The dynamics of the population imbalance of bosons in a double-well potential is investigated from the point of view of many-body quantum mechanics in the framework of the two-mode model. For small initial population imbalances, coherent superpositions of almost equally spaced energy eigenstates lead to Josephson oscillations. The suppression of tunneling at population imbalance beyond a critical value is related to a high concentration of initial state population in the region of the energy spectrum with quasi-degenerate doublets resulting in imbalance oscillations with a very small amplitude. For unaccessible long times, however, the system recovers the regime of Josephson oscillations. The understanding of many-body quantum systems from the theoretical and experimental points of view has undergone a considerable development during the past decade. Unifying concepts of several branches of physics are under development, creating an interdisciplinary scenario for the understanding of quantum mechanical paradigms. One of the simplest many-body systems to be realized experimentally and studied theoretically are ultracold bosons in a double-well potential. This system is very rich exhibiting a great variety of quantum phenomena such as interference [1], tunneling/selftrapping [2,3,4,5,6,7], entanglement of macroscopic superpositions [8]. Lately this system has been extensively studied, especially after the implementation of several experiments in the area. The usual theoretical approach to weakly interacting Bose-Einstein condensates (BECs) is the mean-field approximation, a nonlinear Gross-Pitaevski equation [3,9,10,11,12,13,14,15,16], which has proven very adequate in explaining a wide variety of experiments.More recently, the dynamics of population distribution between two or more wells of an optical lattice have been experimentally investigated. In particular, Josephson oscillations have been observed in a 1D optical lattice [17,18] and recently the density distribution of tunneling 87 Rb particles is directly observed [2]. In this experiment, initial population differences between the left and right well components are controlled by loading the BEC into an asymmetric double-well potential. The Josephson dynamics is initiated at t = 0 by non-adiabatically changing the potential to a symmetric double-well. When the initial population imbalance is below a critical value, the system presents Josephson oscillations between the two sides of the well. However, above this critical value tunneling is not observed. Based on a mean field treatment, this is usually attributed to macroscopic self-trapping. In the present work, we discuss an alternative approach to this system based on exact numerical solutions of the two-mode Bose-Hubbard Hamiltonian [19]:

We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range interactions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle ("spinon") excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.

To explain aspects of the quantum-to-classical transition, quantum Darwinism explores the fact that, due to interactions between a quantum open system and its surrounding environment, information about the system can be spread redundantly to the environment. Here we recall that there are in the literature two distinct and non-equivalent ways to make this statement precise and quantitative. We first point out the difference with some simple but illustrative examples. We then consider a model where Darwinism can be seen from both perspectives. Moreover, the non-Markovianity of our model can be varied with a parameter. In a recent work [F. Galve et al., Sci. Reps. 6, 19607 (2016)], the authors concluded that quantum Darwinism can be hindered by non-Markovianity. We depart from their analysis and argue that, from both perspectives to quantum Darwinism, there is no clear relationship between non-Markovianity and quantum Darwinism in our model. FIG. 1: Three qualitatively distinct possibilities for a partial information plot (PIP). The solid line (a) corresponds to a case where a small fraction of the environment already has average mutual information close to H(S), being the signature of quantum Darwinism. The linear profile (b) can be seen (approximately) in our model for small interaction times (see Sec. V). In profile (c), f δ is close to 0.5, so the redundancy is very small. This kind of profile can be obtained from random pure states drawn according to the Haar measure [13].

The irreversible work during a driving protocol constitutes one of the most widely studied measures in nonequilibrium thermodynamics, as it constitutes a proxy for entropy production. In quantum systems, it has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol. The goal of this paper is to explore this contribution in systems that undergo a quantum phase transition. Substantial effort has been dedicated in recent years to understand the role of quantum criticality in work protocols. However, practically nothing is known about how coherence contributes to it. To shed light on this issue, we study the entropy production in infinitesimal quenches of the one-dimensional XY model. For quenches in the transverse field, we find that for finite temperatures the contribution from coherence can, in certain cases, account for practically all of the entropy production. At low temperatures, however, the coherence presents a finite cusp at the critical point, whereas the entropy production diverges logarithmically. Alternatively, if the quench is performed in the anisotropy parameter, we find that there are situations where all of the entropy produced is due to quantum coherences.

The entropy produced when a quantum system is driven away from equilibrium can be decomposed in two parts, one related with populations and the other with quantum coherences. The latter is usually based on the so-called relative entropy of coherence, a widely used quantifier in quantum resource theories. In this paper we argue that, despite satisfying fluctuation theorems and having a clear resource-theoretic interpretation, this splitting has shortcomings. First, it predicts that at low temperatures the entropy production will always be dominated by the classical term, irrespective of the quantum nature of the process. Second, for infinitesimal quenches, the radius of convergence diverges exponentially as the temperature decreases, rendering the functions non-analytic. Motivated by this, we provide here a complementary approach, where the entropy production is split in a way such that the contributions from populations and coherences are written in terms of a thermal state of a specially dephased Hamiltonian. The physical interpretation of our proposal is discussed in detail. We also contrast the two approaches by studying work protocols in a transverse field Ising chain, and a macrospin of varying dimension.