Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola-Kanai oscillator. The probability density of these coherent states for the Caldirola-Kanai oscillator converged to the center as time goes by, due to the damping constant γ . All the coherent state probability densities for the driven system are somewhat deformed.
The critical behaviour of wavefunctions at the Anderson metal-insulator vansition i s studied by numerical simulation, using as an aample of a system with a mobility edge a two-dimensional light-binding d e l with spin4rbit scattering. It is demonstrated that individual eigeNtal€S have mullifractal fluctuations of their pmtabilily density. The influence of these Ructualions on the two-pedicle mmlations b examined via dculalions of the wavevector and frequenq dependence of the dillksion mnstant 1. Jntmduction
The complex permeability spectra and the magnetoimpedance (MI) are measured as a function of torsional stress and torsion angle in Fe77.5Si7.5B15 amorphous wire. The permeability spectra show irreversible and reversible relaxation with relaxation frequencies of 40 and 300 kHz, respectively. The static permeability resulted from the irreversible magnetization decreases with torsion angle for a negative direction, but increases with a positive angle. The MI profile shows one symmetric peak for the positive torsion angle, which is same MI behavior as in the case of zero torsion. However, there is a hysteresis in the MI profile for negative torsion, that is, there are two asymmetric peaks for decreasing field and one peak for increasing field.
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