Quantum Fluctuation Relations for the Lindblad Master Equation

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula

EXPERIMENTAL-DETERMINATION OF THE ENERGY GENERATED IN NUCLEAR CASCADES BY A HIGH-ENERGY BEAM

An already existing, sub-critical arrangement made of natural uranium and water moderator has been exposed to a low intensity (approximate to 10(9) ppp) proton beam from CERN-PS at several kinetic energies from 600 MeV to 2.75 GeV. The energy delivered by the hadronic cascade induced by the beam in the device has been measured by the temperature rise of small sampling blocks of uranium located in several different positions inside the device and counting the fissions in thin probe foils of natural uranium. We find typically G approximate to 30 in reasonable agreement with calculations, where G is the ratio of the energy produced in the device to the energy delivered by the beam. This result opens the way to the realisation of the so-called Energy Amplifier, a practical device to produce energy from thorium or depleted uranium targets exposed to an intense high energy proton beam. Results show that the optimal kinetic energy is greater than or equal to 1 GeV, below which G decreases but is still acceptable in the energy range explored