François David

Breakdown of universality in multi-cut matrix models

We solve the puzzle of the disagreement between orthogonal polynomials methods and mean-field calculations for random N×N matrices with a disconnected eigenvalue support. We show that the difference does not stem from a 2 symmetry breaking, but from the discreteness of the number of eigenvalues. This leads to additional terms (quasiperiodic in N) which must be added to the naive mean-field expressions. Our result invalidates the existence of a smooth topological large-N expansion and some postulated universality properties of correlators. We derive the large-N expansion of the free energy for the general two-cut case. From it we rederive by a direct and easy mean-field-like method the two-point correlators and the asymptotic orthogonal polynomials. We extend our results to any number of cuts and to non-real potentials.

Integral representation for the dimensionally regularized massive Feynman amplitude

A convergent integral representation for the massive Feynman amplitude in complex dimension D is defined away from ReD equal to some rationals. The Feynman integrand is modified according to the technique of Zimmermann’s forests but each subgraph is subtracted at zero external momenta and zero internal masses; the order of the Taylor subtractions depends upon ReD. The so defined regularized Feynman amplitude is a meromorphic function of D with multiple poles at some rationals, which satisfies field equations and Ward identities. These amplitudes may be used in the construction of a bare Lagrangian field theory.

Hydration thermodynamics of plutonium and transplutonium ions

Abstract Since thermodynamic properties are related to crystallographic radii, we first present sets of precise values of crystallographic radii (R) for ionic charge +2, +3 and +4 and different coordination numbers (CN). These data are based on the values reported by Shannon as well as variations of R with CN as observed for lanthanides, and linear correlations between isoelectronic M m+ and N n+ ions. Accurate measurements of the volume of the unit cell of oxides, fluorides and chlorides carried out recently give reliable radii values. Experimental entropies of actinide aquo ions are limited to Pu 3+ and Th 4+ . Since this property depends on the structure of the hydrated ion, we decompose ionic entropies into three terms, related to electronic configuration, mass of the central ion, and structure of the aquo ion (S h ). We use our data on the structure of trivalent actinide ions to derive S h and therefore to estimate values of trivalent ionic entropies. Entropies of divalent and tetravalent ions are also obtained similarly. Finally, taking into account the structure of the aqueous actinide ions, we calculate hydration enthalpies of +2, +3 and +4 actinide ions.

Liouville quantum gravity on complex tori

In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov [Phys. Lett. B 103, 207 (1981)]. Our approach follows the construction carried out by the authors together with Kupiainen in the case of the Riemann sphere [“Liouville quantum gravity on the Riemann sphere,” e-print arXiv:1410.7318]. The difference is here that the moduli space for complex tori is non-trivial. Modular properties of LQFT are thus investigated. This allows us to integrate the LQFT on complex tori over the moduli space, to compute the law of the random Liouville modulus, therefore recovering (and extending) formulae obtained by physicists, and make conjectures about the relationship with random planar maps of genus one, eventually weighted by a conformal field theory and conformally embedded onto the torus.

Modified Square-Wave Cathodic Stripping Voltammetry for Determination of Se(IV) at Trace and Ultratrace Levels

A method for the improvement of the signal-to-noise ratio in square-wave (SW) voltammetry is proposed. It is based on the modification of a square-wave waveform. This method is applied to cathodic stripping voltammetric (CSV) determination of selenium(IV) in nitric acid solutions. Hanging mercury drop electrode (HMDE) was used in the presence of Cu(II) ions. The optimal conditions were chosen: square-wave waveform mode, pH, time and potential of electrodeposition. Kinetic processes of copper selenide reduction with the use of SWCSV, applying different square-wave waveforms, are studied. Quasi-reversible processes are observed. The standard reaction rate constants are evaluated for different square-wave waveforms. It is shown that the determination of Se(IV) by this modified SWCSV technique is possible with an excellent sensitivity (the detection limit 8×10−12 mol L−1 only for 5 min of electrodeposition) and good reproducibility (Sr<8%) in a wide range of concentration (1×10−11−1×10−6 mol L−1) of Se(IV). The presence of Mo(VI), Pb(II), Ni(II), Zn(II), Cr(VI) metal ions with molar excess around 1000 do not prevent the detection of Se(IV) signals.

Electromigration of Trivalent Lanthanide Ions in Aqueous Solution

The migration velocities of lanthanide aquo-ions (Ce + , N d 3 + , EU , G d 3 + , T b 3 + , T m 3 + and Yb 3 + ) , have been measured as a function of ionic strength and temperature. The relationship between the mobility and the conductibility data has been checked for each lanthanide. A discontinuity near the middle of the series is infered from the plot of the migration velocities as a function of the crystallographic radius. The magnitude of the activation energy of the mobility u is derived from the measurements performed at various temperatures between 9 and 30°C. It confirms the large variation of u with T. From the known temperature dependence of the viscosity, variations of the size of the aquo-ion with Τ are deduced. No change in the structure of the hydrated species can be detected in the temperature range investigated.

Random tree growth by vertex splitting

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalizes the preferential attachment model and Fords α-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from 1 to ∞, depending on the parameters of the model.

Mass distribution exponents for growing trees

We investigate the statistics of trees grown from some initial tree by attaching links to pre-existing vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that measures the repartition of the mass of large trees between their different subtrees. This distribution is shown to be a broad distribution and we derive explicit expressions for scaling exponents that characterize its behaviour when one subtree is much smaller than the others. We show in particular the existence of various regimes with different values of these mass distribution exponents. Our results are corroborated by a number of exact solutions for particular solvable cases, as well as by numerical simulations.

Instanton calculus for the self-avoiding manifold model

We compute the normalisation factor for the large order asymptotics of perturbation theory for the self-avoiding manifold (SAM) model describing flexible tethered (D-dimensional) membranes in d-dimensional space, and the ε-expansion for this problem. For that purpose, we develop the methods inspired from instanton calculus, that we introduced in a previous publication (Nucl. Phys. B 534 (1998) 555), and we compute the functional determinant of the fluctuations around the instanton configuration. This determinant has UV divergences and we show that the renormalized action used to make perturbation theory finite also renders the contribution of the instanton UV-finite. To compute this determinant, we develop a systematic large-d expansion. For the renormalized theory, we point out problems in the interplay between the limits ε→ 0 and d→∞, as well as IR divergences when ε=0. We show that many cancellations between IR divergences occur, and argue that the remaining IR-singular term is associated to amenable non-analytic contributions in the large-d limit when ε=0. The consistency with the standard instanton-calculus results for the self-avoiding walk is checked for D=1.

Importance of reversibility in the quantum formalism.

In this Letter I stress the role of causal reversibility (time symmetry), together with causality and locality, in the justification of the quantum formalism. First, in the algebraic quantum formalism, I show that the assumption of reversibility implies that the observables of a quantum theory form an abstract real C^{⋆} algebra, and can be represented as an algebra of operators on a real Hilbert space. Second, in the quantum logic formalism, I emphasize which axioms for the lattice of propositions (the existence of an orthocomplementation and the covering property) derive from reversibility. A new argument based on locality and Solers theorem is used to derive the representation as projectors on a regular Hilbert space from the general quantum logic formalism. In both cases it is recalled that the restriction to complex algebras and Hilbert spaces comes from the constraints of locality and separability.