Metals with excitonic instabilities are multiband systems with significant electron-electron interaction. The electronic transport in such systems is affected by collective fluctuations of the electrons, leading to anomalous features in the measured transport coefficients. Many of these anomalies have not been well understood because the transport mechanisms in these systems tend to be rather complex. The complexity arises, on the one hand, from the multiband nature and, on the other, from the anisotropic scattering of electrons accompanied by emitting or absorbing collective fluctuations. Previous works considering scattering due to collective fluctuations have mainly focused on single-band systems, for example in the context of the normal-state transport in cuprates. The recent discovery of high-temperature superconductivity in iron pnictides has renewed the interest in multiband systems. Exploring the transport mechanisms in multiband systems, I find some interesting new aspects, which do not occur in single-band systems. In particular, anisotropic scattering in a model with electronlike and holelike Fermi surfaces can lead to a negative conductivity contribution of the minority carriers, i.e., in an electric field, the minority carriers drift in the direction opposite of what one would expect based on their charge. I show that this effect can explain a reduced magnetoresistance in connection with an enhanced Hall coefficient, which has been measured in pnictides. Of particular interest are multiband models with hot spots on the Fermi surface, in part because of their relevance for the iron pnictides. Hot spots are states with enhanced scattering and therefore reduced excitation lifetimes. In single-band systems, the hot spots are found to have a much lower contribution to the total conductivity than other parts of the Fermi surface, which leads to the so-called hot-spot structure. I show that in the multiband case, the conductivity contributions are much more isotropic around the Fermi surface so that hot spots contribute to transport with a similar strength as other parts of the Fermi surface. I discuss this effect on the basis of an approximate analytical solution of the transport problem and numerically calculate the temperature dependence of several transport coefficients. It turns out that in the nematic phase of iron pnictides, the unexpectedly strong conductivity contribution of hot spots can explain the puzzling behavior of the resistive anisotropy. I show that the experimental observations can be explained within a scenario in which the anisotropy is mainly due to the broken symmetry of the spin-fluctuation spectrum in the nematic phase. In the spin-density-wave state, strongly anisotropic scattering can arise due to the propagating magnons. Using a two-band model relevant for iron pnictides, I find that this scattering can lead to an unusual interruption of the orbital motion of electrons in the magnetic field. As a consequence, the low-field magnetoresistance is linear with an alternating sign of the slope as a function of the direction of the current. In strong magnetic fields, the interrupted orbital motion makes the system unstable, which is characterized by a drop of the resistivity to zero.

Semiclassical initial value representations (SC-IVRs) are popular methods for an approximate description of the quantum dynamics of atomic and molecular systems. A very efficient special case is the propagator by Herman and Kluk, which will be the basis for the investigations in this work. It consists of a phase space integration over initial conditions of classical trajectories which are guiding Gaussian wavepackets. A complex phase factor in the integrand allows for interference between different trajectories, which leads to soft quantum effects being naturally included in the description. The underlying classical trajectories allow for an approximate description of the dynamics of large quantum systems that are inaccessible for a full quantum propagation. Moreover, they also provide an intuitive understanding of quantum phenomena in terms of classical dynamics. The main focus of this work is on further approximations to Herman-Kluk propagation whose applicability to complex dynamics is limited by the number of trajectories that are needed for numerical convergence of the phase space integration. The central idea for these approximations is the semiclassical hybrid formalism which utilizes the costly Herman-Kluk propagator only for a small number of system degrees of freedom (DOFs). The remaining environmental DOFs are treated on the level of Heller's thawed Gaussian wavepacket dynamics, a single trajectory method which is exact only for at most harmonic potentials. If the environmental DOFs are weakly coupled and therefore close to their potential minimum, this level of accuracy is sufficient to account for their effect on the system. Thus, the hybrid approximation efficiently combines accuracy and low numerical cost. As a central theoretical result, we apply this hybrid idea to a time-averaging scheme to arrive at a method for the calculation of vibrational spectra of molecules that is both accurate and efficient. This time-averaged hybrid propagation is then used to study the vibrational dynamics of an iodine-like Morse oscillator bilinearly coupled to a Caldeira-Leggett bath of harmonic oscillators. We first validate the method by comparing it to full quantum and Herman-Kluk propagation for appropriately sized environments. After having established its accuracy, we include more bath DOFs to investigate the influence of the Caldeira-Leggett counter term on the shift of the vibrational levels of the Morse oscillator. As a result, we find out that a redshift, which is observed experimentally for, e.g., iodine in a rare gas matrix, occurs only if the counter term is not included in the Hamiltonian. We then move away from the model bath and on to a realistic, experimentally relevant environment consisting of krypton atoms. We put the iodine molecule into a cluster of 17 krypton atoms and investigate the loss of coherence of the iodine vibration upon coupling to just a few normal coordinates of the bath. These modes with the same symmetry as the iodine vibration turn out to be sufficient to reproduce the expected qualitative dependence on bath temperature and initial state of the iodine molecule. With these few normal modes, a full quantum calculation yields values for coherence loss rates that are close to experimental results. Furthermore, a comparison to semiclassical calculations with more bath modes included confirms the importance of the few highly symmetric normal coordinates. Then, we apply the time-averaged hybrid formalism once more to calculate the vibrational spectrum of the iodine molecule in this now anharmonic krypton environment. Using a krypton matrix instead of a cluster geometry, we find the correct qualitative and also quite good quantitative agreement for the shift of the iodine potential. Finally, we will investigate a more fundamental question, namely, if SC-IVRs contain the spin effects due to the Pauli exclusion principle. To this end, we apply a number of SC-IVRs to the scattering of two electrons with initial states corresponding to either parallel or antiparallel spin. We compare the outcome to full quantum results and find that the difference is resolved by those methods that comprise multiple interfering trajectories.

Metals with excitonic instabilities are multiband systems with significant electron-electron interaction. The electronic transport in such systems is affected by collective fluctuations of the electrons, leading to anomalous features in the measured transport coefficients. Many of these anomalies have not been well understood because the transport mechanisms in these systems tend to be rather complex. The complexity arises, on the one hand, from the multiband nature and, on the other, from the anisotropic scattering of electrons accompanied by emitting or absorbing collective fluctuations. Previous works considering scattering due to collective fluctuations have mainly focused on single-band systems, for example in the context of the normal-state transport in cuprates. The recent discovery of high-temperature superconductivity in iron pnictides has renewed the interest in multiband systems. Exploring the transport mechanisms in multiband systems, I find some interesting new aspects, which do not occur in single-band systems. In particular, anisotropic scattering in a model with electronlike and holelike Fermi surfaces can lead to a negative conductivity contribution of the minority carriers, i.e., in an electric field, the minority carriers drift in the direction opposite of what one would expect based on their charge. I show that this effect can explain a reduced magnetoresistance in connection with an enhanced Hall coefficient, which has been measured in pnictides. Of particular interest are multiband models with hot spots on the Fermi surface, in part because of their relevance for the iron pnictides. Hot spots are states with enhanced scattering and therefore reduced excitation lifetimes. In single-band systems, the hot spots are found to have a much lower contribution to the total conductivity than other parts of the Fermi surface, which leads to the so-called hot-spot structure. I show that in the multiband case, the conductivity contributions are much more isotropic around the Fermi surface so that hot spots contribute to transport with a similar strength as other parts of the Fermi surface. I discuss this effect on the basis of an approximate analytical solution of the transport problem and numerically calculate the temperature dependence of several transport coefficients. It turns out that in the nematic phase of iron pnictides, the unexpectedly strong conductivity contribution of hot spots can explain the puzzling behavior of the resistive anisotropy. I show that the experimental observations can be explained within a scenario in which the anisotropy is mainly due to the broken symmetry of the spin-fluctuation spectrum in the nematic phase. In the spin-density-wave state, strongly anisotropic scattering can arise due to the propagating magnons. Using a two-band model relevant for iron pnictides, I find that this scattering can lead to an unusual interruption of the orbital motion of electrons in the magnetic field. As a consequence, the low-field magnetoresistance is linear with an alternating sign of the slope as a function of the direction of the current. In strong magnetic fields, the interrupted orbital motion makes the system unstable, which is characterized by a drop of the resistivity to zero.

Semiclassical initial value representations (SC-IVRs) are popular methods for an approximate description of the quantum dynamics of atomic and molecular systems. A very efficient special case is the propagator by Herman and Kluk, which will be the basis for the investigations in this work. It consists of a phase space integration over initial conditions of classical trajectories which are guiding Gaussian wavepackets. A complex phase factor in the integrand allows for interference between different trajectories, which leads to soft quantum effects being naturally included in the description. The underlying classical trajectories allow for an approximate description of the dynamics of large quantum systems that are inaccessible for a full quantum propagation. Moreover, they also provide an intuitive understanding of quantum phenomena in terms of classical dynamics. The main focus of this work is on further approximations to Herman-Kluk propagation whose applicability to complex dynamics is limited by the number of trajectories that are needed for numerical convergence of the phase space integration. The central idea for these approximations is the semiclassical hybrid formalism which utilizes the costly Herman-Kluk propagator only for a small number of system degrees of freedom (DOFs). The remaining environmental DOFs are treated on the level of Heller's thawed Gaussian wavepacket dynamics, a single trajectory method which is exact only for at most harmonic potentials. If the environmental DOFs are weakly coupled and therefore close to their potential minimum, this level of accuracy is sufficient to account for their effect on the system. Thus, the hybrid approximation efficiently combines accuracy and low numerical cost. As a central theoretical result, we apply this hybrid idea to a time-averaging scheme to arrive at a method for the calculation of vibrational spectra of molecules that is both accurate and efficient. This time-averaged hybrid propagation is then used to study the vibrational dynamics of an iodine-like Morse oscillator bilinearly coupled to a Caldeira-Leggett bath of harmonic oscillators. We first validate the method by comparing it to full quantum and Herman-Kluk propagation for appropriately sized environments. After having established its accuracy, we include more bath DOFs to investigate the influence of the Caldeira-Leggett counter term on the shift of the vibrational levels of the Morse oscillator. As a result, we find out that a redshift, which is observed experimentally for, e.g., iodine in a rare gas matrix, occurs only if the counter term is not included in the Hamiltonian. We then move away from the model bath and on to a realistic, experimentally relevant environment consisting of krypton atoms. We put the iodine molecule into a cluster of 17 krypton atoms and investigate the loss of coherence of the iodine vibration upon coupling to just a few normal coordinates of the bath. These modes with the same symmetry as the iodine vibration turn out to be sufficient to reproduce the expected qualitative dependence on bath temperature and initial state of the iodine molecule. With these few normal modes, a full quantum calculation yields values for coherence loss rates that are close to experimental results. Furthermore, a comparison to semiclassical calculations with more bath modes included confirms the importance of the few highly symmetric normal coordinates. Then, we apply the time-averaged hybrid formalism once more to calculate the vibrational spectrum of the iodine molecule in this now anharmonic krypton environment. Using a krypton matrix instead of a cluster geometry, we find the correct qualitative and also quite good quantitative agreement for the shift of the iodine potential. Finally, we will investigate a more fundamental question, namely, if SC-IVRs contain the spin effects due to the Pauli exclusion principle. To this end, we apply a number of SC-IVRs to the scattering of two electrons with initial states corresponding to either parallel or antiparallel spin. We compare the outcome to full quantum results and find that the difference is resolved by those methods that comprise multiple interfering trajectories.