Trace formula on the p-adic upper half-plane

This article aims at showing a p-adic analogue of Selberg's trace formula, which describes a duality between the spectrum of a Hilbert-Schmidt operator and the length of prime geodesics appearing in the p-adic upper half-plane associated with a hyperbolic discontinuous subgroup of . Then we construct Markov processes on the fundamental domain relative to such subgroups, to whose transition operators the trace formula applied and a p-adic analogue of prime geodesic theorem is proved.     

Examples of non-conjugated holomorphic vector fields and foliations

We consider germs of holomorphic vector fields near the origin of with a saddle-node singularity, and the induced singular foliations. In a previous article we described the invariants addressing the analytical classification of these vector fields. They split into three parts: a formal, an orbital and a tangential component. For a fixed formal class, the orbital invariant (associated to the foliation) was obtained by Martinet and Ramis; we give it an integral representation. We then derive examples of non-orbitally conjugated foliations by the use of a “first-step” normal form, whose first-significative jet is an invariant. The tangential invariant also admits an integral representation, hence we derive explicit examples of vector fields, inducing the same foliation, that are not mutually conjugated. In addition, we provide a family of normal forms for vector fields orbitally equivalent to the model of Poincaré-Dulac.     

On the Physical Reality of Quantum Waves

The main interpretations of the quantum-mechanical wave function are presented emphasizing how they can be divided into two ensembles: The ones that deny and the other ones that attribute a form of reality to quantum waves. It is also shown why these waves cannot be classical and must be submitted to the restriction of the complementarity principle. Applying the concept of smooth complementarity, it is shown that there can be no reason to attribute reality only to the events and not to the wave or to the initial state of a given system. Thereafter, an experiment proposed by the authors is presented, where it is shown that the wave-like behaviour allows predictions that are not allowed on the grounds of a particle-like behaviour. In conclusion, we upheld that quantum waves must be real even if they do not belong to the same ontological level of events, which connected with particle detections.Institute of Philosophy, University of Urbino, Urbino 610 29, Italy; tarizzi@uniurb.it     

Relaxation of Paramagnetic Centers during Modulation of a Stationary Magnetic Field

It has been found that the phase shift _min in the synchronous detection block that ensures the minimum amplitude of the EPR lines of ruby, diphenylpicrylhydrazyl, and MnSO₄·5H₂O, depends on the amplitude of the modulationH _m of a stationary magnetic field. The dependence of _min on H _m is explained by the inertial nature of the recovery of the stationary states of paramagnetic centers on a change in the magnetic field strength.     

Variable temperature system using vortex tube cooling and fiber optic temperature measurement for low temperature magic angle spinning NMR

We describe the construction and operation of a variable temperature (VT) system for a high field fast magic angle spinning (MAS) probe. The probe is used in NMR investigations of biological macromolecules, where stable setting and continuous measurement of the temperature over periods of several days are required in order to prevent sample overheating and degradation. The VT system described is used at and below room temperature. A vortex tube is used to provide cooling in the temperature range of -20 to 20 degrees C, while a liquid nitrogen-cooled heat exchanger is used below -20 degrees C. Using this arrangement, the lowest temperature that is practically achievable is -140 degrees C. Measurement of the air temperature near the spinning rotor is accomplished using a fiber optic thermometer that utilizes the temperature dependence of the absorption edge of GaAs. The absorption edge of GaAs also has a magnetic field dependence that we have measured and corrected for. This dependence was calibrated at several field strengths using the well-known temperature dependence of the (1)H chemical shift difference of the protons in methanol.     

Effect of an impurity on 3-electron quantum dots in magnetic fields

1 Introduction Quantum dots (QDs), often referred to as artificial atoms, are currently under in-tense study because they provide ideal structures used in optical-electronic microdevices, so they are essential in developing microtechniques. They are also essential in the aca-demic aspect, because rich information on microstructures can be extracted both theo-retically and experimentally. Since the early fabrication of the QDs, external magnetic field has been used to control their propertie…     

Spectral anomalies and spectral switches of partially coherent and polychromatic light diffracted at an aperture

Inrecentyearsanewbranchofmodernphysicalopticscalledsingularoptics[1]hasbeendeveloped.In2002theworkinsingularopticswasextendedfrommonochromaticlighttospatiallyfullycoherentandpolychromaticlightbyGburetal.[2—4].Itwasfoundthat,whenaconverging,spatiallyfullycoherentandpolychromaticsphericalwaveisdiffractedatanaperture,anomalousspectralchangestakeplaceclosetozerosoftheintensityinthefarfield;i.e.thespectrumisredshiftedatsomepoints,blueshiftedatothers,andsplitintotwolineselsewhere.Thepredictionsofsp…     

On Gibbs measures of P-adic Potts model on the cayley tree

We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ? _p) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ? p and p ≥ 3 (resp. q ? 2², p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ? p if p ≥ 3 and q ? 2² if p = 2.     

Infrared Variables for the SU(3) Yang–Mills Field

We generalize the self-dual parameterization of the SU(2) Yang–Mills field proposed by Niemi and Faddeev for describing the infrared limit of the theory to the case of the gauge group SU(3). We demonstrate that the duality property intrinsic to the SU(2) gauge field cannot be transferred automatically to the higher-rank group case. We interpret the algebraic structures appearing in the Lagrangian for the new compact variables in terms of the group products SU(2)³.