Stochastic approach to non-equilibrium quantum spin systems

We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as averages over classical stochastic processes. We illustrate this approach for the quantum Ising model by extracting the Loschmidt amplitude and the magnetization dynamics from the numerical solution of stochastic differential equations. We show that dynamical quantum phase transitions following quantum quenches from the ferromagnetic ground state are accompanied by signatures in the classical distribution functions, including enhanced fluctuations. We demonstrate that the method is capable of handling integrable and non-integrable problems in a unified framework, including those in higher dimensions.