Small Bipolarons in the 2-dimensional Holstein-Hubbard Model. I The Adiabatic Limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction $\upsilon \geq 0$, which tends to break them, generates many different ground-states. There are four domains in the $g,\upsilon$ phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small $\upsilon$, large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large $\upsilon$, large g); or 3) be a "quadrisinglet state" which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron

Small Bipolarons in the 2-dimensional Holstein-Hubbard Model. II Quantum Bipolarons

We study the effective mass of the bipolarons and essentially the possibility to get both light and strongly bound bipolarons in the Holstein-Hubbard model and some variations in the vicinity of the adiabatic limit. Several approaches to investigate the quantum mobility of polarons and bipolarons are proposed for this model. It is found that the bipolaron mass generally remains very large except in the vicinity of the triple point of the phase diagram, where the bipolarons have several degenerate configurations at the adiabatic limit (single site (S0), two sites (S1) and quadrisinglet (QS)), while the polarons are much lighter. This degeneracy reduces the bipolaron mass significantly. The triple point of the phase diagram is washed out by the lattice quantum fluctuations which thus suppress the light bipolarons. We show that some model variations, for example a phonon dispersion may increase the stability of the (QS) bipolaron against the quantum lattice fluctuations. The triple point of the phase diagram may be stable to quantum lattice fluctuations and a very sharp mass reduction may occur, leading to bipolaron masses of the order of 100 bare electronic mass for realistic parameters. Thus such very light bipolarons could condense as a superconducting state at relatively high temperature when their interactions are not too large, that is, their density is small enough. This effect might be relevant for understanding the origin of the high Tc superconductivity of doped cuprates far enough from half filling.Comment: accepted Eur. Phys. J. B (january 2000) Ref. B960

Targeted energy transfer between a Rotor and a Morse oscillator: A model for selective chemical dissociation

International audienceStandard Kramers theory of chemical reactions involves a coupling with a Langevin thermal bath which intrinsically forbids the possible existence of Discrete Breathers (DBs) (i.e. local modes). However, it is now known that in complex systems, that energy may focus for long time as Discrete Breathers (local mode). In very special systems, targeted energy transfer may occur subsequently to another selected site and induces an ultraselective chemical reaction operating at low temperature. The dynamics of the reaction is non brownian but highly coherent along a specific path in the phase space where the system is nearly integrable (chemical expressway). A simple toy model illustrating this idea is reduced to a Rotor weakly coupled to a Morse oscillator (supposed to represent two specific local modes in a complex system) which are appropriately tuned for targeted energy transfer. When the Rotor is initially rotating with a frequency resonant with those of theMorse oscillator at rest, the energy of the Rotor is almost completely transferred to the Morse oscillator and induces chemical dissociation. The periodic oscillations of the Rotor andMorse oscillator remain coherent and their frequencies simultaneously vary, but always remain resonant. This process is analytically described within an integrable approximation. Numerical investigations of this model confirm that in the appropriate conditions, the particle in the Morse oscillator is indeed promptly ejected at infinity with a finite velocity (chemical dissociation) despite some chaotic transient manifesting imperfect integrability

Standing wave instabilities in a chain of nonlinear coupled oscillators

We consider existence and stability properties of nonlinear spatially periodic or quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic oscillators. Specifically, we consider Klein-Gordon (KG) chains with either soft (e.g., Morse) or hard (e.g., quartic) on-site potentials, as well as discrete nonlinear Schroedinger (DNLS) chains approximating the small-amplitude dynamics of KG chains with weak inter-site coupling. The SWs are constructed as exact time-periodic multibreather solutions from the anticontinuous limit of uncoupled oscillators. In the validity regime of the DNLS approximation these solutions can be continued into the linear phonon band, where they merge into standard harmonic SWs. For SWs with incommensurate wave vectors, this continuation is associated with an inverse transition by breaking of analyticity. When the DNLS approximation is not valid, the continuation may be interrupted by bifurcations associated with resonances with higher harmonics of the SW. Concerning the stability, we identify one class of SWs which are always linearly stable close to the anticontinuous limit. However, approaching the linear limit all SWs with nontrivial wave vectors become unstable through oscillatory instabilities, persisting for arbitrarily small amplitudes in infinite lattices. Investigating the dynamics resulting from these instabilities, we find two qualitatively different regimes for wave vectors smaller than or larger than pi/2, respectively. In one regime persisting breathers are found, while in the other regime the system rapidly thermalizes.Comment: 57 pages, 21 figures, to be published in Physica D. Revised version: Figs. 5 and 12 (f) replaced, some new results added to Sec. 5, Sec.7 (Conclusions) extended, 3 references adde

Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal to zero or \pi. Incommensurate analytic SWs with |Q|>\pi/2 may however appear as 'quasi-stable', as their instability growth rate is of higher order.Comment: 4 pages, 6 figures, to appear in Phys. Rev. Let

A new generation of veryhigh stability BVA oscillators

International audienceA third generation of “Oscilloquartz” OCXO's using the technique of housing a BVA SC-cut crystal resonator and its associated oscillator components in double oven technology has been developed with the funding support of European Space Operations Centre (E.S.O.C). The main purpose is to provide a local oscillator for high performances ground clock. The main features targeted of that new “8607-C series” are to get significant improvements compared to the classical “state of the art” 8607-B design in a better short term stability @ 1 sec in Allan variance, a better-low phase noise and outstanding short term stability and a better-high isolation from “pressure and humidity” variations

Recruitment of the Major Vault Protein by InlK: A Listeria monocytogenes Strategy to Avoid Autophagy

L. monocytogenes is a facultative intracellular bacterium responsible for listeriosis. It is able to invade, survive and replicate in phagocytic and non-phagocytic cells. The infectious process at the cellular level has been extensively studied and many virulence factors have been identified. Yet, the role of InlK, a member of the internalin family specific to L. monocytogenes, remains unknown. Here, we first show using deletion analysis and in vivo infection, that InlK is a bona fide virulence factor, poorly expressed in vitro and well expressed in vivo, and that it is anchored to the bacterial surface by sortase A. We then demonstrate by a yeast two hybrid screen using InlK as a bait, validated by pulldown experiments and immunofluorescence analysis that intracytosolic bacteria via an interaction with the protein InlK interact with the Major Vault Protein (MVP), the main component of cytoplasmic ribonucleoproteic particules named vaults. Although vaults have been implicated in several cellular processes, their role has remained elusive. Our analysis demonstrates that MVP recruitment disguises intracytosolic bacteria from autophagic recognition, leading to an increased survival rate of InlK over-expressing bacteria compared to InlK− bacteria. Together these results reveal that MVP is hijacked by L. monocytogenes in order to counteract the autophagy process, a finding that could have major implications in deciphering the cellular role of vault particles

The seeds of divergence: the economy of French North America, 1688 to 1760

Generally, Canada has been ignored in the literature on the colonial origins of divergence with most of the attention going to the United States. Late nineteenth century estimates of income per capita show that Canada was relatively poorer than the United States and that within Canada, the French and Catholic population of Quebec was considerably poorer. Was this gap long standing? Some evidence has been advanced for earlier periods, but it is quite limited and not well-suited for comparison with other societies. This thesis aims to contribute both to Canadian economic history and to comparative work on inequality across nations during the early modern period. With the use of novel prices and wages from Quebec—which was then the largest settlement in Canada and under French rule—a price index, a series of real wages and a measurement of Gross Domestic Product (GDP) are constructed. They are used to shed light both on the course of economic development until the French were defeated by the British in 1760 and on standards of living in that colony relative to the mother country, France, as well as the American colonies. The work is divided into three components. The first component relates to the construction of a price index. The absence of such an index has been a thorn in the side of Canadian historians as it has limited the ability of historians to obtain real values of wages, output and living standards. This index shows that prices did not follow any trend and remained at a stable level. However, there were episodes of wide swings—mostly due to wars and the monetary experiment of playing card money. The creation of this index lays the foundation of the next component. The second component constructs a standardized real wage series in the form of welfare ratios (a consumption basket divided by nominal wage rate multiplied by length of work year) to compare Canada with France, England and Colonial America. Two measures are derived. The first relies on a “bare bones” definition of consumption with a large share of land-intensive goods. This measure indicates that Canada was poorer than England and Colonial America and not appreciably richer than France. However, this measure overestimates the relative position of Canada to the Old World because of the strong presence of land-intensive goods. A second measure is created using a “respectable” definition of consumption in which the basket includes a larger share of manufactured goods and capital-intensive goods. This second basket better reflects differences in living standards since the abundance of land in Canada (and Colonial America) made it easy to achieve bare subsistence, but the scarcity of capital and skilled labor made the consumption of luxuries and manufactured goods (clothing, lighting, imported goods) highly expensive. With this measure, the advantage of New France over France evaporates and turns slightly negative. In comparison with Britain and Colonial America, the gap widens appreciably. This element is the most important for future research. By showing a reversal because of a shift to a different type of basket, it shows that Old World and New World comparisons are very sensitive to how we measure the cost of living. Furthermore, there are no sustained improvements in living standards over the period regardless of the measure used. Gaps in living standards observed later in the nineteenth century existed as far back as the seventeenth century. In a wider American perspective that includes the Spanish colonies, Canada fares better. The third component computes a new series for Gross Domestic Product (GDP). This is to avoid problems associated with using real wages in the form of welfare ratios which assume a constant labor supply. This assumption is hard to defend in the case of Colonial Canada as there were many signs of increasing industriousness during the eighteenth and nineteenth centuries. The GDP series suggest no long-run trend in living standards (from 1688 to circa 1765). The long peace era of 1713 to 1740 was marked by modest economic growth which offset a steady decline that had started in 1688, but by 1760 (as a result of constant warfare) living standards had sunk below their 1688 levels. These developments are accompanied by observations that suggest that other indicators of living standard declined. The flat-lining of incomes is accompanied by substantial increases in the amount of time worked, rising mortality and rising infant mortality. In addition, comparisons of incomes with the American colonies confirm the results obtained with wages— Canada was considerably poorer. At the end, a long conclusion is provides an exploratory discussion of why Canada would have diverged early on. In structural terms, it is argued that the French colony was plagued by the problem of a small population which prohibited the existence of scale effects. In combination with the fact that it was dispersed throughout the territory, the small population of New France limited the scope for specialization and economies of scale. However, this problem was in part created, and in part aggravated, by institutional factors like seigneurial tenure. The colonial origins of French America’s divergence from the rest of North America are thus partly institutional