"Get your conductivity the typical way"

 

 

Understanding transport and relaxation in quantum many-body systems is at the heart of many topics ranging from fundamental questions of thermalization to issues of novel devices design. I will provide insights which emerge from the new concept of quantum typical pure-state propagation as applied to the real-time dynamics of spin- and energy currents in quasi one-dimensional spin chain and ladder systems at finite temperature. It will be shown, that typicality is satisfied over a substantial range of temperatures, is fulfilled both, in integrable and nonintegrable systems, and significantly improves existing results from exact diagonalization, Lanczos, and time-dependent density matrix renormalization group. For the integrable case, the long-time dynamics of the spin currents and the spin Drude weight will be extracted beyond previously accessible combinations of system sizes and time domains. Strong evidence will be provided for the high-temperature Drude weight to vanishes at the isotropic point. For the nonintegrable cases, chains in staggered fields and spin ladders will be considered. I will discuss the relaxation curve of the energy current and determine the heat conductivity as a function of magnetic field, exchange anisotropy, and temperature. For the spin ladder a comprehensive picture of the thermal conductivity over the entire range from weak to strong rung coupling will be provided.

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