We study the decoherence of a one-particle system, whose classical correspondent is chaotic, when it evolves coupled to a weak quenched environment. This is done by analytical evaluation of the Loschmidt echo (i.e., the revival of a localized density excitation upon reversal of its time evolution), in the presence of the perturbation. We predict an exponential decay for the Loschmidt echo with a (decoherence) rate which is asymptotically given by the mean Lyapunov exponent of the classical system, and therefore independent of the perturbation strength, within a given range of strengths. Our results are consistent with recent experiments of polarization echoes in nuclear magnetic resonance and numerical simulations.

A study of the conductance in a disordered linear chain of finite length L including inelastic scattering processes is presented. Inelastic scatterers are introduced as defined by Büttiker and are assumed to be uniformly distributed along the system. This defines an inelastic scattering time ${\mathrm{\tau }}_{\mathrm{in}}$ plus a condition of charge conservation which in turn introduces incoherent electrons. The four-probe conductance of the system is then reduced to a Landauer-like behavior G=2(${\mathit{e}}^2$/h)${\mathit{T}}_{\mathrm{eff}}$/ (1-${\mathit{T}}_{\mathrm{eff}}$), where the effective transmission through the sample, ${\mathit{T}}_{\mathrm{eff}}$, is the sum of two terms, one of which accounts for the phase-coherent electrons which have not suffered any inelastic collision and another for electrons which have suffered at least one inelastic collision in their journey. To show explicitly this point, the conductance of an ordered system is analyzed. Analytical and numerical results are presented for disordered chains, where resonances in the transmission present a width which is associated with the minimum between the escape time and the relaxation time. Because of the denominator in the Landauer formula, strong fluctuations on the conductance are present even in the weak-disordered situation in which the localization length λ>L, but we observed that they become of order ${\mathit{e}}^2$/h when the inelastic scattering length ${\mathit{L}}_{\mathrm{in}}$=L. Further decrease of the inelastic length causes the fluctuations to reduce following similar laws to that of the metallic regime.

Could a laser field lead to the much sought-after tunable band gaps in graphene? By using Floquet theory combined with Green's functions techniques, we predict that a laser field in the mid-infrared range can produce observable band gaps in the electronic structure of graphene. Furthermore, we show how they can be tuned by using the laser polarization. Our results could serve as a guidance to design optoelectronic nanodevices.

A generalization of the Landauer-Büttiker picture of transport applicable to time-dependent problems in the presence of dissipation is presented. Starting from the Schrödinger equation in the Keldysh formalism under appropriate boundary conditions and using a linear-response approximation, we find that an ideal voltage probe is described by a generalized Landauer-Büttiker equation (GLBE). Thus, the GLBE may be considered as a particular case of the Keldysh kinetic equation. The transmission probabilities become retarded functions of the elapsed time, and are evaluated in terms of the retarded and advanced Green’s functions. The interpretation of the mathematical formalism is emphasized. The GLBE is applied to get the time-dependent dissipative resonant tunneling by considering a resonant dot coupled with (a) a dephasing process and (b) a finite side probe. For case (a), we find that the resonant-tunneling conductance G is associated with an inductance L≊${\mathrm{\tau }}_{\mathit{q}}$/G which accounts for the response in the low-frequency regime; G depends on the dissipation inside the resonant region, while ${\mathrm{\tau }}_{\mathit{q}}$, being twice the natural lifetime of the resonant state, does not. For case (b), we find an additional delay in the response accounting for the ‘‘inertia’’ of the side probe. This result clarifies the concepts of ideal voltage probe and voltage source as applied in the case of time-dependent transport.

The reversal of the time evolution of the local polarization in an interacting spin system involves a sign change of the effective dipolar Hamiltonian which refocuses the “spin diffusion” process generating a polarization echo. Here, the attenuation of these echo amplitudes as a function of evolution time is presented for cymantrene and ferrocene polycrystalline samples, involving one and two five spin rings per molecule, respectively. We calculate the fraction of polarization which is not refocused because only the secular part of the dipolar Hamiltonian is inverted. The results indicate that, as long as the spin dynamics is restricted to a single ring, the non-inverted part of the Hamiltonian is not able by itself to explain the whole decay of the polarization echoes. A crossover from exponential (cymantrene) to Gaussian (ferrocene) attenuation is experimentally observed. This is attributed to an increase of the relative importance of the spin dynamics, as compared with irreversible interactions, which favors dynamical irreversibility.