Work Statistics and Energy Transitions in Driven Quantum Systems

Thermodynamic quantities of small systems fluctuate and have to be characterised by their appropriate probability distributions. Within the two-point energy measurement prescription, the distribution of work in a quantum system can be derived from the transition probability from initial to final energy. We consider a simple yet representative model system starting in thermodynamic equilibrium and driven by an external force, and compare two different numerical techniques to determine this transition probability with respect to accuracy and numerical effort. In addition, we perform a semi-classical analysis of the process using the WKB approximation. The results agree well with the numerically exact values if Airy-tails modelling the tunnelling into classically forbidden regions of phase space are properly taken into account.