Unitary Dual of GL_n at archimedean places and global Jacquet-Langlands correspondence

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are established, under the condition that the local inner forms are split at archimedean places. In this paper, we extend the main local results of [7] to archimedean places so that this assumption can be removed. Along the way, we collect several results about the unitary dual of general linear groups over \bbR, \bbC or \bbH of independent interest

On unitarizability in the case of classical p-adic groups

In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we shall give additional evidence in generalized cuspidal rank (up to) three.Comment: This paper is a merged and revised version of ealier preprints arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul

Scaling of avalanche queues in directed dissipative sandpiles

We simulate queues of activity in a directed sandpile automaton in 1+1 dimensions by adding grains at the top row with driving rate $0 < r \leq 1$. The duration of elementary avalanches is exactly described by the distribution $P_1(t) \sim t^{-3/2}\exp{(-1/L_c)}$, limited either by the system size or by dissipation at defects $L_c= \min (L,\xi)$. Recognizing the probability $P_1$ as a distribution of service time of jobs arriving at a server with frequency $r$, the model represents a new example of the $$ server queue in the queue theory. We study numerically and analytically the tail behavior of the distributions of busy periods and energy dissipated in the queue and the probability of an infinite queue as a function of driving rate.Comment: 11 pages, 9 figures; To appear in Phys. Rev.

Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba

Collective Charge Fluctuations in Single-Electron Processes on Nano-Networks

Using numerical modeling we study emergence of structure and structure-related nonlinear conduction properties in the self-assembled nanoparticle films. Particularly, we show how different nanoparticle networks emerge within assembly processes with molecular bio-recognition binding. We then simulate the charge transport under voltage bias via single-electron tunnelings through the junctions between nanoparticles on such type of networks. We show how the regular nanoparticle array and topologically inhomogeneous nanonetworks affect the charge transport. We find long-range correlations in the time series of charge fluctuation at individual nanoparticles and of flow along the junctions within the network. These correlations explain the occurrence of a large nonlinearity in the simulated and experimentally measured current-voltage characteristics and non-Gaussian fluctuations of the current at the electrode.Comment: 10 pages, 7 figure

Nuclear structure in nonmesonic weak decay of hypernuclei

A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed. It involves a partial wave expansion of the emitted nucleon waves, preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak Λ-core coupling formalism. The hypernuclei are grouped having in view their A-1 cores, that is in those with even-even, even-odd and odd-odd cores. It is shown that in all three cases the nuclear structure manifests itself basically through Pauli Principle, and very simple expressions are derived for the neutron and proton induced decays rates Γn and Γp, which does not involve the spectroscopic factors. For the strangeness-Changing weak ΛN → NN transition potential we use the One-Meson-Exchange Model (OMEM), which comprises the exchange of the complete pseudoscalar and vector meson octets (π,η, K, ρ, ω, K*). We evaluate 3H, 4H 4ΛHe, 5ΛHe,11B, 12ΛC, 16ΛO, 17ΛO, and 28ΛSi hypernuclei, with commonly used parametrization for the OMEM, and compare the results with the available experimental information, The calculated rates ΓNM = Γn + Γp are consistent with the data, but the measurements of Γn/p = Γn/Γp are not well accounted for by the theory. It is suggested that, unless additional degrees of freedom are incorporated, the OMEM parameters should be radically modified.Facultad de Ciencias Exacta

Relativistički model kvarkova

A general Lorentz-covariant quark model of mesons, whose nonrelativistic limit corresponds to Isgur-Scora-Grinstein-Wise model, is constructed. It possesses the heavy quark symmetry and can be easily applied to calculation of form factors. Besides it can be engaged in novel tasks, such a the investigation of the two photon decay of scalar mesons. Its behaviour in the infinite momentum frame and the light cone is discussed.Izveli smo poopćeni Lorentz-kovarijantni model mezona čiji nerelativistički limes odgovara Isgur-Scora-Grinstein-Wiseovom modelu. Model ima teško-kvarkovsku simetriju i može se primijeniti za računanje faktora oblika. Osim toga u ovom se modelu mogu rješavati nove zadaće kao što je dvofotonski raspad skalarnih mezona. Raspravljamo svojstva modela u sustavu beskonačnog impulsa i na svjetlosnom stošcu

Weak Magnetism in Two Neutrino Double Beta Decay

We have extended the formalism for the two-neutrino double beta decay by including the weak-magnetism term, as well as other second-forbidden corrections. The weak magnetism diminishes the calculated half-lives in $\sim 10$, independently of the nuclear structure. Numerical computations were performed within the pn-QRPA, for $^{76}Ge$, $^{82}Se$, $^{100} Mo$, $^{128}Te$ and $^{130}Te$ nuclei. No one of the second-forbidden corrections modifies significantly the spectrum shapes. The total reduction in the calculated half lives varies from 6% up to 32%, and strongly depend on the nuclear interaction in the particle-particle $S=1,T=0$ channel. We conclude that the higher order effects in the weak Hamiltonian would hardly be observed in the two-neutrino double beta experiments.Comment: 8 pages, latex, 1ps figure, to appear in Phys. Lett.

Growing Networks: Limit in-degree distribution for arbitrary out-degree one

We compute the stationary in-degree probability, $P_{in}(k)$, for a growing network model with directed edges and arbitrary out-degree probability. In particular, under preferential linking, we find that if the nodes have a light tail (finite variance) out-degree distribution, then the corresponding in-degree one behaves as $k^{-3}$. Moreover, for an out-degree distribution with a scale invariant tail, $P_{out}(k)\sim k^{-\alpha}$, the corresponding in-degree distribution has exactly the same asymptotic behavior only if $2<\alpha<3$ (infinite variance). Similar results are obtained when attractiveness is included. We also present some results on descriptive statistics measures %descriptive statistics such as the correlation between the number of in-going links, $D_{in}$, and outgoing links, $D_{out}$, and the conditional expectation of $D_{in}$ given $D_{out}$, and we calculate these measures for the WWW network. Finally, we present an application to the scientific publications network. The results presented here can explain the tail behavior of in/out-degree distribution observed in many real networks.Comment: 12 pages, 6 figures, v2 adds a section on descriptive statistics, an analisis on www network, typos adde