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

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

Rigged Hilbert Space Approach to the Schrodinger Equation

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an eigenket to each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wave function. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page

The Luminosity Profiles of Brightest Cluster Galaxies

(Abridged) We have derived detailed R band luminosity profiles and structural parameters for a total of 430 brightest cluster galaxies (BCGs), down to a limiting surface brightness of 24.5 mag/arcsec^2. Light profiles were initially fitted with a Sersic's R^(1/n) model, but we found that 205 (~48) BCGs require a double component model to accurately match their light profiles. The best fit for these 205 galaxies is an inner Sersic model, with indices n~1-7, plus an outer exponential component. Thus, we establish the existence of two categories of the BCGs luminosity profiles: single and double component profiles. We found that double profile BCGs are brighter ~0.2 mag than single profile BCG. In fact, the Kolmogorov-Smirnov test applied to these subsamples indicates that they have different total magnitude distributions, with mean values M_R=-23.8 +/- 0.6 mag for single profile BCGs and M_R=-24.0 +/- 0.5 mag for double profile BCGs. We find that partial luminosities for both subsamples are indistinguishable up to r = 15 kpc, while for r > 20 kpc the luminosities we obtain are on average 0.2 mag brighter for double profile BCGs. This result indicates that extra-light for double profile BCGs does not come from the inner region but from the outer regions of these galaxies. The best fit slope of the Kormendy relation for the whole sample is a = 3.13 +/- 0.04$. However, when fitted separately, single and double profile BCGs show different slopes: a_(single) = 3.29 +/- 0.06 and a_(double)= 2.79 +/- 0.08. On the other hand, we did not find differences between these two BCGs categories when we compared global cluster properties such as the BCG-projected position relative to the cluster X-ray center emission, X-ray luminosity, or BCG orientation with respect to the cluster position angle.Comment: August 2011 issue of ApJS, volume 195, 15 http://iopscience.iop.org/0067-0049/195/2/1

Heat exchange between two interacting nanoparticles beyond the fluctuation-dissipation regime

We show that the observed non-monotonic behavior of the thermal conductance between two nanoparticles when they are brought into contact is originated by an intricate phase space dynamics. Here it is assumed that this dynamics results from the thermally activated jumping through a rough energy landscape. A hierarchy of relaxation times plays the key role in the description of this complex phase space behaviour. Our theory enables us to analyze the heat transfer just before and at the moment of contact.Comment: 4 pages, 1 figure, approved for publication in Physical Review Letter

The Hilbert space of Chern-Simons theory on the cylinder. A Loop Quantum Gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.Comment: Minor changes and some references added. Latex, 16 pages, 1 figur

Infall and Outflow around the HH 212 protostellar system

HH 212 is a highly collimated jet discovered in H2 powered by a young Class 0 source, IRAS 05413-0104, in the L1630 cloud of Orion. We have mapped around it in 1.33 mm continuum, 12CO ($J=2-1$), 13CO ($J=2-1$), C18O ($J=2-1$), and SO ($J_K = 6_5-5_4$) emission at $\sim$ \arcs{2.5} resolution with the Submillimeter Array. A dust core is seen in the continuum around the source. A flattened envelope is seen in C18O around the source in the equator perpendicular to the jet axis, with its inner part seen in 13CO. The structure and kinematics of the envelope can be roughly reproduced by a simple edge-on disk model with both infall and rotation. In this model, the density of the disk is assumed to have a power-law index of $p=-1.5$ or -2, as found in other low-mass envelopes. The envelope seems dynamically infalling toward the source with slow rotation because the kinematics is found to be roughly consistent with a free fall toward the source plus a rotation of a constant specific angular momentum. A 12CO outflow is seen surrounding the H2 jet, with a narrow waist around the source. Jetlike structures are also seen in 12CO near the source aligned with the H2 jet at high velocities. The morphological relationship between the H2 jet and the 12CO outflow, and the kinematics of the 12CO outflow along the jet axis are both consistent with those seen in a jet-driven bow shock model. SO emission is seen around the source and the H2 knotty shocks in the south, tracing shocked emission around them.Comment: 17 pages, 11 figures, Accepted by the Ap

Duality covariant quantum field theory on noncommutative Minkowski space

We prove that a scalar quantum field theory defined on noncommutative Minkowski spacetime with noncommuting momentum coordinates is covariant with respect to the UV/IR duality which exchanges coordinates and momenta. The proof is based on suitable resonance expansions of charged noncommutative scalar fields in a background electric field, which yields an effective description of the field theory in terms of a coupled complex two-matrix model. The two independent matrix degrees of freedom ensure unitarity and manifest CT-invariance of the field theory. The formalism describes an analytic continuation of the renormalizable Grosse-Wulkenhaar models to Minkowski signature.Comment: 32 pages; v2: Typos corrected; v3: Further typos corrected - Final version to appear in JHE