Nonperturbative effects and nonperturbative definitions in matrix models and topological strings

We develop techniques to compute multi-instanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding trans-series solutions, i.e. formal solutions with exponentially small corrections, to the recursion relations characterizing the free energy. We illustrate this method in the Hermitian, quartic matrix model, and we provide a detailed description of the instanton corrections in the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel resummation techniques and results from the theory of resurgent functions to relate the formal multi-instanton series to the nonperturbative definition of the matrix model. We study this relation in the case of the GWW model and its double-scaling limit, providing in this way a nice illustration of various mechanisms connecting the resummation of perturbative series to nonperturbative results, like the cancellation of nonperturbative ambiguities. Finally, we argue that trans-series solutions are also relevant in the context of topological string theory. In particular, we point out that in topological string models with both a matrix model and a large N gauge theory description, the nonperturbative, holographic definition involves a sum over the multi-instanton sectors of the matrix modelComment: 50 pages, 12 figures, comments and references added, small correction

Structure, Time Propagation and Dissipative Terms for Resonances

For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the numerical determination of such eigenvalues, and also discuss the connection to the case of purely imaginary coupling, which is PT-symmetric. Moreover, we show that a suitable generalization of the complex scaling method leads to an algorithm for the time propagation of wave packets in potentials which give rise to unstable resonances. This leads to a certain unification of the structure and the dynamics. Our time propagation results agree with known quantum dynamics solvers and allow for a natural incorporation of structural perturbations (e.g., due to dissipative processes) into the quantum dynamics.Comment: 14 pages; LaTeX; minor change

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

[Electrophysiological demonstration of more structures in the atrioventricular node (author's transl)].

Three types of atrioventricular nodal conduction curves, relating A1A2 to H1H2, generated with atrial extrastimulus technique, are known. The first type is smooth, suggesting the homogeneous structure of A-V node. The second type, with abrupt increase in H1H2 response over a critical range of A1A2 coupling intervals, suggests the presence of fast and slow A-V nodal pathways. We have found in five patients the third tipe of A-V conduction curve, giving evidence of an intranodal final common pathway, distal to the fast and slow A-V nodal pathways. The thyrd type of curve enables us to know also some alectrophysiological properties of final common pathway. Indeed we have defined effective and functional refractory periods of fast, slow and final common pathways as far as we can in this type of curve. Paced heart rate variations and atropine medications have led the third type of A-V conduction curve to change into the second type in three cases, into first type in one case. These changes of A-V nodal conduction curves are related to different influence of cardiac cycle lenghts and autonomic nervous system on refractory periods and conduction velocity of the outlined intranodal structures

On the Existence of Quasipattern Solutions of the Swift-Hohenberg Equation

Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this paper, we consider 8-fold, 10-fold, 12-fold, and higher order quasipattern solutions of the Swift-Hohenberg equation. We prove that a formal solution, given by a divergent series, may be used to build a smooth quasiperiodic function which is an approximate solution of the pattern-forming partial differential equation (PDE) up to an exponentially small error

Congenital hypothyroid goiter and amiodarone

Amiodarone is an anti-arrhythmic drug with a content of 39% iodine. No adverse effects on fetal thyroid function have previously been observed with maternal ingestion of amiodarone during pregnancy. A case of severe congenital hypothyroidism with goiter, associated with maternal ingestion of 200 mg amiodarone daily from the 13th week of pregnancy, is described here. No other environmental causes of goiter, nor a congenital organic thyroid disorder could be demonstrated.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Riparare l\u2019umano. Lezioni da un manicomio di frontiera

Partendo dal doppio significato che il verbo riparare ha in italiano, aggiustare e proteggere, si mettono a confronto l\u2019architettura, che da sempre ha il compito primario di offrire un rifugio e che oggi si propone di riaggiustare preesistenze e tessuti urbani riportandoli alla funzionalit\ue0, e la psichiatria, che nella sua storia ha preteso di riparare la mente del folle, proteggendo lui, e al tempo stesso la societ\ue0, attraverso l\u2019internamento. Il confronto tra architettura e psichiatria \ue8 utile se si intendono progettare interventi di riuso in un ex manicomio, ma diventa indispensabile se il manicomio in questione \ue8 quello in cui, nel 1961, nasce la rivoluzione della psichiatria italiana, che porter\ue0 al riconoscimento dei diritti delle persone con disturbi mentali e, con la legge Basaglia del 1978, alla messa \u201cfuori legge\u201d di una tipologia architettonica, quella dell\u2019ospedale psichiatrico, divenuta simbolo della negazione di quei diritti. La storia di questo ospedale, marginale e al tempo stesso sempre al centro di travagliati incroci e spostamenti di confini, governi, identit\ue0 e lingue, ne fa un luogo emblematico per il contemporaneo. In questa sua complessit\ue0 \ue8 stato proposto alla riflessione di pi\uf9 saperi e di diverse pratiche progettuali