We investigate nuclear matter at a finite temperature and density, including the formation of light clusters up to the $\alpha${} particle (1$\leqslant${}A$\leqslant${}4). The novel feature of this work is to include the formation of clusters as well as their dissolution due to medium effects in a systematic way using two many-body theories: a microscopic quantum statistical (QS) approach and a generalized relativistic mean-field (RMF) model. Nucleons and clusters are modified by medium effects. While the nucleon quasiparticle properties are determined within the RMF model from the scalar and vector self-energies, the cluster binding energies are reduced because of Pauli blocking shifts calculated in the QS approach. Both approaches reproduce the limiting cases of nuclear statistical equilibrium (NSE) at low densities and cluster-free nuclear matter at high densities. The treatment of the cluster dissociation is based on the Mott effect due to Pauli blocking, implemented in slightly different ways in the QS and the generalized RMF approaches. This leads to somewhat different results in the intermediate density range of about 10-3 to 10-1$\hskip0.3em${}fm-3, which gives an estimate of the present accuracy of the theoretical predictions. We compare the numerical results of these models for cluster abundances and thermodynamics in the region of medium excitation energies with temperatures T$\leqslant${}20\,MeV and baryon number densities from zero to a few times saturation density. The effects of cluster formation on the liquid-gas phase transition and on the density dependence of the symmetry energy are studied. It is demonstrated that the parabolic approximation for the asymmetry dependence of the nuclear equation of state breaks down at low temperatures and at subsaturation densities because of cluster formation. Comparison is made with other theoretical approaches, in particular, those that are commonly used in astrophysical calculations. The results are relevant for heavy-ion collisions and astrophysical applications.

An effective $\alpha$-particle equation is derived for cases where an $\alpha$ particle is bound to a doubly magic nucleus. As an example, we consider ${}^{212}\mathrm{Po}$ with the $\alpha$ on top of the ${}^{208}\mathrm{Pb}$ core. We consider the core nucleus infinitely heavy, so that the $\alpha$ particle moves with respect to a fixed center; that is, recoil effects are neglected. The fully quantal solution of the problem is discussed. The approach is inspired by the Tohsaki-Horiuchi-Schuck-Röpke wave function concept that has been successfully applied to light nuclei. Shell-model calculations are improved by including four-particle ($\alpha$-like) correlations that are of relevance when the matter density becomes low. In the region where the $\alpha$-like cluster penetrates the core nucleus, the intrinsic bound-state wave function transforms at a critical density into an unbound four-nucleon shell-model state. Exploratory calculations for ${}^{212}\mathrm{Po}$ are presented. Such preformed cluster states are very difficult to describe with shell-model calculations. Reasons for the different physics behavior of an $\alpha$-like cluster with respect to a deuteron-like cluster are discussed.

A microscopic calculation of $\alpha$-cluster preformation probability and $\alpha$-decay width in the typical $\alpha$ emitter ${}^{212}\mathrm{Po}$ is presented. Results are obtained by improving a recent approach to describe $\alpha$ preformation in ${}^{212}\mathrm{Po}$ [ Phys. Rev. C 90, 034304 (2014)] implementing four-nucleon correlations (quartetting). Using the actually measured density distribution of the ${}^{208}\mathrm{Pb}$ core, the calculated $\alpha$-decay width of ${}^{212}\mathrm{Po}$ agrees fairly well with the measured one.

We study a model of dephasing (decoherence) in a two-state quantum system (qubit) coupled to a bath of harmonic oscillators. An exact analytic solution for the reduced dynamics of a two-state system in this model has been obtained previously for factorizing initial states of the combined system. We show that the model admits exact solutions for a large class of correlated initial states which are typical in the theory of quantum measurements. We derive exact expressions for the off-diagonal elements of the qubit density matrix, which hold for an arbitrary strength of coupling between the qubit and the bath. The influence of initial correlations on decoherence is considered for different bath spectral densities. Time behavior of the qubit entropy in the decoherence process is discussed.

We present a microscopic calculation of $\alpha$-cluster formation in heavy nuclei by using the quartetting wave function approach. The interaction of the quartet with the core nucleus is taken in local density approximation. The $\alpha$-cluster formation is found to be particularly sensitive to the interplay of the mean field felt by the $\alpha$-cluster and the Pauli blocking as a consequence of antisymmetrization. The striking feature of $\alpha$-cluster formation probability across the major shell closures of 82 protons and 126 neutrons is reproduced. The shell (or subshell) effects on the $\alpha$-cluster formation in superheavy nuclei are also analyzed.