Abstract:
The kinematics of the decay of a bound proton is governed by the proton spectral function. We evaluate this quantity in 16O using the information from nuclear physics experiments. It also includes a correlated part. The reliability of this evaluation is sufficient to open the possibility of correlated cuts in the missing mass and momentum variables in order to identify the decay events from the bound protons with a possible increase of the signal to noise ratio.

Abstract:
Tremendous advances in laser pump-probe techniques open the door for the observation in real time of ultrafast \textit{electronic} processes. Particularly attractive is the visualization of interatomic processes where one can follow the process of energy transfer from one atom to another. The interatomic Coulombic decay (ICD) provides such a process which is abundant in nature. A multielectron wavepacket propagation method enables now to trace fully ab initio the electron dynamics of the process in real time and in space taking into account all electrons of the system and their correlations. The evolution of the electronic cloud throughout the ICD process in the rare gas cluster NeAr following Ne2s ionization is computed and analyzed. The process takes place on a femtosecond timescale, and a surprisingly strong response is found at a much shorter attosecond timescale.

Abstract:
The dynamics of symmetry breaking is an important issue in many branches of physics including the real time onset of the Higgs-effect. In this thesis I examine the linear and non-linear evolution of different systems in the broken symmetric phase. The method of the analytical investigation is to derive effective equations of motion for the soft modes of the theory. Numerical investigation were performed for out-of-equilibrium classical systems. The dynamics of the one-component scalar theory both in the linear-response approximation and for large deviations from equilibrium is investigated. The real time characterisation of the Goldstone effect when a condensate breaks the O(N) symmetry of the quantum and classical field theory is given. The corrections to the Hard Thermal Loop dynamics in the Abelian Higgs model, which reflect the presence of the scalar condensate are calculated. An equation of motion for the soft gauge field that incorporates the effect of the scalar condensate is proposed to be used deep in the broken phase of the Abelian Higgs model.

Abstract:
A novel comparison between the data and the theory is proposed for the nonmesonic (NM) weak decay of hypernuclei. Instead of confronting the primary decay rates, as is usually done, we focus attention on the effective decay rates that are straightforwardly related with the number of emitted particles. Proton kinetic energy spectra of $^5_\Lambda$He, $^7_\Lambda$Li, $^9_\Lambda$Be, $^{11}_\Lambda$B, $^{12}_{\Lambda}$C, $^{13}_\Lambda$C, $^{15}_{\Lambda}$N and $^{16}_{\Lambda}$O, measured by FINUDA, are evaluated theoretically. The Independent Particle Shell Model (IPSM) is used as the nuclear structure framework, while the dynamics is described by the One-Meson-Exchange (OME) potential. Only for the $^{5}_{\Lambda}$He, $^{7}_{\Lambda}$Li, and $^{12}_{\Lambda}$C hypernuclei is it possible to make a comparison with the data, since for the rest there is no published experimental information on number of produced hypernuclei. Considering solely the one-nucleon-induced ($1N$-NM) decay channel, the theory reproduces correctly the shapes of all three spectra at medium and high energies ($E_p \geq 40 $ MeV). Yet, it greatly overestimates their magnitudes, as well as the corresponding transition rates when the full OME ($\pi+K+ \eta+\rho+\omega+K^*$) model is used. The agreement is much improved when only the $\pi+K$ mesons with soft dipole cutoff parameters participate in the decay process. We find that the IPSM is a fair first order approximation to disentangle the dynamics of the $1N$-NM decay, the knowledge of which is indispensable to inquire about the baryon-baryon strangeness-flipping interaction. It is shown that the IPSM provides very useful insights regarding the determination the $2N$-NM decay rate. In a new analysis of the FINUDA data, we derive two results for this quantity with one of them close to that obtained previously.

Abstract:
We study the non-equilibrium dynamics of solitons in model Hamiltonians for Peierls dimerized quasi-one dimensional conducting polymers and commensurate charge density wave systems. The real time equation of motion for the collective coordinate of the soliton and the associated Langevin equation is found in a consistent adiabatic expansion in terms of the ratio of the optical phonon or phason frequency to the soliton mass. The equation of motion for the soliton collective coordinate allows to obtain the frequency dependent soliton conductivity. In lowest order we find that although the coefficient of static friction vanishes, there is dynamical dissipation represented by a non-Markovian dissipative kernel associated with two-phonon processes. The correlation function of the noise in the quantum Langevin equation and the dissipative kernel are related by a generalized quantum fluctuation dissipation relation. To lowest adiabatic order we find that the noise is gaussian, additive and colored. We numerically solve the equations of motion in lowest adiabatic order and compare to the Markovian approximation which is shown to fail both in the $\phi^4$ and the Sine Gordon models even at large temperatures.

Abstract:
We discuss a role of diproton correlation in two-proton emission from the ground state of a proton-rich nucleus, $^6$Be. Assuming the three-body structure of $\alpha + p + p$ configuration, we develop a time-dependent approach, in which the two-proton emission is described as a time-evolution of a three-body metastable state. With this method, the dynamics of the two-proton emission can be intuitively discussed by monitoring the time-dependence of the two-particle density distribution. With a model Hamiltonian which well reproduces the experimental two-proton decay width, we show that a strongly correlated diproton emission is a dominant process in the early stage of the two-proton emission. When the diproton correlation is absent, the sequential two-proton emission competes with the diproton emission, and the decay width is underestimated. These results suggest that the two-proton emission decays provide a good opportunity to probe the diproton correlation in proton-rich nuclei beyond the proton drip-line.

Abstract:
A hybrid approach to nonequilibrium dynamics of quantum impurity systems is presented. The numerical renormalization group serves as a means to generate a suitable low-energy Hamiltonian, allowing for an accurate evaluation of the real-time dynamics of the problem up to exponentially long times using primarily the time-adaptive density-matrix renormalization group. We extract the decay time of the interaction-enhanced oscillations in the interacting resonant-level model and show their quadratic divergence with the interaction strength U. Our numerical analysis is in excellent agreement with analytic predictions based on an expansion in 1/U.

Abstract:
A detailed derivation of the recently proposed time-dependent numerical renormalization-group (TD-NRG) approach to nonequilibrium dynamics in quantum impurity systems is presented. We demonstrate that the method is suitable for fermionic as well as bosonic baths. A comparison with exact analytical results for the charge relaxation in the resonant-level model and for dephasing in the spin-boson model establishes the accuracy of the method. The real-time dynamics of a single spin coupled to both types of baths is investigated. We use the TD-NRG to calculate the spin relaxation and spin precession of a single Kondo impurity. The short- and long-time dynamics is studied as a function of temperature in the ferromagnetic and antiferromagnetic regimes. The short-time dynamics agrees very well with analytical results obtained at second order in the exchange coupling $J$. In the ferromagnetic regime, the long-time spin decay is described by the scaling variable $x = 2\rho_F J(T) T t$. In the antiferromagnetic regime it is governed for $T < T_K$ by the Kondo time scale $1/T_K$. Here $\rho_F$ is the conduction-electron density of states and $T_K$ is the Kondo temperature. Results for spin precession are obtained by rotating the external magnetic field from the x axis to the z axis.

Abstract:
We study the real-time dynamics of string breaking in quantum electrodynamics in one spatial dimension. A two-stage process with a clear separation of time and energy scales for the fermion--antifermion pair creation and subsequent charge separation leading to the screening of external charges is found. Going away from the traditional setup of external static charges, we establish the phenomenon of multiple string breaking by considering dynamical charges flying apart.

Abstract:
The real time exponential decay laws for meta-stable charged particles are shown to require radiative corrections. The methods employed are well known to be valid for radiatively correcting Breit-Wigner line shapes. Radiative corrections contribute substantially to precision life time measurements of muons and pions when initially stopped in condensed matter.