Imaginary Phases in Two-Level Model with Spontaneous Decay

We study a two-level model coupled to the electromagnetic vacuum and to an external classic electric field with fixed frequency. The amplitude of the external electric field is supposed to vary very slow in time. Garrison and Wright [{\it Phys. Lett.} {\bf A128} (1988) 177] used the non-hermitian Hamiltonian approach to study the adiabatic limit of this model and obtained that the probability of this two-level system to be in its upper level has an imaginary geometric phase. Using the master equation for describing the time evolution of the two-level system we obtain that the imaginary phase due to dissipative effects is time dependent, in opposition to Garrison and Wright result. The present results show that the non-hermitian hamiltonian method should not be used to discuss the nature of the imaginary phases in open systems.Comment: 11 pages, new version, to appear in J. Phys.

A new class of sum rules for products of Bessel functions

In this paper we derive a new class of sum rules for products of the Bessel functions of first kind. Using standard algebraic manipulations we extend some of the well known properties of $J_n$. Some physical applications of the results are also discussed. A comparison with the Newberger[J. Math. Phys. \textbf{23} (1982) 1278] sum rules is performed on a typical example.Comment: Published in Journal of Mathematical Physics, 9 pages, no picture

Accidental Degeneracy and Berry Phase of Resonant States

We study the complex geometric phase acquired by the resonant states of an open quantum system which evolves irreversibly in a slowly time dependent environment. In analogy with the case of bound states, the Berry phase factors of resonant states are holonomy group elements of a complex line bundle with structure group C*. In sharp contrast with bound states, accidental degeneracies of resonances produce a continuous closed line of singularities formally equivalent to a continuous distribution of "magnetic" charge on a "diabolical" circle, in consequence, we find different classes of topologically inequivalent non-trivial closed paths in parameter space.Comment: 23 pages, 2 Postscript figures, LaTex, to be published in: Group 21: Symposium on Semigroups and Quantum Irreversibility (Proc. of the XXI Int. Colloquium on Group Theoretical Methods in Physics

Logarithmic perturbation theory for quasinormal modes

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Poschl-Teller potential is briefly discussed. A numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st

SARS-CoV-2 serological profile in healthcare professionals of a Southern Italy hospital

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the first coronavirus that has caused a pandemic. Assessing the prevalence of anti-SARS-CoV-2 in healthcare worker groups offers a unique opportunity to study the correlation between seroconversion and immunization because of their occupational exposure and a higher risk of contagion. The study enrolled 3242 asymptomatic employees of “Policlinico Riuniti”, Foggia. After the first screening, we collected sequential serum samples for up to 23 weeks from the same subjects. In order to perform a longitudinal follow-up study and get information about the titration of IgG levels, we analyzed data from subjects (33) with at least two consecutive serological IgG—positive tests; 62 (1.9%; 95% CI: 1.4–2.3) tested positive for at least one anti-SARS-CoV-2 antibody. The seroprevalence was lower in the high-risk group 1.4% (6/428; 95% CI: 0.5–2.6) vs. the intermediate-risk group 2.0% (55/2736; 95% CI: 1.5–2.5). Overall, within eight weeks, we detected a mean reduction of –17% in IgG levels. Our data suggest a reduction of about 9.27 AU/mL every week (R2 = 0.35, p = 0.0003). This study revealed the prevalence of SARS-CoV-2 antibodies among Foggia’s hospital healthcare staff (1.9%). Moreover, the IgG level reduction suggests that the serological response fades fast in asymptomatic infections

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press

Gamma ray flares from Mrk421 in 2008 observed with the ARGO-YBJ detector

In 2008 the blazar Markarian 421 entered a very active phase and was one of the brightest sources in the sky at TeV energies, showing frequent flaring episodes. Using the data of ARGO-YBJ, a full coverage air shower detector located at Yangbajing (4300 m a.s.l., Tibet, China), we monitored the source at gamma ray energies E > 0.3 TeV during the whole year. The observed flux was variable, with the strongest flares in March and June, in correlation with X-ray enhanced activity. While during specific episodes the TeV flux could be several times larger than the Crab Nebula one, the average emission from day 41 to 180 was almost twice the Crab level, with an integral flux of (3.6 +-0.6) 10^-11 photons cm^-2 s^-1 for energies E > 1 TeV, and decreased afterwards. This paper concentrates on the flares occurred in the first half of June. This period has been deeply studied from optical to 100 MeV gamma rays, and partially up to TeV energies, since the moonlight hampered the Cherenkov telescope observations during the most intense part of the emission. Our data complete these observations, with the detection of a signal with a statistical significance of 3.8 standard deviations on June 11-13, corresponding to a gamma ray flux about 6 times larger than the Crab one above 1 TeV. The reconstructed differential spectrum, corrected for the intergalactic absorption, can be represented by a power law with an index alpha = -2.1 extending up to several TeV. The spectrum slope is fully consistent with previous observations reporting a correlation between the flux and the spectral index, suggesting that this property is maintained in different epochs and characterizes the source emission processes.Comment: Accepted for publication on ApJ

Observation of TeV gamma rays from the Cygnus region with the ARGO-YBJ experiment

We report the observation of TeV gamma-rays from the Cygnus region using the ARGO-YBJ data collected from 2007 November to 2011 August. Several TeV sources are located in this region including the two bright extended MGRO J2019+37 and MGRO J2031+41. According to the Milagro data set, at 20 TeV MGRO J2019+37 is the most significant source apart from the Crab Nebula. No signal from MGRO J2019+37 is detected by the ARGO-YBJ experiment, and the derived flux upper limits at 90% confidence level for all the events above 600 GeV with medium energy of 3 TeV are lower than the Milagro flux, implying that the source might be variable and hard to be identified as a pulsar wind nebula. The only statistically significant (6.4 standard deviations) gamma-ray signal is found from MGRO J2031+41, with a flux consistent with the measurement by Milagro.Comment: 14 pages, 4 figure

Proton-air cross section measurement with the ARGO-YBJ cosmic ray experiment

The proton-air cross section in the energy range 1-100 TeV has been measured by the ARGO-YBJ cosmic ray experiment. The analysis is based on the flux attenuation for different atmospheric depths (i.e. zenith angles) and exploits the detector capabilities of selecting the shower development stage by means of hit multiplicity, density and lateral profile measurements at ground. The effects of shower fluctuations, the contribution of heavier primaries and the uncertainties of the hadronic interaction models, have been taken into account. The results have been used to estimate the total proton-proton cross section at center of mass energies between 70 and 500 GeV, where no accelerator data are currently available.Comment: 14 pages, 9 figure