Quantum Theory of an Electron in a Uniform Time Dependent Field

Ayan Pal, Erik G. C. P. van Loon, F. Aryasetiawan

Nonequilibrium quantum physics greatly simplifies in the case of time-periodic Hamiltonians, since Floquet theory provides an analog to Bloch's theorem in the time domain. Still, the formal properties of Floquet many-body theory remain underexplored. Here, we study what happens to the uniform electron gas when a space-time periodic potential of arbitrary strength is applied, which leads to band splitting. The case of a potential traveling at constant speed is special, since the problem can be made time independent by transforming to a comoving frame. We perform linear-response theory, in the sense that we apply an additional perturbatively small but nonperiodic probing field, for which we illustrate the analogy of Fermi's golden rule and the photoemission spectrum of a many-electron system. As in the equilibrium case, the latter is related to the spectral function which is positive definite. We also analyze the parameter dependence of the controllable photoemission spectra by virtue of Floquet-Bloch engineering.

Frank Großmann

S V Mousavi, M Golshani

The de Broglie–Bohm interpretation of quantum mechanics with and without spin-dependence is used to determine electron trajectories, arrival-time distribution of electrons and the mean arrival time of spin-1/2 particles (including electrons) in the presence of a uniform field and a barrier separately. The difference for the mean arrival times, which are calculated with different guidance equations, is examined versus mass of the arriving particle and versus group velocity of the arriving electron wave packet and also versus the width of the barrier. Numerical calculations show that these differences are of the order of 10 −18 –10 −17 s. Another feature of the modified guidance law is that Bohmian trajectories cross each other, but this does not contradict the single-valuedness of the wavefunction.

John F. Seely

Frank Großmann

C. Leubner

The nature of gauge transformations and gauge invariance in quantum mechanics about which there exists so much confusion in the literature is simply and pedagogically illuminated by first carefully investigating in various gauges the elementary problem of a free electron subject to a spatially uniform time-dependent electric field, and by then utilizing the findings from this particular example to clarify some general misconceptions.