Fourier Analysis of the Parametric Resonance of the Neutrino Oscillation in the Presence of Inhomogeneous Matter

Parametric Resonance in Neutrino Oscillation: A Guide to Control the Effects of Inhomogeneous Matter Density

Effects of the inhomogeneous matter density on the three-generation neutrino oscillation probability are analyzed. Realistic profile of the matter density is expanded into a Fourier series. Taking in the Fourier modes one by one, we demonstrate that each mode has its corresponding target energy. The high Fourier mode selectively modifies the oscillation probability of the low-energy region. This rule is well described by the parametric resonance between the neutrino oscillation and the matter effect. The Fourier analysis gives a simple guideline to systematically control the uncertainty of the…

Fourier Analysis of the Parametric Resonance in Neutrino Oscillations

Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscilla…

Parametric resonance after hilltop inflation caused by an inhomogeneous inflaton field

We study preheating after hilltop inflation where the inflaton couples to another scalar field, e.g. a right-handed sneutrino, which provides a mechanism for generating the correct initial conditions for inflation and also a decay channel for the inflaton that allows for reheating and non-thermal leptogenesis. In the presence of such a coupling, we find that after the phases of tachyonic preheating and tachyonic oscillations, during which the inflaton field becomes inhomogeneous, there can be a subsequent preheating phase where the fluctuations of the other field get resonantly enhanced, from …

从有限 Fourier 信息对部分子分布进行简单的非参数重建

A simple non-parametric reconstruction of parton distributions from limited Fourier information

针对第一性原理计算中部分子分布仅有有限 Fourier 模的问题，本文提出以 Gaussian process 为 Bayesian 先验的非参数逆积分重建方法，并通过物理方式确定超参数。

Reheating in the Presence of Inhomogeneous Noise

Explosive particle production due to parametric resonance is a crucial feature of reheating in an inflationary cosmology. Coherent oscillations of the inflaton field lead to a periodically varying mass in the evolution equation of matter and gravitational fluctuations and often induce a parametric resonance instability. In a previous paper (hep-ph/9709273) it was shown that homogeneous (i.e. space independent) noise leads to an increase of the generalized Floquet exponent for all modes, at least if the noise is temporally uncorrelated. Here we extend the results to the physically more realisti…

The Lame equation in parametric resonance after inflation

We show that the most general inflaton potential in Minkowski spacetime for which the differential equation for the Fourier modes of the matter fields reduces to Lamé's equation is of the form $V(ϕ)= λϕ^4/4+Kϕ^2/2+μ/(2ϕ^2)+V_0$. As an application, we study the preheating phase after inflation for the above potential with K=0 and arbitrary $λ,μ>0$. For certain values of the coupling constant between the inflaton and the matter fields, we calculate the instability intervals and the characteristic exponents in closed form.