Time reversal symmetry in time-dependent correlation functions for systems in a constant magnetic field

A generalised time reversal symmetry for systems subject to a constant magnetic field is introduced, based on the analogy between the evolution equations of these systems and those of a system subject to shear. This generalisation makes it possible to derive symmetry relations for time correlation functions that do not require to change the sign of the magnetic field upon time reversal. This is to be contrasted with the standard Kubo result in which the sign of the magnetic field does change, thus establishing a symmetry relation between two distinct physical situations. Our result implies, for example, that Onsager-Casimir relations may be replaced by Onsager reciprocal relations even in the presence of a constant magnetic field. It is also of practical importance to interpret experiments and numerical simulations in which the systems considered are in a single magnetic field. Copyright (C) EPLA, 2014