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

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

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

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

Flickering of 1.3 cm Sources in Sgr B2: Towards a Solution to the Ultracompact HII Region Lifetime Problem

Accretion flows onto massive stars must transfer mass so quickly that they are themselves gravitationally unstable, forming dense clumps and filaments. These density perturbations interact with young massive stars, emitting ionizing radiation, alternately exposing and confining their HII regions. As a result, the HII regions are predicted to flicker in flux density over periods of decades to centuries rather than increasing monotonically in size as predicted by simple Spitzer solutions. We have recently observed the Sgr B2 region at 1.3 cm with the VLA in its three hybrid configurations (DnC, CnB and BnA) at a resolution of 0.25''. These observations were made to compare in detail with matched continuum observations from 1989. At 0.25'' resolution, Sgr B2 contains 41 UC HII regions, 6 of which are hypercompact. The new observations of Sgr B2 allow comparison of relative peak flux densites for the HII regions in Sgr B2 over a 23 year time baseline (1989-2012) in one of the most source-rich massive star forming regions in the Milky Way. The new 1.3 cm continuum images indicate that four of the 41 UC HII regions exhibit significant changes in their peak flux density, with one source (K3) dropping in peak flux density, and the other 3 sources (F10.303, F1 and F3) increasing in peak flux density. The results are consistent with statistical predictions from simulations of high mass star formation, suggesting that they offer a solution to the lifetime problem for ultracompact HII regions.Comment: 12 pages, 3 figures, Accepted for publication in the Astrophysical Journal Letter

Accretions of Various Types of Dark Energies onto Morris-Thorne Wormhole

In this work, we have studied accretion of the dark energies onto Morris-Thorne wormhole. For quintessence like dark energy, the mass of the wormhole decreases and phantom like dark energy, the mass of wormhole increases. We have assumed two types of dark energy like variable modified Chaplygin gas (VMCG) and generalized cosmic Chaplygin gas (GCCG). We have found the expression of wormhole mass in both cases. We have found the mass of the wormhole at late universe and this is finite. For our choices the parameters and the function $B(a)$, these models generate only quintessence dark energy (not phantom) and so wormhole mass decreases during evolution of the universe. Next we have assumed 5 kinds of parametrizations of well known dark energy models. These models generate both quintessence and phantom scenarios. So if these dark energies accrete onto the wormhole, then for quintessence stage, wormhole mass decreases upto a certain value (finite value) and then again increases to infinite value for phantom stage during whole evolution of the universe. We also shown these results graphically.Comment: 9 pages, 7 figures. arXiv admin note: text overlap with arXiv:1112.615

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

Minisuperspace Models in M-theory

We derive the full canonical formulation of the bosonic sector of 11-dimensional supergravity, and explicitly present the constraint algebra. We then compactify M-theory on a warped product of homogeneous spaces of constant curvature, and construct a minisuperspace of scale factors. First classical behaviour of the minisuperspace system is analysed, and then a quantum theory is constructed. It turns out that there similarities with the "pre-Big Bang" scenario in String Theory.Comment: 35 pages, 2 figures, added additional discussion of gauge fixing and self-adjointness of the Hamiltonian, added reference

Stochastic Resonance in Nonpotential Systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit, and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.Comment: Submitted to Phys. Rev.