相关论文: Transverse modes for flat inter-bunch wakes
We develop the theory of the resonant formation of coupled topological-collective coherent modes in the presence of a quantized trap and classical external field. The coupling between the topological and the collective modes can be linear…
We define a turning of a rank-$2k$ vector bundle $E \to B$ to be a homotopy of bundle automorphisms $\psi_t$ from $\mathbb{Id}_E$, the identity of $E$, to $-\mathbb{Id}_E$, minus the identity, and call a pair $(E, \psi_t)$ a turned bundle.…
Cosmological soft theorems (or consistency relations) provide a powerful probe for the physics of inflation. These relations rely on minimal assumptions and hold very generally. Consequently, any violation of these relations would rule out…
The Transformer architecture has achieved tremendous success in natural language processing, computer vision, and scientific computing through its self-attention mechanism. However, its core components-positional encoding and attention…
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced…
Threshold of the transverse mode coupling instability is calculated in frameworks of the square well model at arbitrary value of space charge tune shift. A new method of calculation is developed beyond the traditional expansion technique.…
Interconnecting power systems has a number of advantages such as better electric power quality, increased reliability of power supply, economies of scales through production and reserve pooling and so forth. Simultaneously, it may…
Modular invariance is a necessary condition for the consistency of any closed string theory. In particular, it imposes stringent constraints on the spectrum of orbifold theories, and in principle determines their spectrum uniquely up to…
Transverse mode-coupling instability (TMCI) is known to limit bunch intensity. Since space charge (SC) changes the spectra of the collective modes, it affects the TMCI threshold as well. In agreement with results of M. Blaskiewicz and V.…
It is easy to imagine that a subvariety of a vector bundle, whose intersection with every fibre is a vector subspace of constant dimension, must necessarily be a sub-bundle. We give two examples to show that this is not true, and several…
For a single hadron bunch in a circular accelerator at zero chromaticity, without multi-turn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability, or TMCI.…
We consider T(x), a tensor of arbitrary rank that is symmetric in all of its indices and conserved in the sense that the divergence on any one index vanishes. Our conjecture is that all integral moments of this tensor will vanish if the…
We study obstructions to a direct limit preserving right exact functor $F$ between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. When the domain scheme is affine, or if $F$ is exact, all…
One novel arena for designing superconductors with high $T_C$ is the flat-band systems. A basic idea is that flat bands, arising from quantum mechanical interference, give unique opportunities for enhancing $T_C$ with (i) many…
In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales. We show that some such results remain valid for metric spaces with non-unique…
We study flips of moduli schemes of stable torsion free sheaves as wall-crossing phenomena of moduli schemes of stable modules over certain finite dimensional algebra. They are described as stratified Grassmann bundles.
The structure of the divergences for transverse theories of gravity is studied to one-loop order. These theories are invariant only under those diffeomorphisms that enjoy unit Jacobian determinant (TDiff), so that the determinant of the…
Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation…
In this paper, we give a characterization of homogeneous quandles with abelian inner automorphism groups. In particular, we show that such a quandle is expressed as an abelian extension of a trivial quandle. Our construction is a…
The interface between two materials described by spectrally gapped Hamiltonians is expected to host an in-gap interface mode, whenever a certain topological invariant changes across the interface. We provide a precise statement of this…