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We consider an adiabatic Landau-Zener model of two-level system diagonally coupled to an Ohmic bosonic bath of large spectral width and derive through fermionization its exact solution at a special value of the coupling constant. From this solution we obtain the characteristic function of the distribution of energy transferred to the bath during the evolution of the system ground state as a functional determinant of a single particle operator. At zero temperature this distribution is further found to be exponential and at finite temperature the first three moments of the distribution are calculated.

Statistics of heat generated in a solvable dissipative Landau-Zener model