Wenyu Wang

A freely falling chain from a cup at a certain height can jump. The process can be divided into two parts: a stable suspension and an accelerating procedure. Variational principle and force analysis demonstrate that the shape of the stable suspension is an inverted catenary. The requirement of the jumping and the parameters to describe the jumping catenary have been studied in detail, and experiments have been conducted to verify the theoretical analysis. The physical picture of the falling chain could be useful in certain falling systems, providing valuable insights into the dynamical system.

Based on the relationship between proper distance and coordinate distance, the geometrical phenomenon caused by the passing gravitational waves can not be observed locally. The electromagnetic wave equations in the background gravitational waves are studied. We find that the expansion and contraction of wave lengths are always synchronous with the objects it measures. The background of the gravitational waves leads to dissipation and dispersion in the propagation of electromagnetic wave. The phase of the gravitational waves control the dissipation term and dispersion term in the telegrapher’s equation. The linearly polarized laser beam propagating in the direction of the incoming gravitational waves can give a possible measurement on the local metric. In case of the pulsed beats passing by, the relaxation time is greater than the period of the gravitational waves, thus the detector may only show a signal of the modulation of the beats. Finally we proposed a non-local interference experiment to detect the high-frequency gravitational waves. It is similar to the measurement of redshift caused by gravitation. Together with the ordinary detector, it will give us further and mutually measurements of the gravitational waves.

This paper commences with the Fermi's Golden Rule in quantum mechanics, employing concepts corresponding to quantum principles to elucidate fundamental notions in field theory such as particle decay widths and scattering cross-sections. It further establishes the intrinsic relationships among these concepts. By analyzing the transition rate under time-dependent perturbation theory, the physical meaning of the transition matrix element and density of states in decay and scattering processes is elucidated. Furthermore, this paper also shows the relativistically covariant formulas for decay width and scattering cross-section by using phase-space integral formulations. A simplified model, which describes interactions among three scalar particles, is constructed for a demonstration of particle decay and scattering in one-dimensional space. This approach intuitively reveals the kinematic and dynamic characteristics of particle scattering. It facilitates a natural transition for learner from quantum mechanics to the framework of quantum field theory, offering instructive insights for understanding collider physics.

In 1926, E.Schrödinger found an analytical solution for the time evolution of the one-dimensional harmonic oscillator Schrödinger Equation. This solution is not in the form of a summation of energy eigenstate wave functions, which provides a new perspective on the time evolution in quantum mechanics. This paper mainly analyzes this analytical time evolution solution and presents two derivation methods. Then the paper further generalizes to obtain more non-series analytical solutions for time evolution oscillator, and finds the recursive relation to obtain these analytical solutions. Finally, the educational significance and applications of these analytical solutions are discussed.

This article examines the resolution of a problem in thermodynamics and statistical physics, demonstrating the derivation of physical processes under the standard dimension analysis, and presenting results in a standard form. The paper provides a brief elucidation of the Π theorem and furnishes examples of dimensional analysis employing the Π theorem for physical systems. Given the significance of dimensional analysis in physics, it warrants ample emphasis in the instruction of foundational physics courses. Additionally, the appendix of the paper offers standard representations of formulas sourced from the sixth edition of “Thermodynamics and Statistical Physics” written by Wang Zhi-Cheng.

We examine the Sommerfeld enhancement effect for the puffy self-interacting dark matter. We find out two new parameters to classify the self-scattering cross section into the Born, the resonance and the classical regimes for the puffy dark matter. Then we observe that the resonance peaks for the puffy dark matter self-scattering and for the Sommerfeld enhancement effect have the same locations. Further, we find that for a large ratio between R _χ (radius of a puffy dark matter particle) and 1/m _ϕ (force range), the Sommerfeld enhancement factor approaches to 1 (no enhancement). Finally, for the puffy SIDM scenario to solve the small-scale problems, the values of the Sommerfeld enhancement factor are displayed in the allowed parameter regions.

In direct dark matter (DM) detection via scattering off the electrons, the momentum transfer plays a crucial role. Previous work showed that for self-interacting DM, if the DM particle has a size (the so-called puffy DM), the radius effect could dominate the momentum transfer and become another source of velocity dependence for self-scattering cross section. In this work we investigate the direct detection of puffy DM particles with different radii through electron recoil. We find that comparing with the available experimental exclusion limits dominated by the mediator effect for XENON10, XENON100 and XENON1T, the constraints on the puffy DM-electron scattering cross-section become much weaker for large radius DM particles. For small-radius DM particles, the constraints remain similar to the point-like DM case.

For the light relativistic dark matter (DM) boosted by high energy cosmic ray, its scattering cross section with the nucleon is sensitively dependent on the momentum-transfer and such an dependence is caused by the mediator in the scattering. For puffy DM particle with a size, the momentum-transfer dependence can also arise from the DM radius effect. All these momentum-transfer dependences should be considered. In this note we study the direct detection limits on the cosmic ray-boosted puffy DM for a simplified model with a light mediator. For comparison, we first re-derive the direct detection limits on the cosmic ray-boosted point-like DM. We display the limits on various planes of parameters and find that the limits for the cosmic ray-boosted puffy DM are stronger than for the point-like DM.