Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate

The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate $h_{\mathrm{KS}}$ given by the sum of all positive Lyapunov exponents of the system. We prove a quantum version of this result valid for bosonic systems with unstable quadratic Hamiltonian. The derivation takes into account the case of time-dependent Hamiltonians with Floquet instabilities. We show that the entanglement entropy $S_A$ of a Gaussian state grows linearly for large times in unstable systems, with a rate $\Lambda_A \leq h_{KS}$ determined by the Lyapunov exponents and the choice of the subsystem $A$. We apply our results to the analysis of entanglement production in unstable quadratic potentials and due to periodic quantum quenches in many-body quantum systems. Our results are relevant for quantum field theory, for which we present three applications: a scalar field in a symmetry-breaking potential, parametric resonance during post-inflationary reheating and cosmological perturbations during inflation. Finally, we conjecture that the same rate $\Lambda_A$ appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.Comment: 50+17 Pages, 11 figure

Gravitational quantum switch on a superposition of spherical shells

The existence of states describing quantum superpositions of distinct spacetime geometries is a feature that is generally expected in theories of quantum gravity. Phenomenological models have recently been explored for the analysis of possible effects due to a superposition of geometries, including the occurrence of processes with indefinite order. In a gravitational quantum switch, in particular, the order of operations applied by two agents on a target system is entangled with the state of the geometry. We consider a model describing the superposition of geometries produced by distinct arrangements of spherical mass shells, and show that a protocol for the implementation of a gravitational quantum switch can be formulated in such a system. The geometries in superposition are identical in an exterior region outside a given radius, and differ within such a radius. The exterior region provides a classical frame from which the superposition of geometries in the interior region can be probed. One of the agents crosses the interior region and becomes entangled with the geometry, which is explored as a resource for the implementation of the quantum switch. Novel features of the protocol include the superposition of nonisometric geometries, the existence of a region with a definite geometry, and the fact that the agent that experiences the superposition of geometries is in free fall, preventing information on the global geometry to be obtained from within its laboratory.Comment: 22 pages, 5 figures. References adde

Topological low-temperature limit of Z(2) spin-gauge theory in three dimensions

We study Z(2) lattice gauge theory on triangulations of a compact 3-manifold. We reformulate the theory algebraically, describing it in terms of the structure constants of a bidimensional vector space H equipped with algebra and coalgebra structures, and prove that in the low-temperature limit H reduces to a Hopf Algebra, in which case the theory becomes equivalent to a topological field theory. The degeneracy of the ground state is shown to be a topological invariant. This fact is used to compute the zeroth- and first-order terms in the low-temperature expansion of Z for arbitrary triangulations. In finite temperatures, the algebraic reformulation gives rise to new duality relations among classical spin models, related to changes of basis of H.Comment: 10 pages, no figure

In vivo single cell analysis reveals Gata2 dynamics in cells transitioning to hematopoietic fate

Cell fate is established through coordinated gene expression programs in individual cells. Regulatory networks that include the Gata2 transcription factor play central roles in hematopoietic fate establishment. Although Gata2 is essential to the embryonic development and function of hematopoietic stem cells that form the adult hierarchy, little is known about the in vivo expression dynamics of Gata2 in single cells. Here, we examine Gata2 expression in single aortic cells as they establish hematopoietic fate in Gata2Venus mouse embryos. Time-lapse imaging reveals rapid pulsatile level changes in Gata2 reporter expression in cells undergoing endothelial-to-hematopoietic transition. Moreover, Gata2 reporter pulsatile expression is dramatically altered in Gata2+/- aortic cells, which undergo fewer transitions and are reduced in hematopoietic potential. Our novel finding of dynamic pulsatile expression of Gata2 suggests a highly unstable genetic state in single cells concomitant with their transition to hematopoietic fate. This reinforces the notion that threshold levels of Gata2 influence fate establishment and has implications for transcription factor-related hematologic dysfunctions

Cell signalling by reactive lipid species: new concepts and molecular mechanisms

The process of lipid peroxidation is widespread in biology and is mediated through both enzymatic and non-enzymatic pathways. A significant proportion of the oxidized lipid products are electrophilic in nature, the RLS (reactive lipid species), and react with cellular nucleophiles such as the amino acids cysteine, lysine and histidine. Cell signalling by electrophiles appears to be limited to the modification of cysteine residues in proteins, whereas non-specific toxic effects involve modification of other nucleophiles. RLS have been found to participate in several physiological pathways including resolution of inflammation, cell death and induction of cellular antioxidants through the modification of specific signalling proteins. The covalent modification of proteins endows some unique features to this signalling mechanism which we have termed the ‘covalent advantage’. For example, covalent modification of signalling proteins allows for the accumulation of a signal over time. The activation of cell signalling pathways by electrophiles is hierarchical and depends on a complex interaction of factors such as the intrinsic chemical reactivity of the electrophile, the intracellular domain to which it is exposed and steric factors. This introduces the concept of electrophilic signalling domains in which the production of the lipid electrophile is in close proximity to the thiol-containing signalling protein. In addition, we propose that the role of glutathione and associated enzymes is to insulate the signalling domain from uncontrolled electrophilic stress. The persistence of the signal is in turn regulated by the proteasomal pathway which may itself be subject to redox regulation by RLS. Cell death mediated by RLS is associated with bioenergetic dysfunction, and the damaged proteins are probably removed by the lysosome-autophagy pathway