Abstract:
Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix $\rho_1$, obtained by integrating out the degrees of freedom of one of the particles. To quantify the generation of entanglement, we calculate the purity ${\cal P}(t)={\rm Tr}[\rho_1(t)^2]$. We find that entanglement generation sensitively depends (i) on the interaction potential, especially on its strength and range, and (ii) on the nature of the underlying classical dynamics. Under general statistical assumptions, and for short-scaled interaction potentials, we find that ${\cal P}(t)$ decays exponentially fast if the two particles are required to interact in a chaotic environment, whereas it decays only algebraically in a regular system. In the chaotic case, the decay rate is given by the golden rule spreading of one-particle states due to the two-particle coupling, but cannot exceed the system's Lyapunov exponent.

Abstract:
We calculate the interaction kernel K for two-dimensional diffusive electrons. The screening of the Coulomb interaction together with the Fermi statistics induces a spin selection rule for electron-electron scattering so that in leading order in the inverse conductance only pairs of electrons with antiparallel spins do scatter. At low temperature, this results in a larger coherence length for fully polarized electrons and thus in a positive in-plane magnetoresistance. An applied in-plane magnetic field also induces a nonmonotonous behavior of K at finite temperature. Alternatively, the vanishing of the scattering in the triplet channel strongly reduces ferromagnetism deep in the metallic regime. These effects weaken as the density of charge carriers is reduced.

Abstract:
We investigate the influence that classical dynamics has on interference patterns in coherence experiments. We calculate the time-integrated probability current through an absorbing screen and the conductance through a doubly connected ballistic cavity, both in an Aharonov-Bohm geometry with forward scattering only. We show how interference fringes in the probability current generically disappear in the case of a chaotic system with small openings, and how they may persist in the case of an integrable cavity. Simultaneously, the typical, sample dependent amplitude of the flux-sensitive part $g(\phi)$ of the conductance survives in all cases, and becomes universal in the case of a chaotic cavity. In presence of dephasing by fluctuations of the electric potential in one arm of the Aharonov-Bohm loop, we find an exponential damping of the flux-dependent part of the conductance, $g(\phi) \propto \exp[-\tau_{\rm L}/\tau_\phi]$, in term of the traversal time $\tau_{\rm L}$ through the arm and the dephasing time $\tau_\phi$. This extends previous works on dephasing in ballistic systems to the case of many conducting channels.

Abstract:
The spectral properties of a disordered system with few interacting three-dimensional spinless fermions are investigated. We show the existence of a critical spacings distribution which is invariant upon increase of the system size, but strongly depends on the number of particles. At the critical point, we report a substantial decrease of the degree of level repulsion as the number of particles increases indicating a decrease of nearest level correlations associated with the sparsity of the Hamiltonian matrix.

Abstract:
It is shown that off-diagonal fluctuations of interaction lead to the breakdown of perturbation theory in the immediate vicinity of the ground-state of a fermionic system at a rate inversely proportional to the number of considered particles. This rate is parametrically much faster than previously expected. It is shown that this follows from the coherent addition of many small second order contributions to the energy of low-lying levels.

Abstract:
Motivated by the recent experiments of Amasha {\it et al.} [Phys. Rev. B {\bf 78}, 041306(R) (2008)], we investigate single electron tunneling into an empty quantum dot in presence of a magnetic field. We numerically calculate the tunneling rate from a laterally confined, few-channel external lead into the lowest orbital state of a spin-orbit coupled quantum dot. We find two mechanisms leading to a spin-dependent tunneling rate. The first originates from different electronic $g$-factors in the lead and in the dot, and favors the tunneling into the spin ground (excited) state when the $g$-factor magnitude is larger (smaller) in the lead. The second is triggered by spin-orbit interactions via the opening of off-diagonal spin-tunneling channels. It systematically favors the spin excited state. For physical parameters corresponding to lateral GaAs/AlGaAs heterostructures and the experimentally reported tunneling rates, both mechanisms lead to a discrepancy of $\sim$10% in the spin up vs spin down tunneling rates. We conjecture that the significantly larger discrepancy observed experimentally originates from the enhancement of the $g$-factor in laterally confined lead.

Abstract:
We investigate nonlinear transport through quantum coherent metallic conductors contacted to superconducting components. We find that in certain geometries, the presence of superconductivity generates a large, finite-average rectification effect. Specializing to Andreev interferometers, we show that the direction and magnitude of rectification can be controlled by a magnetic flux tuning the superconducting phase difference at two contacts. In particular, this results in the breakdown of an Onsager reciprocity relation at finite bias. The rectification current is macroscopic in that it scales with the linear conductance, and we find that it exceeds 5% of the linear current at sub-gap biases of few tens of \mu eV's.

Abstract:
We investigate the time-dependent variance of the fidelity with which an initial narrow wavepacket is reconstructed after its dynamics is time-reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time $t_c$, after which it decays. To leading order in the effective Planck's constant $\hbar_{\rm eff}$, this decay is given by the sum of a classical term $\simeq \exp[-2 \lambda t]$, a quantum term $\simeq 2 \hbar_{\rm eff} \exp[-\Gamma t]$ and a mixed term $\simeq 2 \exp[-(\Gamma+\lambda)t]$. Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent $\lambda$ in a larger parameter range. Our results are confirmed by numerical simulations.

Abstract:
We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time tau_E. The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from a long-time regime of fully-developed wave chaos. For a vanishing Ehrenfest time the quantum systems display a degree of universality which is well described by random-matrix theory. In the semiclassical limit, tau_E becomes parametrically larger than the scattering time off the boundaries and the dwell time in the system. This results in the emergence of an increasing number of deterministic transport and escape modes, which induce strong deviations from random-matrix universality. We discuss these deviations for a variety of physical phenomena, including shot noise, conductance fluctuations, decay of quasibound states, and the mesoscopic proximity effect in Andreev billiards.

Abstract:
We investigate the quasiparticle density of states in disordered d-wave superconductors. By constructing a quantum map describing the quasiparticle dynamics in such a medium, we explore deviations of the density of states from its universal form ($\propto E$), and show that additional low-energy quasiparticle states exist provided (i) the range of the impurity potential is much larger than the Fermi wavelength [allowing to use recently developed semiclassical methods]; (ii) classical trajectories exist along which the pair-potential changes sign; and (iii) the diffractive scattering length is longer than the superconducting coherence length. In the classically chaotic regime, universal random matrix theory behavior is restored by quantum dynamical diffraction which shifts the low energy states away from zero energy, and the quasiparticle density of states exhibits a linear pseudogap below an energy threshold $E^* \ll \Delta_0$.