arXiv subjects

Xingpao Suo

Publications and source records attributed to Xingpao Suo.

4 recordsLinked to original sources

arXiv2025

Hamiltonian with Energy Levels Corresponding to Riemann Zeros

A Hamiltonian with eigenenergy $ E_n = ρ_n(1 - ρ_n) $ has been constructed, where $ ρ_n $ denotes the $ n $-th non-trivial zero of the Riemann zeta function. To construct such a Hamiltonian, we generalize the Berry-Keating paradigm and encode number-theoretic information into the Hamiltonian using modular forms.Although our construction does not resolve the Hilbert-Pólya conjecture (since the eigenstates corresponding to $ E_n $ are \emph{not} normalizable), it provides a novel physical perspective on the Riemann Hypothesis (RH). In particular, we propose a physical interpretation of RH, which could offer a potential pathway toward its proof.

quant-ph↗

arXiv2023

A new type of window functions constructed with exponential function

The Discrete Fourier Transform (DFT) is widely utilized for signal analysis but is plagued by spectral leakage, leading to inaccuracies in signal approximation. Window functions play a crucial role in mitigating spectral leakage by providing weighting mechanisms for discrete signals. In this paper, we introduce a novel window type based on exponential function, allowing for adjustable parameters and diverse variations. We present the formulation, properties, and motivation behind the design of the new window functions. Additionally, we analyze their behavior and evaluate their performance by comparing them with mainstream window functions using six parameters. Our findings demonstrate that these new window functions exhibit outstanding flexibility and versatility in signal analysis.

eess.SP↗

arXiv2023

Relieving the $S_8$ Tension: Exploring the Surface-type DBI Model as a Dark Matter Paradigm

Recent observations from weak gravitational lensing (WL) surveys indicate a smoother Universe compared to the predictions of the Cosmic Microwave Background (CMB). This inconsistency is commonly referred to as the $σ_8$ tension or $S_8$ tension, where $σ_8$ represents the present root-mean-square matter fluctuation averaged over a sphere of radius $8 h^{-1} \mathrm{Mpc}$, and $S_8 \equiv σ_8\sqrt{Ω_m/0.3}$. In this article, we investigate a kind of general Dirac-Born-Infeld (DBI) Lagrangian referred to as \textit{surface-type DBI} (sDBI) model. We find that up to the linear order, the constraints on the sDBI model with high-redshift probe (CMB) and low-redshift probes (WL and Galaxy Clustering, GC) yield $S_8= 0.7448_{-0.21}^{+0.031}$ and $0.7426_{-0.085}^{+0.054}$, respectively. Remarkably, these values not only demonstrate self-consistency but also align with the values obtained from the majority of low-redshift probes. Furthermore, we present a discussion on exploring the non-linear effects of this model, which holds the potential to address additional challenges associated with Cold Dark Matter (CDM) on small scales.

astro-ph.CO↗

arXiv2023

The spherical Fast Multipole Method (sFMM) for Gravitational Lensing Simulation

In this paper, we present a spherical Fast Multipole Method (sFMM) for ray tracing simulation of gravitational lensing (GL) on a curved sky. The sFMM is a non-trivial extension of the Fast Multiple Method (FMM) to sphere $\mathbb S^2$, and it can accurately solve the Poisson equation with time complexity of $O(N)\log(N)$, where $N$ is the number of particles. It is found that the time complexity of the sFMM is near $O(N)$ and the computational accuracy can reach $10^{-10}$ in our test. In addition, compared with the Fast Spherical Harmonic Transform (FSHT), the sFMM is not only faster but more accurate, as it has the ability to reserve high-frequency components of the density field. These merits make the sFMM an optimum method to simulate the gravitational lensing on a curved sky, which is the case for upcoming large-area sky surveys, such as the Vera Rubin Observatory and the China Space Station Telescope.

astro-ph.IM↗