A fast high-order method to calculate wakefield forces in an electron beam

In this paper we report on a high-order fast method to numerically calculate wakefield forces in an electron beam given a wake function model. This method is based on a Newton-Cotes quadrature rule for integral approximation and an FFT method for discrete summation that results in an $O(Nlog(N))$ computational cost, where $N$ is the number of grid points. Using the Simpson quadrature rule with an accuracy of $O(h^4)$, where $h$ is the grid size, we present numerical calculation of the wakefields from a resonator wake function model and from a one-dimensional coherent synchrotron radiation (CSR) wake model. Besides the fast speed and high numerical accuracy, the calculation using the direct line density instead of the first derivative of the line density avoids numerical filtering of the electron density function for computing the CSR wakefield force

Fermion Families from Two Layer Warped Extra Dimensions

In extra dimensions, the quark and lepton mass hierarchy can be reproduced from the same order bulk mass parameters, and standard model fermion families can be generated from one generation in the high dimensional space. We try to explain the origin of the same order bulk mass parameters and address the family replication puzzle simultaneously. We show that they correlate with each other. We construct models that families are generated from extra dimensional space, and in the meantime the bulk mass parameters of same order emerge naturally. The interesting point is that the bulk mass parameters, which are in same order, correspond to the eigenvalues of a Schr\"{o}dinger-like equation. We also discuss the problem existing in this approach.Comment: 21 latex pages, final version to appear in JHE

Entanglement in a second order topological insulator on a square lattice

In a $d$-dimensional topological insulator of order $d$, there are zero energy states on its corners which have close relationship with its entanglement behaviors. We studied the bipartite entanglement spectra for different subsystem shapes and found that only when the entanglement boundary has corners matching the lattice, exact zero modes exist in the entanglement spectrum corresponding to the zero energy states caused by the same physical corners. We then considered finite size systems in which case these corner states are coupled together by long range hybridizations to form a multipartite entangled state. We proposed a scheme to calculate the quadripartite entanglement entropy on the square lattice, which is well described by a four-sites toy model and thus provides another way to identify the higher order topological insulators from the multipartite entanglement point of view.Comment: 5 pages, 3 figure

Kolmogorov's law of the iterated logarithm for noncommutative martingales

We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales. The commutative case was due to Stout. The key ingredient is an exponential inequality proved recently by Junge and the author.Comment: Revise

Revisit the Concept of PEKS: Problems and a Possible Solution

Since Boneh et al. propose the concept, non-interactive\ud Public-key Encryption with Keyword Search (PEKS) has attracted lots of attention from cryptographers. Non-interactive PEKS enables a third party to test whether or not a tag, generated by the message sender, and a trapdoor, generated by the receiver, contain the same keyword without revealing further information. In this paper we investigate a non-interactive PEKS application proposed by Boneh et al. and show our observations, especially that privacy is\ud not protected against a curious server. We propose the notion of interactive PEKS, which, in contrast to non-interactive PEKS, requires the tag to be generated interactively by the message sender and the receiver. For this new primitive, we identify two types of adversaries, namely a curious user and a curious server, and provide\ud security formulations for the desirable properties. We propose a construction for interactive PEKS and prove its security in the proposed security model