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Tao Ma

Publications and source records attributed to Tao Ma.

71 records · Page 4Linked to original sources
arXiv2013

Cosmogenic Nuclei Production Rate on the Lunar Surface

A physical model of Geant4-based simulation of galactic cosmic ray (GCR) particles interaction with the lunar surface matter has been developed to investigate the production rate of cosmogenic nuclei. In this model the GCRs, mainly very high energy protons and $α$ particles, bombard the surface of the Moon and produce many secondary particles such as protons and neutrons. The energies of proton and neutron at different depths are recorded and saved into ROOT files, and the analytical expressions for the differential proton and neutron fluxes are obtained through the best-fit procedure under the ROOT software. To test the validity of this model, we calculate the production rates of long-lived nuclei $^{10}$Be and $^{26}$Al in the Apollo 15 long drill core by combining the above differential fluxes and the newly evaluated spallation reaction cross sections. Numerical results show that the theoretical production rates agree quite well with the measured data. It means that this model works well. Therefore, it can be expected that this model can be used to investigate the cosmogenic nuclei in lunar samples returned by Chinese lunar exploration program and can be extended to study other objects, such as the meteorites and the Earth's atmosphere.

astro-ph.EP↗
arXiv2013

Spectral and Parametric Averaging for Integrable Systems

We analyze two theoretical approaches to ensemble averaging for integrable systems in quantum chaos - spectral averaging and parametric averaging. For spectral averaging, we introduce a new procedure - rescaled spectral averaging. Unlike traditional spectral averaging, it can describe the correlation function of spectral staircase and produce persistent oscillations of the interval level number variance. Parametric averaging, while not as accurate as rescaled spectral averaging for the correlation function of spectral staircase and interval level number variance, can also produce persistent oscillations of the global level number variance and better describes saturation level rigidity as a function of the running energy. Overall, it is the most reliable method for a wide range of statistics.

quant-ph↗
arXiv2013

Distribution of Human Response Times

We demonstrate that distributions of human response times have power-law tails and, among closed-form distributions, are best fit by the generalized inverse gamma distribution. We speculate that the task difficulty tracks the half-width of the distribution and show that it is related to the exponent of the power-law tail.

q-bio.NC↗
arXiv2013

A Model for Stock Returns and Volatility

We prove that Student's t-distribution provides one of the better fits to returns of S&P component stocks and the generalized inverse gamma distribution best fits VIX and VXO volatility data. We further argue that a more accurate measure of the volatility may be possible based on the fact that stock returns can be understood as the product distribution of the volatility and normal distributions. We find Brown noise in VIX and VXO time series and explain the mean and the variance of the relaxation times on approach to the steady-state distribution.

q-fin.ST↗
arXiv2013

Weighted variation inequalities for differential operators and singular integrals

We prove weighted strong $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators. For the first family of operators the weights used can be either Sawyer's one-sided $A^+_p$ weights or Muckenhoupt's $A_p$ weights according to that the differential operators in consideration are one-sided or symmetric. We use only Muckenhoupt's $A_p$ weights for the second family. All these inequalities hold equally in the vector-valued case, that is, for functions with values in $\el^ρ$ for $1<ρ<\infty$. As application, we show variation inequalities for mean bounded positive invertible operators on $L^p$ with positive inverses.

math.CA↗
arXiv2012

Regularity estimates in Hölder spaces for Schrödinger operators via a T1 theorem

We derive Hölder regularity estimates for operators associated with a time independent Schrödinger operator of the form $-Δ+V$. The results are obtained by checking a certain condition on the function $T1$. Our general method applies to get regularity estimates for maximal operators and square functions of the heat and Poisson semigroups, for Laplace transform type multipliers and also for Riesz transforms and negative powers $(-Δ+V)^{-γ/2}$, all of them in a unified way.

math.AP↗
arXiv2012

Distribution Of Wealth In A Network Model Of The Economy

We show, analytically and numerically, that wealth distribution in the Bouchaud-Mézard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any two agents linked, it reduces to the inverse gamma distribution.

q-fin.ST↗
arXiv2012

Global Level Number Variance in Integrable Systems

We study previously un-researched second order statistics - correlation function of spectral staircase and global level number variance - in generic integrable systems with no extra degeneracies. We show that the global level number variance oscillates persistently around the saturation spectral rigidity. Unlike other second order statistics - including correlation function of spectral staircase - which are calculated over energy scales much smaller than the running spectral energy, these oscillations cannot be explained within the diagonal approximation framework of the periodic orbit theory. We give detailed numerical illustration of our results using four integrable systems: rectangular billiard, modified Kepler problem, circular billiard and elliptic billiard.

quant-ph↗
arXiv2011

Regularity properties of Schrödinger operators

Let L be a Schrödinger operator of the form L=-Δ+V, where the nonnegative potential V satisfies a reverse Hölder inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted Hölder spaces. We give a pointwise description of L-Hölder spaces and provide some characterizations in terms of the growth of fractional derivatives of any order and Carleson measures. Applications to fractional powers of L and multipliers of Laplace transform type developed.

math.AP↗
arXiv2011

Elliptic billiard - a non-trivial integrable system

We investigate the semiclassical energy spectrum of quantum elliptic billiard. The nearest neighbor spacing distribution, level number variance and spectral rigidity support the notion that the elliptic billiard is a generic integrable system. However, second order statistics exhibit a novel property of long-range oscillations. Classical simulation shows that all the periodic orbits except two are not isolated. In Fourier analysis of the spectrum, all the peaks correspond to periodic orbits. The two isolated periodic orbits have small contribution to the fluctuation of level density, while non-isolated periodic orbits have the main contribution. The heights of the majority of the peaks match our semiclassical theory except for type-O periodic orbits. Elliptic billiard is a nontrivial integrable system that will enrich our understanding of integrable systems.

quant-ph↗
arXiv2010

Quantum mechanical calculation of spectral statistics of modified Kepler problem

Discrepancy between periodic orbit theory and numerical calculation of a modified Kepler problem is cleared by a quantum mechanical calculation. The diagonal approximation already gives a good fit for the numerical calculation. A better result yet is gained by considering the coherent interference between the classical periodic orbits and the Balian-Bloch term. This approach produces improved results for the rectangular billiards as well.

quant-ph↗
arXiv2010

Level Repulsion in Integrable Systems

Contrary to conventional wisdom, level repulsion in semiclassical spectrum is not just a feature of classically chaotic systems, but classically integrable systems as well. While in chaotic systems level repulsion develops on a scale of the mean level spacing, regardless of location in the spectrum, in integrable systems it develops on a much longer scale - geometric mean of the mean level spacing and the running energy in the spectrum. We show that at this scale level correlations in integrable systems have a universal dependence on level separation, as well as discuss their exact form at any scale. These correlations have dramatic consequences, including deviations from Poissonian statistics in the nearest level spacing distribution and persistent oscillations of level number variance as a function of the interval width. We illustrate our findings on two models - a rectangular infinite well and a modified Kepler problem - that serve as generic types of hard-wall billiards and potential problems. Our theory is based on the concept of parametric averaging, which allows for a statistical ensemble of integrable systems at a given spectral location (running energy).

quant-ph↗
arXiv2007

Exact solution of one class of Maryland model

The Hamiltonian H of one-body Maryland model is defined as the sum of a linear unperturbed Hamiltonian H_0 and the interaction V, which is a Toeplitz matrix. Maryland model with a doubly infinite Hilbert space are exactly solved. Special cases of one-body Maryland model include the original Maryland model (Phys. Rev. Lett. 49, 833 (1982) and Physica 10D, 369 (1984)), which describes a quantum kickied linear rotator and single band Bloch oscillations. Maryland model and single band Bloch oscillations are the same Hamiltonian in two different representations. A special case of many-body Maryland model is Luttinger model.

quant-ph↗
arXiv2007

Floquet system, Bloch oscillation, and Stark ladder

We prove the multi-band Bloch oscillation and Stark ladder in the $nk$ and site representation from the Floquet theorem. The proof is also possible from the equivalence between the Floquet system, Bloch oscillation, and the rotator with spin. We also exactly solve the periodically driven two level atom and two band Bloch oscillation in terms of Heun function.

cond-mat.other↗
arXiv2007

Localization and delocalization in the quantum kicked prime number rotator

The quantum kicked prime number rotator (QKPR) is defined as the rotator whose energy levels are prime numbers. The long time behavior is decided by the kick period $τ$ and kick strength $k$. When $\fracτ{2π}$ is irrational, QKPR is localized because of the equidistribution theorem. When $\fracτ{2π}$ is rational, QKPR is localized for small $k$, because the system seems like a generalized kicked dimer model. We argue for rational $\fracτ{2π}$ QKPR delocalizes for large k.

nlin.CD↗
arXiv2007

General Theory of the Quantum Kicked Rotator. I

This is the first of a series of two papers. We discuss some basic problems of the quantum kicked rotator (QKR) and review some important results in the literature. We point out the flaws in the inverse Cayley transform method to prove dynamic localization. When $τ/2π$, where $τ$ is the kick period, is very close to a rational number, the localization length is larger than the typical localization length. We analytically prove anomalous localization and confirm it by numerical calculations. We point out open problems that need further work.

nlin.CD↗