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Due to experiments in cold-atom gases, the problem of quenched dynamics i.e, the time evolution of interacting systems arising due to sudden change in system parameters has become a topic of great current interest. I will present results for the time-evolution of some 1-dimensional models for an initial state corresponding to a spatially inhomogeneous domain wall pattern. First I will present results for the exactly solvable XX-spin chain with the z-component of spins initially arranged in a domain wall profile. Here we will find that at long times even though the magnetization has locally vanished to zero, the transverse spin correlation function does not reach the ground state value, but instead acquires a spatially oscillating form with the wavelength of the oscillation related in a simple way to the initial domain wall profile. I will show that this state corresponds to a nonequilbrium steady state where a net current flows between the regions of positive and negative magnetization at the two extremes of the chain. Following this I will present results for the quantum sine-Gordon model for an initial domain wall density profile. Here too results will be presented for the time-evolution of the density, current and various two-point correlation functions. The results for the sine-Gordon model will be obtained in two complementary ways. One is by using the semiclassical Truncated Wigner Approximation and the second is by doing Keldysh perturbation theory in the back-scattering term.
This work has been done in collaboration with Jarrett Lancaster (NYU) and Emanuel Gull (Columbia University) and has been supported by NSF-DMR.
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