Adiabatic vs Sudden Flux Insertion and Nonlinear Electric Conduction

Masaki Oshikawa

ISSP, University of Tokyo



The adiabatic insertion of the magnetic flux can be regarded as an
application of an infinitesimal uniform electric field over a long period of time. This can induce a “persistent current” which does not decay in the ideal limit. The coefficient of proportionality is called Drude weight. On the other hand, we can consider the limit of instantaneous flux insertion,
which produces a delta-function pulse of the electric field. This may be also regarded as a particular type of a quantum quench process. These two limits are quite different but still share many topological properties in common. By considering these two limits, we can understand the Kohn formula for the Drude weight  and the f-sum rule of  the
AC conductivity in a unified manner. Furthermore, both the Kohn formula and the f-sum rule can be naturally extended to nonlinear electric conduction at all orders.

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