The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter

Understand

We study the statistics of the work done on a quantum critical system by quenching a control parameter in the Hamiltonian.

• We elucidate the relation between the probability distribution of the work and the Loschmidt echo, a quantity emerging usually in the context of dephasing.
• Using this connection we characterize the statistics of the work done on a quantum Ising chain by quenching locally or globally the transverse field.
• We show that for local quenches starting at criticality the probability distribution of the work displays an interesting edge singularity.