Electric circuit networks equivalent to chaotic quantum billiards

We formulate two types of electric RLC resonance network equivalent to quantum billiards. In the network of inductors grounded by capacitors squared resonant frequencies are eigenvalues of the quantum billiard. In the network of capacitors grounded by inductors squared resonant frequencies are given by inverse eigen values of the billiard. In both cases local voltages play role of the wave function of the quantum billiard. However as different from quantum billiards there is a heat power because of resistance of the inductors. In the equivalent chaotic billiards we derive the distribution of the heat power which well describes numerical statistics.Comment: 9 pages, 7 figure

Thermo-optic hysteresis with bound states in the continuum

We consider thermo-optic hysteresis in a silicon structure supporting bound state in the continuum. Taking into account radiative heat transfer as a major cooling mechanism we constructed a non-linear model describing the optical response. It is shown that the thermo-optic hysteresis can be obtained with low intensities of incident light $I_0\approx 1~\rm{W/m^2}$ at the red edge of the visible under the critical coupling condition

Effect of Quadratic Zeeman Energy on the Vortex of Spinor Bose-Einstein Condensates

The spinor Bose-Einstein condensate of atomic gases has been experimentally realized by a number of groups. Further, theoretical proposals of the possible vortex states have been sugessted. This paper studies the effects of the quadratic Zeeman energy on the vortex states. This energy was ignored in previous theoretical studies, although it exists in experimental systems. We present phase diagrams of various vortex states taking into account the quadratic Zeeman energy. The vortex states are calculated by the Gross-Pitaevskii equations. Several new kinds of vortex states are found. It is also found that the quadratic Zeeman energy affects the direction of total magnetization and causes a significant change in the phase diagrams.Comment: 6 pages, 5 figures. Published in J. Phys. Soc. Jp

Bound states in the continuum in open Aharonov-Bohm rings

Using formalism of effective Hamiltonian we consider bound states in continuum (BIC). They are those eigen states of non-hermitian effective Hamiltonian which have real eigen values. It is shown that BICs are orthogonal to open channels of the leads, i.e. disconnected from the continuum. As a result BICs can be superposed to transport solution with arbitrary coefficient and exist in propagation band. The one-dimensional Aharonov-Bohm rings that are opened by attaching single-channel leads to them allow exact consideration of BICs. BICs occur at discrete values of energy and magnetic flux however it's realization strongly depend on a way to the BIC's point.Comment: 5 pgaes, 4 figure

Fast linear algebra is stable

In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of $n$-by-$n$ matrices can be done by any algorithm in $O(n^{\omega + \eta})$ operations for any $\eta > 0$, then it can be done stably in $O(n^{\omega + \eta})$ operations for any $\eta > 0$. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in $O(n^{\omega + \eta})$ operations.Comment: 26 pages; final version; to appear in Numerische Mathemati

Weak localization in ferromagnets with spin-orbit interaction

Weak localization corrections to conductivity of ferromagnetic systems are studied theoretically in the case when spin-orbit interaction plays a significant role. Two cases are analyzed in detail: (i) the case when the spin-orbit interaction is due to scattering from impurities, and (ii) the case when the spin-orbit interaction results from reduced dimensionality of the system and is of the Bychkov-Rashba type. Results of the analysis show that the localization corrections to conductivity of ferromagnetic metals lead to a negative magnetoresistance -- also in the presence of the spin-orbit scattering. Positive magnetoresistance due to weak antilocalization, typical of nonmagnetic systems, does not occur in ferromagnetic systems. In the case of two-dimensional ferromagnets, the quantum corrections depend on the magnetization orientation with respect to the plane of the system.Comment: 14 pages with 10 figures, corrected and extended version, Sec.7 adde