Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''

In this reply, we show that when we apply standard distribution theory to the Lippmann-Schwinger equation, the resulting spaces of test functions would comply with the Hardy axiom only if classic results of Paley and Wiener, of Gelfand and Shilov, and of the theory of ultradistributions were wrong. As well, we point out several differences between the ``standard method'' of constructing rigged Hilbert spaces in quantum mechanics and the method used in Time Asymmetric Quantum Theory.Comment: 13 page

Massive envelopes and filaments in the NGC 3603 star forming region

The formation of massive stars and their arrival on the zero-age main-sequence occurs hidden behind dense clouds of gas and dust. In the giant Hii region NGC 3603, the radiation of a young cluster of OB stars has dispersed dust and gas in its vicinity. At a projected distance of 2:5 pc from the cluster, a bright mid-infrared (mid-IR) source (IRS 9A) had been identified as a massive young stellar object (MYSO), located on the side of a molecular clump (MM2) of gas facing the cluster. We investigated the physical conditions in MM2, based on APEX sub-mm observations using the SABOCA and SHFI instruments, and archival ATCA 3 mm continuum and CS spectral line data. We resolved MM2 into several compact cores, one of them closely associated with IRS 9A. These are likely infrared dark clouds as they do not show the typical hot-core emission lines and are mostly opaque against the mid-IR background. The compact cores have masses of up to several hundred times the solar mass and gas temperatures of about 50 K, without evidence of internal ionizing sources. We speculate that IRS 9A is younger than the cluster stars, but is in an evolutionary state after that of the compact cores

The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets

The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbert space rather than just the Hilbert space. It is also argued that this analytic continuation entails the imposition of a time asymmetric boundary condition upon the group time evolution, resulting into a semigroup time evolution. Physically, the semigroup time evolution is simply a (retarded or advanced) propagator.Comment: 32 pages, 3 figure

On the inconsistency of the Bohm-Gadella theory with quantum mechanics

The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann-Schwinger equation are functionals over spaces of Hardy functions. The preparation-registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that the Hardy axiom is incorrect, because the solutions of the Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also shown that the derivation of the preparation-registration arrow of time is flawed. Thus, Hardy functions neither appear when we solve the Lippmann-Schwinger equation nor they should appear. It is also shown that the Bohm-Gadella theory does not rest on the same physical principles as quantum mechanics, and that it does not solve any problem that quantum mechanics cannot solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page

Facial identity and emotional expression as predictors during economic decisions

Two sources of information most relevant to guide social decision making are the cooperative tendencies associated with different people and their facial emotional displays. This electrophysiological experiment aimed to study how the use of personal identity and emotional expressions as cues impacts different stages of face processing and their potential isolated or interactive processing. Participants played a modified trust game with 8 different alleged partners, and in separate blocks either the identity or the emotions carried information regarding potential trial outcomes (win or loss). Behaviorally, participants were faster to make decisions based on identity compared to emotional expressions. Also, ignored (nonpredictive) emotions interfered with decisions based on identity in trials where these sources of information conflicted. Electrophysiological results showed that expectations based on emotions modulated processing earlier in time than those based on identity. Whereas emotion modulated the central N1 and VPP potentials, identity judgments heightened the amplitude of the N2 and P3b. In addition, the conflict that ignored emotions generated was reflected on the N170 and P3b potentials. Overall, our results indicate that using identity or emotional cues to predict cooperation tendencies recruits dissociable neural circuits from an early point in time, and that both sources of information generate early and late interactive patterns

Simple Pendulum Revisited

We describe a 8085 microprocessor interface developed to make reliable time period measurements. The time period of each oscillation of a simple pendulum was measured using this interface. The variation of the time period with increasing oscillation was studied for the simple harmonic motion (SHM) and for large angle initial displacements (non-SHM). The results underlines the importance of the precautions which the students are asked to take while performing the pendulum experiment.Comment: 17 pages with 10 figure

Monitoring of the radio galaxy M 87 during a low-emission state from 2012 to 2015 with MAGIC

M87 is one of the closest (z = 0.004 36) extragalactic sources emitting at very high energies (VHE, E \u3e 100 GeV). The aim of this work is to locate the region of the VHE gamma-ray emission and to describe the observed broad-band spectral energy distribution (SED) during the low VHE gamma-ray state. The data fromM87 collected between 2012 and 2015 as part of aMAGIC monitoring programme are analysed and combined with multiwavelength data from Fermi-LAT, Chandra, HST, EVN, VLBA, and the Liverpool Telescope. The averaged VHE gamma-ray spectrum can be fitted from ∼100 GeV to ∼10 TeV with a simple power law with a photon index of (−2.41 ± 0.07), while the integral flux above 300 GeV is (1.44 ± 0.13) × 10−12 cm−2 s−1. During the campaign between 2012 and 2015, M87 is generally found in a low-emission state at all observed wavelengths. The VHE gamma-ray flux from the present 2012–2015M 87 campaign is consistent with a constant flux with some hint of variability (∼ 3 σ) on a daily time-scale in 2013. The low-state gamma-ray emission likely originates from the same region as the flare-state emission. Given the broad-band SED, both a leptonic synchrotron self-Compton and a hybrid photohadronic model reproduce the available data well, even if the latter is preferred. We note, however, that the energy stored in the magnetic field in the leptonic scenario is very low, suggesting a matter-dominated emission region

Heat transfer between nanoparticles: Thermal conductance for near-field interactions

We analyze the heat transfer between two nanoparticles separated by a distance lying in the near-field domain in which energy interchange is due to Coulomb interactions. The thermal conductance is computed by assuming that the particles have charge distributions characterized by fluctuating multipole moments in equilibrium with heat baths at two different temperatures. This quantity follows from the fluctuation-dissipation theorem (FDT) for the fluctuations of the multipolar moments. We compare the behavior of the conductance as a function of the distance between the particles with the result obtained by means of molecular dynamics simulations. The formalism proposed enables us to provide a comprehensive explanation of the marked growth of the conductance when decreasing the distance between the nanoparticles