Time-Reversal Symmetry in Non-Hermitian Systems

For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys \Theta^2=-1, but no such a degeneracy exists when \Theta^2=+1. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when \Theta^2=+1. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.Comment: 40 pages, 2 figures; typos fixed, references adde

DEM slope-failure analysis of the Minami-Aso / Tateno area during the 2016 Kumamoto earthquakes

The Kumamoto earthquakes, which occurred on April 16, 2016, included deep large-scale landslides in the Minami-Aso village / Tateno area; the Aso Bridge collapsed completely because of this slope failure. Aso Bridge is considered to have collapsed for various reasons, e.g., fault displacements, earthquake accelerations, and landslide sediment depositions on the bridge. In this study, the possibility of landslide-sediment depositions on the bridge was assessed as a reason for the bridge collapse using the discrete element method (DEM), and the landslides at Aso Bridge were reproduced. An experiment and analysis were conducted on the large deformation of aluminum-bar laminated ground with wall movement, to confirm the applicability of DEM to large ground-deformation problems. Next, the Aso Bridge slope-failure analysis was carried out, based on different analysis conditions, and the sediment distribution was compared with field observation results from qualitative and quantitative viewpoints. It was concluded that sediment deposition on the bridge was not a cause of the Aso Bridge failure

Large deformation analysis of ground with wall movement or hallow foundation under extremely low confining pressure using PIV

Large-scale natural disasters have occurred frequently in recent years. In such disasters, large ground deformation has been a recurring phenomenon. As it directly affects the structure, has dureable design is necessitated to minimize the damages. Additionally, the fracture process zones are predicted using numerical analysis, and thereafter, the results of the analysis are validated after comparison with the experimental ones. In this study, image analysis is performed using particle image velocimetry (PIV), and subsequently, the analysis results are validated by the comparison. We herein aim to improve the precision of the image-analysis results, and examine the experimental or analytical condition of reproducing the deformation

Quantum scattering in one dimension

A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concept of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.Comment: 8 page

Symmetry-breaking and chaos in electron transport in semiconductor superlattices

We study the motion of electrons in a single miniband of a semiconductor superlattice driven by THz electric field polarized along the growth direction. We work in the semiclassical balance-equation model, including different elastic and inelastic scattering rates, and incorporating the self-consistent electric field generated by electron motion. We explore regions of complex dynamics, which can include chaotic behaviour and symmetry-breaking. We estimate the magnitudes of dc current and dc voltage that spontaneously appear in regions of broken-symmetry for parameters characteristic of modern semiconductor superlattices. This work complements PRL 80(1998)2669 [ cond-mat/9709026 ].Comment: 4 pages, 3 figures, RevTEX, EPS

Effect of nonlinearity on the dynamics of a particle in dc field-induced systems

Dynamics of a particle in a perfect chain with one nonlinear impurity and in a perfect nonlinear chain under the action of dc field is studied numerically. The nonlinearity appears due to the coupling of the electronic motion to optical oscillators which are treated in adiabatic approximation. We study for both the low and high values of field strength. Three different range of nonlinearity is obtained where the dynamics is different. In low and intermediate range of nonlinearity, it reduces the localization. In fact in the intermediate range subdiffusive behavior in the perfect nonlinear chain is obtained for a long time. In all the cases a critical value of nonlinear strength exists where self-trapping transition takes place. This critical value depends on the system and the field strength. Beyond the self-trapping transition nonlinearity enhances the localization.Comment: 9 pages, Revtex, 6 ps figures include

Electronic Structure of Three-Dimensional Superlattices Subject to Tilted Magnetic Fields

Full quantum-mechanical description of electrons moving in 3D structures with unidirectional periodic modulation subject to tilted magnetic fields requires an extensive numerical calculation. To understand magneto-oscillations in such systems it is in many cases sufficient to use the quasi-classical approach, in which the zero-magnetic-field Fermi surface is considered as a magnetic-field-independent rigid body in k-space and periods of oscillations are related to extremal cross-sections of the Fermi surface cut by planes perpendicular to the magnetic-field direction. We point out cases where the quasi-classical treatment fails and propose a simple tight-binding fully-quantum-mechanical model of the superlattice electronic structure.Comment: 8 pages, 7 figures, RevTex, submitted to Phys. Rev.

Dynamical Instabilities and Deterministic Chaos in Ballistic Electron Motion in Semiconductor Superlattices

We consider the motion of ballistic electrons within a superlattice miniband under the influence of an alternating electric field. We show that the interaction of electrons with the self-consistent electromagnetic field generated by the electron current may lead to the transition from regular to chaotic dynamics. We estimate the conditions for the experimental observation of this deterministic chaos and discuss the similarities of the superlattice system with the other condensed matter and quantum optical systems.Comment: 6 pages, RevTEX; 4 fig

Terahertz superlattice parametric oscillator

We report a GaAs/AlAs superlattice parametric oscillator. It was pumped by a microwave field (power few mW) and produced 3rd harmonic radiation (frequency near 300 GHz). The nonlinearity of the active superlattice was due to Bragg reflections of conduction electrons at the superlattice planes. A theory of the nonlinearity indicates that parametric oscillation should be possible up to frequencies above 10 THz. The active superlattice may be the object of further studies of predicted extraordinary nonlinearities for THz fields.Comment: 10 pages, 4 figure