Motions of the String Solutions in the XXZ Spin Chain under a Varying Twist

We determine the motions of the roots of the Bethe ansatz equation for the ground state in the XXZ spin chain under a varying twist angle. This is done by analytic as well as numerical study at a finite size system. In the attractive critical regime $0< \Delta <1$, we reveal intriguing motions of strings due to the finite size corrections to the length of the strings: in the case of two-strings, the roots collide into the branch points perpendicularly to the imaginary axis, while in the case of three-strings, they fluctuate around the center of the string. These are successfully generalized to the case of $n$-string. These results are used to determine the final configuration of the momenta as well as that of the phase shift functions. We obtain these as well as the period and the Berry phase also in the regime $\Delta \leq -1$, establishing the continuity of the previous results at $-1 < \Delta < 0$ to this regime. We argue that the Berry phase can be used as a measure of the statistics of the quasiparticle ( or the bound state) involved in the process.Comment: An important reference is added and mentioned at the end of the tex

Left atrial extension of metastatic lung tumor via pulmonary vein: report on the first case of Ewing sarcoma

Extension of metastatic lung tumors into the left atrium via pulmonary veins is rare. Here, we report the first case of Ewing sarcoma exhibiting such extension. A 31-year-old man with pulmonary metastasis from Ewing sarcoma presented with a mass in the left lung, extending to the left atrium through the left inferior pulmonary vein. As the patient was considered to be at risk of tumor embolism, the mass was excised surgically

Spin hall effect associated with SU(2) gauge field

In this paper, we focus on the connection between spin Hall effect and spin force. Here we investigate that the spin force due to spin-orbit coupling, which in two-dimensional system is equivalent to forces of Hirsch and Chudnovsky besides constant factors 3 and 3/2 respectively, is a part of classic Anandan force, and that the spin Hall effect is an anomalous Hall effect. Furthermore, we develop the method of AC phase to derive the formula for the spin force, and find that the most basic spin Hall effect originates from the AC phase and is therefore an intrinsic quantum mechanical property of spin. This method differs from approach of Berry phase in the study of anomalous Hall effect, which is the intrinsic property of the perfect crystal. On the other hand, we use an elegant skill to show that the Chudnovsky-Drude model is reasonable, and further have improved the theoretical values of spin Hall conductivity of Chudnovsky. Compared to the theoretical values of spin Hall conductivity in the Chudnovsky-Drude model, ours are in better agreement with experimentation. Finally, we discuss the relation between spin Hall effect and fractional statistics.Comment: 16 pages, 5 figures, 1 tabl