Topologically protected quantization of work

The transport of a particle in the presence of a potential that changes periodically in space and in time can be characterized by the amount of work needed to shift a particle by a single spatial period of the potential. In general, this amount of work, when averaged over a single temporal period of the potential, can take any value in a continuous fashion. Here we present a topological effect inducing the quantization of the average work. We find that this work is equal to the first Chern number calculated in a unit cell of a space-time lattice. Hence, this quantization of the average work is topologically protected. We illustrate this phenomenon with the example of an atom whose center of mass motion is coupled to its internal degrees of freedom by electromagnetic waves.Comment: 10 pages (including Supplemental Material), 1 figure, 1 table; closer to published versio

A theorem regarding families of topologically non-trivial fermionic systems

We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a $\mathbb{Z}_2-$ topological invariant $p(\textbf{k})$ (the Pfaffian polynomial). The topological invariant is not only the first Chern number, but also the sign of the Pfaffian polynomial coming from a notion of duality. Such Hamiltonian can describe non-trivial Chern insulators, single band superconductors or multiorbital superconductors. The topological features of these families are completely determined as a consequence of our theorem. Some specific model examples are explicitly worked out, with the computation of different possible topological invariants.Comment: 6 page

Nontrivial quantum geometry of degenerate flat bands

The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and nondegenerate bands can be naturally described via the geometry of different Grassmannian manifolds, specific to the band degeneracies. Contrary to the (Abelian) Berry curvature, the quantum metric of a degenerate band resulting from the collapse of a collection of bands is not simply the sum of the individual quantum metrics. We provide a physical interpretation of this phenomenon in terms of transition dipole matrix elements between two bands. By considering a toy model, we show that the quantum metric gets enhanced, reduced, or remains unaffected depending on which bands collapse. The dc longitudinal conductivity and the superfluid stiffness are known to be proportional to the quantum metric for flat-band systems, which makes them suitable candidates for the observation of this phenomenon.Comment: 6+15 pages (including Supplemental Material), 2+2 figures; closer to published versio

Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics

We study finite-temperature Dynamical Quantum Phase Transitions (DQPTs) by means of the fidelity and the interferometric Loschmidt Echo (LE) induced metrics. We analyse the associated dynamical susceptibilities (Riemannian metrics), and derive analytic expressions for the case of two-band Hamiltonians. At zero temperature the two quantities are identical, nevertheless, at finite temperatures they behave very differently. Using the fidelity LE, the zero temperature DQPTs are gradually washed away with temperature, while the interferometric counterpart exhibits finite-temperature Phase Transitions (PTs). We analyse the physical differences between the two finite-temperature LE generalisations, and argue that, while the interferometric one is more sensitive and can therefore provide more information when applied to genuine quantum (microscopic) systems, when analysing many-body macroscopic systems, the fidelity-based counterpart is a more suitable quantity to study. Finally, we apply the previous results to two representative models of topological insulators in 1D and 2D.Comment: 20 pages, 8 figure

High purity galacto-oligosaccharides enhance specific Bifidobacterium species and their metabolic activity in the mouse gut microbiome

Prebiotics are selectively fermented ingredients that result in specific changes in the composition and/or activity of the gastrointestinal microbiota, thus conferring benefit(s) upon the host health. The aim of this study was to evaluate the influence of a β (1–4) galacto-oligosaccharides formulation consisting of 90% pure GOS (GOS90), on the composition and activity of the mouse gut microbiota. Germ-free mice were colonized with microbiota from four pathogen-free wt 129 mice donors (SPF), and stools were collected during a feeding trial in which GOS90 was delivered orally for 14 days. Pyrosequencing of 16S rDNA amplicons showed that Bifidobacterium and specific Lactobacillus, Bacteroides and Clostridiales were more prevalent in GOS90-fed mice after 14 days, although the prebiotic impact on Bifidobacterium varied among individual mice. Prebiotic feeding also resulted in decreased abundance of Bacteroidales, Helicobacter and Clostridium. High-throughput quantitative PCR showed an increased abundance of Bifidobacterium adolescentis, B. pseudocatenulatum, B. lactis and B. gallicum in the prebiotic-fed mice. Control female mice showed a higher diversity (Phylogenetic Diversity PD = 15.1 ± 3.4 in stools and PD = 13.0 ± 0.6 in intestinal contents) than control males (PD = 7.8 ± 1.6 in stool samples and PD = 9.5 ± 1.0 in intestinal contents). GOS90 did not modify inflammatory biomarkers (IL-6, IL-12, IL-1β, IFN-γ and TNF-α). Decreased butyrate, acetate and lactate concentrations in stools of prebiotic fed mice suggested an increase in colonic absorption and reduced excretion. Overall, our results demonstrate that GOS90 is capable of modulating the intestinal microbiome resulting in expansion of the probiome (autochtonous commensal intestinal bacteria considered to have a beneficial influence on health)