Exact results for time evolution of a many-body quantum system (a transverse field Ising spin chain) under the action of several pulses of an external field are obtained. Unlike the situation with a single pulse, the magnetization depends on time for the sequence of two pulses. For the two-pulse case the magnetization does not depend on the value of the time spacing between pulses, in sharp contrast with the standard spin echo cases. Modulated oscillations of magnetization with time do not decay if the energy of eigenstates of the system before pulses is $k$ independent $(k$ is the quasimomentum), while for $k$-dependent initial eigenstates the modulated oscillations of magnetization decay (without inclusion of the “external” relaxation) to the steady-state value, depending on the parameters of pulses; i.e., the oscillations reveal time irreversibility.

• Received 11 March 2018
• Revised 13 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.054414