Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models

We introduce two generalizations of the Jaynes-Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes-Cummings interactions, while the second model is written as a simultaneous Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novelty problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.Comment: 16 page

Search for water in a super-Earth atmosphere: High-resolution optical spectroscopy of 55 Cancri e

We present the analysis of high-resolution optical spectra of four transits of 55Cnc e, a low-density, super-Earth that orbits a nearby Sun-like star in under 18 hours. The inferred bulk density of the planet implies a substantial envelope, which, according to mass-radius relationships, could be either a low-mass extended or a high-mass compact atmosphere. Our observations investigate the latter scenario, with water as the dominant species. We take advantage of the Doppler cross-correlation technique, high-spectral resolution and the large wavelength coverage of our observations to search for the signature of thousands of optical water absorption lines. Using our observations with HDS on the Subaru telescope and ESPaDOnS on the Canada-France-Hawaii Telescope, we are able to place a 3-sigma lower limit of 10 g/mol on the mean-molecular weight of 55Cnc e's water-rich (volume mixing ratio >10%), optically-thin atmosphere, which corresponds to an atmospheric scale-height of ~80 km. Our study marks the first high-spectral resolution search for water in a super-Earth atmosphere and demonstrates that it is possible to recover known water-vapour absorption signals, in a nearby super-Earth atmosphere, using high-resolution transit spectroscopy with current ground-based instruments.Comment: Accepted for publication in ApJ 12 pages, 9 figures. Email: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]

Blind Signal Detection in Massive MIMO: Exploiting the Channel Sparsity

In practical massive MIMO systems, a substantial portion of system resources are consumed to acquire channel state information (CSI), leading to a drastically lower system capacity compared with the ideal case where perfect CSI is available. In this paper, we show that the overhead for CSI acquisition can be largely compensated by the potential gain due to the sparsity of the massive MIMO channel in a certain transformed domain. To this end, we propose a novel blind detection scheme that simultaneously estimates the channel and data by factorizing the received signal matrix. We show that by exploiting the channel sparsity, our proposed scheme can achieve a DoF very close to the ideal case, provided that the channel is sufficiently sparse. Specifically, the achievable degree of freedom (DoF) has a fractional gap of only $1/T$ from the ideal DoF, where $T$ is the channel coherence time. This is a remarkable advance for understanding the performance limit of the massive MIMO system. We further show that the performance advantage of our proposed scheme in the asymptotic SNR regime carries over to the practical SNR regime. Numerical results demonstrate that our proposed scheme significantly outperforms its counterpart schemes in the practical SNR regime under various system configurations.Comment: 32 pages, 9 figures, submitted to IEEE Trans. Commu

Space and time inversions of stochastic processes and Kelvin transform

Let $X$ be a standard Markov process. We prove that a space inversion property of $X$ implies the existence of a Kelvin transform of $X$-harmonic, excessive and operator-harmonic functions and that the inversion property is inherited by Doob $h$-transforms. We determine new classes of processes having space inversion properties amongst transient processes {satisfying the} time inversion property. {For these processes, some explicit inversions, which are often not the spherical ones, and excessive functions are given explicitly.} We treat in details the examples of free scaled power Bessel processes, non-colliding Bessel particles, Wishart processes, Gaussian Ensemble and Dyson Brownian Motion

Boundedness of stable solutions to semilinear elliptic equations: a survey

This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known $L^{\infty}$ estimates that hold for all nonlinearities. Such estimates are known to hold up to dimension 4. They are expected to be true also in dimensions 5 to 9, but this is still an open problem which has only been established in the radial case

A cosmologically motivated reference formulation of numerical relativity

The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as possible, we investigate a novel formulation of Einstein's equations. This formulation evolves differences from a "reference" solution describing the dominant behavior of the spacetime, which mitigates error due to both truncation and approximate finite difference calculations. We find that the error in solutions obtained using the reference formulation can be smaller by an order of magnitude or more, with the level of improvement depending on how well the reference solution approximates the exact solution.Comment: 15 pages, 5 figures, planning to submit to CQ

A new method of joint nonparametric estimation of probability density and its support

In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density is not the whole real line. To avoid the unknown boundary effects, our estimator detects the boundary, and eliminates the boundary-bias of the estimator simultaneously. Moreover, we refer an extension to a simple multivariate case, and propose an improved estimator free from the unknown boundary bias

Global Phase Diagram of Disordered Type-II Weyl Semimetals

With electron and hole pockets touching at the Weyl node, type-II Weyl semimetal is a newly proposed topological state distinct from its type-I cousin. We numerically study the localization effect for tilted type-I as well as type-II Weyl semimetals and give the global phase diagram. For dis- ordered type-I Weyl semimetal, an intermediate three-dimensional quantum anomalous Hall phase is confirmed between Weyl semimetal phase and diffusive metal phase. However, this intermediate phase is absent for disordered type-II Weyl semimetal. Besides, near the Weyl nodes, comparing to its type-I cousin, type-II Weyl semimetal possesses even larger ratio between the transport lifetime along the direction of tilt and the quantum lifetime. Near the phase boundary between the type-I and the type-II Weyl semimetals, infinitesimal disorder will induce an insulating phase so that in this region, the concept of Weyl semimetal is meaningless for real materials.Comment: 7 pages, 5 figure

Quasinormal modes as a distinguisher between general relativity and f(R) gravity

Quasi-Normal Modes (QNM) or ringdown phase of gravitational waves provide critical information about the structure of compact objects like Black Holes. Thus, QNMs can be a tool to test General Relativity (GR) and possible deviations from it. In the case of GR, it is known for a long time that a relation between two types of Black Hole perturbations: scalar (Zerilli) and vector (Regge-Wheeler), leads to an equal share of emitted gravitational energy. With the direct detection of Gravitational waves, it is now natural to ask: whether the same relation (between scalar and vector perturbations) holds for modified gravity theories? If not, whether one can use this as a way to probe deviations from General Relativity. As a first step, we show explicitly that the above relation between Regge-Wheeler and Zerilli breaks down for a general f (R) model, and hence the two perturbations do not share equal amounts of emitted gravitational energy. We discuss the implication of this imbalance on observations and the no-hair conjecture.Comment: 9 pages, 2 figures, version as accepted in Physical Review

How Wave - Wavelet Trading Wins and "Beats" the Market

The purpose of this paper is to showcase trading strategies that give solutions to three difficult and intriguing problems in business finance, economics and statistics. The paper discusses trading strategies for both commodities and stocks but the main focus is on stock market trading at the New York Stock Exchange. Problem 1: Buy Low and Sell High. The buy low and sell high problem can be summarized like this: suppose the price of a commodity or stock fluctuates indefinitely, is there any explicit strategy for a trader to "ride the price waves" by buying low and selling high to eventually win even if price does not increase? Problem 2: "Beat" the Market. In Part 2, the trading system presented in Part 1 is transformed into a strategy that always outperforms the market eventually. Problem 3: Can a Trader Outperform a geometric Brownian Motion? The general belief is that it is impossible to "beat" a GBM since technical analysis of historical prices is useless in predicting future prices. The last part of the paper shows that the answer to Problem 3 is actually a "YES", which is quite surprising. The trading strategies presented are based mainly on information obtained from the movements of waves and wavelets created by large and small fluctuations of market prices. They do not involve any forecasting or prediction of future prices. Behavioral economics also plays a role in the decision making process of the Wavelet Trading program. My website AgateTrading.com is available to the public