The effect of orbital damping during planet migration on the Inclination and Eccentricity Distributions of Neptune Trojans

We explore planetary migration scenarios for formation of high inclination Neptune Trojans (NTs) and how they are affected by the planetary migration of Neptune and Uranus. If Neptune and Uranus's eccentricity and inclination were damped during planetary migration, then their eccentricities and inclinations were higher prior and during migration than their current values. Using test particle integrations we study the stability of primordial NTs, objects that were initially Trojans with Neptune prior to migration. We also study Trans-Neptunian objects captured into resonance with Neptune and becoming NTs during planet migration. We find that most primordial NTs were unstable and lost if eccentricity and inclination damping took place during planetary migration. With damping, secular resonances with Neptune can increase a low eccentricity and inclination population of Trans-Neptunian objects increasing the probability that they are captured into 1:1 resonance with Neptune, becoming high inclination NTs. We suggest that the resonant trapping scenario is a promising and more effective mechanism explaining the origin of NTs that is particularly effective if Uranus and Neptune experienced eccentricity and inclination damping during planetary migration.Comment: 9 pages, 11 figures, accepted by MNRA

Coherence as a resource for source-independent quantum random-number generation

Measuring quantum states provides means to generate genuine random numbers. It has been shown that genuine randomness can be obtained even with an uncharacterized quantum source. In this work, we propose a framework that formalizes the idea of realizing source-independent quantum random number generation via measuring coherence. Without full state tomography, the coherence of the source can be estimated by coherence witnesses. The existing uncertainty-relation-based schemes can be treated as special cases under the coherence framework, as we design a nonlinear coherence witness that can essentially yield the same results. Meanwhile, we propose a source-independent random number generation scheme, which can achieve a higher randomness generation rate than the uncertainty-relation-based ones.Comment: 17 pages, 5 figure

Operational interpretation of coherence in quantum key distribution

Quantum coherence was recently formalized as a physical resource to measure the strength of superposition. Based on the resource theory, we present a systematic framework that connects a coherence measure to the security of quantum key distribution. By considering a generic entanglement-based key distribution protocol under the collective attack scenario, we show that the key rate can be quantified by the coherence of the shared bipartite states. This framework allows us to derive the key rate of the BB84 and six-state protocols. By utilizing fine-grained parameters, we also derive the improved key rates of both protocols within the coherence-based framework. Furthermore, we apply it to a practical issue, detection efficiency mismatch, and obtain an improved result. In conclusion, this framework demonstrates the interplay among coherence, entanglement, and quantum key distribution at a fundamental level.Comment: 22 pages, 4 figure

Quark-Lepton Nonuniversality

There is new experimental evidence which may be interpreted as a small departure from quark-lepton universality. We propose to understand this as the result of a hierarchy of mass scales in analogy to $m_u, m_d << \Lambda_{QCD}$ for strong isospin. We show $(G_F)^{NC}_{lq} < (G_F)^{CC}_{lq} < (G_F)^{CC}_{ll} < (G_F)^{NC}_{ll}$ in principle, but all are still approximately equal. New physics is predicted at the TeV scale.Comment: 3 pages, talk by E. Ma at XXIII ENFPC, Aguas de Lindoia, Brazil (Oct 2002

How to reach the orbital configuration of the inner three planets in HD 40307 Planet System ?

The formation of the present configuration of three hot super-Earths in the planet system HD 40307 is a challenge to dynamical astronomers. With the two successive period ratios both near and slightly larger than 2, the system may have evolved from pairwise 2:1 mean motion resonances (MMRs). In this paper, we investigate the evolutions of the period ratios of the three planets after the primordial gas disk was depleted. Three routines are found to probably result in the current configuration under tidal dissipation with the center star, they are: (i) through apsidal alignment only; (ii) out of pairwise 2:1 MMRs, then through apsidal alignment; (iii) out of the 4:2:1 Laplace Resonance (LR) , then through apsidal alignment. All the three scenarios require the initial eccentricities of planets $\sim0.15$, which implies a planetary scattering history during and after the gas disk was depleted. All the three routines will go through the apsidal alignment phase, and enter a state with near-zero eccentricities finally. We also find some special characteristics for each routine. If the system went through pairwise 2:1 MMRs at the beginning, the MMR of the outer two planets would be broken first to reach the current state. As for routine (iii), the planets would be out of the Laplace Resonance at the place where some high-order resonances are located. At the high-order resonances 17:8 or 32:15 of the planets c and d, the system will possibly enter the current state as the final equilibrium.Comment: 16 pages, 8 figures, Accepted by SCIENCE CHINA Physics, Mechanics & Astronom

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u=2(ln f)_x and u=2(ln f)_{xx}, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations

Puzzle of W Leptonic Decay Branching Fractions and Gauge Model of Generation Nonuniversality

Lepton generation universality holds very well in Z decays, but appears to be violated in recent LEP data of W leptonic decay branching fractions. If this trend persists, a consistent and natural explanation is a model of generation nonuniversality, based on the gauge group SU(2)_L X U(1)_R X U(1)_{B-L}.Comment: 16 pages, no figur

Gauge Model of Quark-Lepton Nonuniversality

We propose a gauge model where quark-lepton universality is an accidental symmetry which is only approximate, in analogy to the well-accepted notion that strong isospin is accidental and approximate. This is a natural framework for explaining possible small deviations of quark-lepton universality which is applicable to the recently reported apparent nonunitarity of the quark mixing matrix. As a result, small departures from quark-lepton universality are expected in Z decays as well as in the recent neutrino data of the NuTeV collaboration and in future low-energy experiments. New physics is predicted at the TeV scale.Comment: 11 pages, no figur

State-Augmentation Transformations for Risk-Sensitive Reinforcement Learning

In the framework of MDP, although the general reward function takes three arguments-current state, action, and successor state; it is often simplified to a function of two arguments-current state and action. The former is called a transition-based reward function, whereas the latter is called a state-based reward function. When the objective involves the expected cumulative reward only, this simplification works perfectly. However, when the objective is risk-sensitive, this simplification leads to an incorrect value. We present state-augmentation transformations (SATs), which preserve the reward sequences as well as the reward distributions and the optimal policy in risk-sensitive reinforcement learning. In risk-sensitive scenarios, firstly we prove that, for every MDP with a stochastic transition-based reward function, there exists an MDP with a deterministic state-based reward function, such that for any given (randomized) policy for the first MDP, there exists a corresponding policy for the second MDP, such that both Markov reward processes share the same reward sequence. Secondly we illustrate that two situations require the proposed SATs in an inventory control problem. One could be using Q-learning (or other learning methods) on MDPs with transition-based reward functions, and the other could be using methods, which are for the Markov processes with a deterministic state-based reward functions, on the Markov processes with general reward functions. We show the advantage of the SATs by considering Value-at-Risk as an example, which is a risk measure on the reward distribution instead of the measures (such as mean and variance) of the distribution. We illustrate the error in the reward distribution estimation from the direct use of Q-learning, and show how the SATs enable a variance formula to work on Markov processes with general reward functions

Entanglement Distribution in Star Network Based on Spin Chain in Diamond

Since star network of spins was proposed, generating entanglement directly through spin interactions between distant parties became much possible. We propose an architecture which involves coupled spin chains based on nitrogen-vacancy centers and nitrogen defect spins to expand star network, the numerical analysis shows that the length of spin chains $M$ and spin noise can determine the maximally achievable entanglement $E_m$. The entanglement capability of this configuration under effect of disorder and spin loss is also studied. Moreover, it is shown that with this kind of architecture, star network of spins is feasible in measurement of magnetic-field gradient.Comment: 5 pages, 8 figure