Applicability of the Friedberg-Lee-Zhao method

Friedberg, Lee and Zhao proposed a method for effectively evaluating the eigenenergies and eigen wavefunctions of quantum systems. In this work, we study several special cases to investigate applicability of the method. Concretely, we calculate the ground-state eigenenergy of the Hellmann potential as well as the Cornell potential, and also evaluate the energies of the systems where linear term is added to the Coulomb and harmonic oscillator potentials as a perturbation. The results obtained in this method have a surprising agreement with the traditional method or the numerical results. Since the results in this method have obvious analyticity compared to that in other methods, and because of the simplicity for calculations this method can be applied to solving the Schr\"{o}dinger equation and provides us better understanding of the physical essence of the concerned systems. But meanwhile applications of the FLZ method are restricted at present, especially for certain potential forms, but due to its obvious advantages, it should be further developed.Comment: 14 pages,no figure

Iterative time-domain method for resolving multiple gravitational wave sources in Pulsar Timing Array data

The sensitivity of ongoing searches for gravitational wave (GW) sources in the ultra-low frequency regime ($10^{-9}$~Hz to $10^{-7}$~Hz) using Pulsar Timing Arrays (PTAs) will continue to increase in the future as more well-timed pulsars are added to the arrays. It is expected that next-generation radio telescopes, namely, the Five-hundred-meter Aperture Spherical radio Telescope (FAST) and the Square Kilometer Array (SKA), will grow the number of well-timed pulsars to $O(10^3)$. The higher sensitivity will result in greater distance reach for GW sources, uncovering multiple resolvable GW sources in addition to an unresolved population. Data analysis techniques are, therefore, required that can search for and resolve multiple signals present simultaneously in PTA data. The multisource resolution problem in PTA data analysis poses a unique set of challenges such as non-uniformly sampled data, a large number of so-called pulsar phase parameters, and poor separation of signals in the Fourier domain due to a small number of cycles in the observed waveforms. We present a method that can address these challenges and demonstrate its performance on simulated data from PTAs with $10^2$ to $10^3$ pulsars. The method estimates and subtracts sources from the data iteratively using multiple stages of refinement, followed by a cross-validation step to mitigate spurious identified sources. The performance of the method compares favorably with the global fit approaches that have been proposed so far.Comment: 15 pages, 8 figure

Liquid Metal-Enabled Filtering Switches and Switchplexers

The via-pad-slot (VPS) structure, as the switchable element, has been used to demonstrate a single-pole-triple-throw (SPTT) filtering switch and a switchplexer. The VPS can be flexibily switched using liquid metal (LM) or high dielectric constant materials to either cover or uncover the slot. Since the LM only moves on the surface of the VPS and the substrate-integrated waveguide (SIW), the implementation and actuation of the LM is simple and does not cause excessive loss on the device. In the switchplexer design, all channels can be switched on and off to form filters or multiplexers of various channel combinations. Additional transmission zeros (TZs) can be generated by the loaded, partially switched-off channel. The generation of the TZs was discussed and analyzed using coupling matrix approach. The demonstrated &lt;italic&gt;X&lt;/italic&gt;-band (9.56&amp;#x2013;10.44 GHz) cross-shaped SPTT fifth-order filtering switch exhibits a suppression level of better than 40 dB at 8 and 12 GHz, an insertion loss (IL) of 1.55 dB at 10 GHz, and an isolation level of 58 dB at 10 GHz. The &lt;italic&gt;X&lt;/italic&gt;-band switchplexer operates at three frequency bands, e.g., 11.08&amp;#x2013;11.55 GHz, 10.61&amp;#x2013;10.99 GHz, and 9.76&amp;#x2013;10.33 GHz. The LM-enabled VPS-based switchable element can be integrated with other multifunctional circuits and systems for channel control and reconfiguration.</p