Symmetric Tensor Decomposition Description of Fermionic Many-Body Wavefunctions

The configuration interaction (CI) is a versatile wavefunction theory for interacting fermions but it involves an extremely long CI series. Using a symmetric tensor decomposition (STD) method, we convert the CI series into a compact and numerically tractable form. The converted series encompasses the Hartree-Fock state in the first term and rapidly converges to the full-CI state, as numerically tested using small molecules. Provided that the length of the STD-CI series grows only moderately with the increasing complexity of the system, the new method will serve as one of the alternative variational methods to achieve full-CI with enhanced practicability.Comment: 10 pages, 6 figure

対称テンソル分解によるフェルミ粒子系の波動関数の記述

学位の種別:課程博士University of Tokyo(東京大学

Discovery of X-ray polarization angle rotation in active galaxy Mrk 421

The magnetic field conditions in astrophysical relativistic jets can be probed by multiwavelength polarimetry, which has been recently extended to X-rays. For example, one can track how the magnetic field changes in the flow of the radiating particles by observing rotations of the electric vector position angle $\Psi$. Here we report the discovery of a $\Psi_{\mathrm x}$ rotation in the X-ray band in the blazar Mrk 421 at an average flux state. Across the 5 days of Imaging X-ray Polarimetry Explorer (IXPE) observations of 4-6 and 7-9 June 2022, $\Psi_{\mathrm x}$ rotated in total by $\geq360^\circ$. Over the two respective date ranges, we find constant, within uncertainties, rotation rates ($80 \pm 9$ and $91 \pm 8 ^\circ/\rm day$) and polarization degrees ($\Pi_{\mathrm x}=10\%\pm1\%$). Simulations of a random walk of the polarization vector indicate that it is unlikely that such rotation(s) are produced by a stochastic process. The X-ray emitting site does not completely overlap the radio/infrared/optical emission sites, as no similar rotation of $\Psi$ was observed in quasi-simultaneous data at longer wavelengths. We propose that the observed rotation was caused by a helical magnetic structure in the jet, illuminated in the X-rays by a localized shock propagating along this helix. The optically emitting region likely lies in a sheath surrounding an inner spine where the X-ray radiation is released

Magnetic Field Properties inside the Jet of Mrk 421: Multiwavelength Polarimetry Including the Imaging X-ray Polarimetry Explorer

We conducted a polarimetry campaign from radio to X-ray wavelengths of the high-synchrotron-peak (HSP) blazar Mrk 421, including Imaging X-ray Polarimetry Explorer (IXPE) measurements on 2022 December 6-8. We detected X-ray polarization of Mrk 421 with a degree of $\Pi_{\rm X}$=14$\pm$1$\%$ and an electric-vector position angle $\psi_{\rm X}$=107$\pm$3$^{\circ}$ in the 2-8 keV band. From the time variability analysis, we find a significant episodic variation in $\psi_{\rm X}$. During 7 months from the first IXPE pointing of Mrk 421 in 2022 May, $\psi_{\rm X}$ varied across the range of 0$^{\circ}$ to 180$^{\circ}$, while $\Pi_{\rm X}$ maintained similar values within $\sim$10-15$\%$. Furthermore, a swing in $\psi_{\rm X}$ in 2022 June was accompanied by simultaneous spectral variations. The results of the multiwavelength polarimetry show that the X-ray polarization degree was generally $\sim$2-3 times greater than that at longer wavelengths, while the polarization angle fluctuated. Additionally, based on radio, infrared, and optical polarimetry, we find that rotation of $\psi$ occurred in the opposite direction with respect to the rotation of $\psi_{\rm X}$ over longer timescales at similar epochs. The polarization behavior observed across multiple wavelengths is consistent with previous IXPE findings for HSP blazars. This result favors the energy-stratified shock model developed to explain variable emission in relativistic jets. The accompanying spectral variation during the $\psi_{\rm X}$ rotation can be explained by a fluctuation in the physical conditions, e.g., in the energy distribution of relativistic electrons. The opposite rotation direction of $\psi$ between the X-ray and longer-wavelength polarization accentuates the conclusion that the X-ray emitting region is spatially separated from that at longer wavelengths.Comment: 17 pages, 13 figures, 4 tables; Accepted for publication in A&