Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W+/-, II

We do the spectral analysis of the Hamiltonian for the weak leptonic decay of the gauge bosons W+/-. Using Mourre theory, it is shown that the spectrum between the unique ground state and the first threshold is purely absolutely continuous. Neither sharp neutrino high energy cutoff nor infrared regularization are assumed.Comment: To appear in Ann. Henri Poincar\'

Quantum interference in nanofractals and its optical manifestation

We consider quantum interferences of ballistic electrons propagating inside fractal structures with nanometric size of their arms. We use a scaling argument to calculate the density of states of free electrons confined in a simple model fractal. We show how the fractal dimension governs the density of states and optical properties of fractal structures in the RF-IR region. We discuss the effect of disorder on the density of states along with the possibility of experimental observation.Comment: 19 pages, 6 figure

Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree-Fock equations of atoms. We show, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number $Z$ is sufficiently large compared to the number $N$ of electrons. More specifically, a two-electron atom with atomic number $Z\geq 35$ has a unique Hartree-Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some $Z>1$, which exhibits a phase segregation.Comment: 18 page

(Non)Invariance of dynamical quantities for orbit equivalent flows

We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are shown to either remain invariant, transform according to a multiplicative factor or transform through a convoluted dependence that may take the form of an integral over the initial local values. We discuss the significance of these results for the apparent non-invariance of chaos in general relativity and explore applications to the synchronization of equilibrium states and the elimination of expansions

On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum

We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate |V(t)_{m,n}|0, p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and \epsilon is small enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where \sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was discussed earlier in the literature by Howland

Localization on a quantum graph with a random potential on the edges

We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in analogy to the well-studied case of random Schroedinger operators.Comment: LaTeX2e, 18 page

New characterizations of the region of complete localization for random Schr\"odinger operators

We study the region of complete localization in a class of random operators which includes random Schr\"odinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding model. We establish new characterizations or criteria for this region of complete localization, given either by the decay of eigenfunction correlations or by the decay of Fermi projections. (These are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region.) Using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity

Widths of the Hall Conductance Plateaus

We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the disordered-broadened Landau bands whose energies are smaller than a certain value determined by the strength of the uniform magnetic field. We also prove that, when the Fermi level lies in the localization regime, the Hall conductance is quantized to the desired integer and shows the plateau of the bulk order for varying the filling factor of the electrons rather than the Fermi level.Comment: 94 pages, v2: a revision of Sec. 5; v3: an error in Sec. 7 is corrected, major revisions of Sec. 7 and Appendix E, Sec. 7 is enlarged to Secs. 7-12, minor corrections; v4: major revisions, accepted for publication in Journal of Statistical Physics; v5: minor corrections, accepted versio

An Improved Combes-Thomas Estimate of Magnetic Schr\"{o}dinger Operators

In the present paper, we prove an improved Combes-Thomas estimate, i.e., the Combes-Thomas estimate in trace-class norms, for magnetic Schr\"{o}dinger operators under general assumptions. In particular, we allow unbounded potentials. We also show that for any function in the Schwartz space on the reals the operator kernel decays, in trace-class norms, faster than any polynomial.Comment: 25 pages, some errors correcte

Selective accumulation of langerhans-type dendritic cells in small airways of patients with COPD

<p>Abstract</p> <p>Background</p> <p>Dendritic cells (DC) linking innate and adaptive immune responses are present in human lungs, but the characterization of different subsets and their role in COPD pathogenesis remain to be elucidated. The aim of this study is to characterize and quantify pulmonary myeloid DC subsets in small airways of current and ex-smokers with or without COPD.</p> <p>Methods</p> <p>Myeloid DC were characterized using flowcytometry on single cell suspensions of digested human lung tissue. Immunohistochemical staining for langerin, BDCA-1, CD1a and DC-SIGN was performed on surgical resection specimens from 85 patients. Expression of factors inducing Langerhans-type DC (LDC) differentiation was evaluated by RT-PCR on total lung RNA.</p> <p>Results</p> <p>Two segregated subsets of tissue resident pulmonary myeloid DC were identified in single cell suspensions by flowcytometry: the langerin+ LDC and the DC-SIGN+ interstitial-type DC (intDC). LDC partially expressed the markers CD1a and BDCA-1, which are also present on their known blood precursors. In contrast, intDC did not express langerin, CD1a or BDCA-1, but were more closely related to monocytes.</p> <p>Quantification of DC in the small airways by immunohistochemistry revealed a higher number of LDC in current smokers without COPD and in COPD patients compared to never smokers and ex-smokers without COPD. Importantly, there was no difference in the number of LDC between current and ex-smoking COPD patients.</p> <p>In contrast, the number of intDC did not differ between study groups. Interestingly, the number of BDCA-1+ DC was significantly lower in COPD patients compared to never smokers and further decreased with the severity of the disease. In addition, the accumulation of LDC in the small airways significantly correlated with the expression of the LDC inducing differentiation factor activin-A.</p> <p>Conclusions</p> <p>Myeloid DC differentiation is altered in small airways of current smokers and COPD patients resulting in a selective accumulation of the LDC subset which correlates with the pulmonary expression of the LDC-inducing differentiation factor activin-A. This study identified the LDC subset as an interesting focus for future research in COPD pathogenesis.</p