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The macroscopic characteristics of a solid, such as its thermal, optical or transport properties are determined by the available microscopic states above its lowest energy level. These slightly higher quantum states are described by elementary excitations and dictate the response of the system under external stimuli. The spectrum of these excitations, obtained typically from inelastic neutron and x-ray scattering, is the spatial and temporal Fourier transform of the density-density correlation function of the system, which dictates how a perturbation propagates in space and time. As frequency-domain measurements do not generally contain phase information, time-domain measurements of these fluctuations could yield a more direct method for investigating the excitations of solids and their interactions both in equilibrium and far-from equilibrium. Here we show that the diffuse scattering of femtosecond x-ray pulses produced by a free electron laser (FEL) can directly measure these density-density correlations due to lattice vibrations in the time domain. We obtain spectroscopic information of the lattice excitations with unprecedented momentum- and frequency- resolution, without resolving the energy of the outgoing photon. Correlations are created via an acoustic analog of the dynamical Casimir effect, where a femtosecond laser pulse slightly quenches the phonon frequencies, producing pairs of squeezed phonons at momenta +q and -q. These pairs of phonons manifest as macroscopic, time-dependent coherences in the displacement correlations that are then probed directly by x-ray scattering. Since the time-dependent correlations are preferentially created in regions of strong electron-phonon coupling, the time-resolved approach is natural as a spectroscopic tool of low energy collective excitations in solids, and their microscopic interactions, both in linear response and beyond.
We analyze possible nonlinear exciton-exciton correlation effects in the optical response of semiconductors by using a time-dependent density-functional theory (TDDFT) approach. For this purpose, we derive the nonlinear (third-order) TDDFT equation f
Excitons are electron-hole pairs appearing below the band gap in insulators and semiconductors. They are vital to photovoltaics, but are hard to obtain with time-dependent density-functional theory (TDDFT), since most standard exchange-correlation (x
I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in
The time-dependent density functional based tight-binding (TD-DFTB) approach is generalized to account for fractional occupations. In addition, an on-site correction leads to marked qualitative and quantitative improvements over the original method.
We investigate optical absorption spectra obtained through time-dependent density functional theory (TD-DFT) based on nonempirical hybrid functionals that are designed to correctly reproduce the dielectric function. The comparison with state-of-the-a