Dynamic and ergodic properties of an impurity in a harmonic-oscillator chain

A. O. García Rodríguez, G. G. Cabrera

孝 利根川

James T. Hynes, Raymond Kapral, Michael C. Weinberg

M. Howard Lee, J. Florencio, J. M. Hong

There is an exact equivalence in the time-dependent behaviour of a zero-temperature two-dimensional interacting electron gas at long wavelengths and a classical harmonic oscillator chain with one impurity mass. The mass difference m-m 0 , where m 0 is the impurity mass, acts as the electron-electron interaction. Time evolution is asymmetric in m-m 0 about m=m 0 .

Surajit Sen

Relaxation phenomena in a class of nondissipative systems with two highly disparate time scales (i.e., Brownian systems) have unique commonalities quantifiable via two scalars. It is shown that the exactly solvable problem of the dynamics of a weakly linked impurity spin in a s=1/2 XY chain belongs to this dynamical universality class and so does that of a heavy mass in an infinite harmonic oscillator chain and a spinless quasi two-dimensional attractive Fermi gas in the long-wavelength limit. The case of the strongly linked impurity in the XY chain is also discussed along with the corresponding limits in the harmonic oscillator chain and the electron-gas problems. \textcopyright{} 1996 The American Physical Society.

A. O. García Rodríguez, G. G. Cabrera

We test the time evolution of quite general initial states in a model that is exactly solvable, $i.e.$ a semi-infinite $XY$ spin chain with an impurity at the boundary. The dynamics is portrayed through the observation of the site magnetization along the chain, focusing on the long-time behavior of the magnetization, which is estimated using the stationary phase method. Localized states are split off from the continuum for some regions of the impurity parameter space. Bound states are essential for the non-ergodic behavior reported here. When two impurity states exist, the quantum interference between them leads to magnetization oscillations which settle over very long times with the absence of damping. The frequency of the remanent oscillation is recognized as being the Rabi frequency of the localized levels.