices, the relevant physics can be best described by the motion of
polarization charges over the branches of the circuit that are in general
related to the node charges in a highly nonlocal way. Here, we present a
method, dual to the conventional approach, for quantizing planar circuits in
terms of loop charges. In this way, the polarization charges are directly
obtained as the differences of the two loop charges on the neighboring loops.
The loop charges trace the motion of fluxes through the circuit loops. We show
that loop charges yield a simple description of the flux transport across
phase-slip junctions. We outline a concrete construction of circuits based on
phase-slip junctions that are electromagnetically dual to arbitrary planar
Josephson junction circuits. We argue that loop charges also yield a simple
description of the flux transport in conventional Josephson junctions shunted
by large impedances. We show that a mixed circuit description in terms of node
fluxes and loop charges yields an insight into the flux decompactification of a
Josephson junction shunted by an inductor. As an application, we show that the
fluxonium qubit is well approximated as a phase-slip junction for the
experimentally relevant parameters. Moreover, we argue that the - qubit
is effectively the dual of a Majorana Josephson junction.Comment: 20 pages, 11 figures. Version accepted for publication in PRB.
Changes: introduction has become less technical and an example for the
inclusion of offset charges has been adde
- …