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We describe coupled electron-phonon systems semiclassically - Ehrenfestdynamics for the phonons and quantum mechanics for the electrons - using aclassical Monte Carlo approach that determines the nonequilibrium response to alarge pump field. The semiclassical approach is quite accurate, because thephonons are excited to average energies much higher than the phonon frequency,eliminating the need for a quantum description. The numerical efficiency ofthis method allows us to perform a self-consistent time evolution out to verylong times (tens of picoseconds) enabling us to model pump-probe experiments ofa charge density wave (CDW) material. Our system is a half-filled,one-dimensional (1D) Holstein chain that exhibits CDW ordering due to a Peierlstransition. The chain is subjected to a time-dependent electromagnetic pumpfield that excites it out of equilibrium, and then a second probe pulse isapplied after a time delay. By evolving the system to long times, we capturethe complete process of lattice excitation and subsequent relaxation to a newequilibrium, due to an exchange of energy between the electrons and thelattice, leading to lattice relaxation at finite temperatures. We employ anindirect (impulsive) driving mechanism of the lattice by the pump pulse due tothe driving of the electrons by the pump field. We identify two drivingregimes, where the pump can either cause small perturbations or completelyinvert the initial CDW order. Our work successfully describes the ringing ofthe amplitude mode in CDW systems that has long been seen in experiment, butnever successfully explained by microscopic theory.

Theoretical description of time-resolved photoemission in charge-density-wave materials out to long times