21 research outputs found
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
[Trans-placental passage of amiodarone: electrocardiographic evidence and pharmacological findings in a newborn infant].
[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