Dual Pair Correspondence in Physics: Oscillator Realizations and Representations

We study general aspects of the reductive dual pair correspondence, also known as Howe duality. We make an explicit and systematic treatment, where we first derive the oscillator realizations of all irreducible dual pairs: $(GL(M,\mathbb R), GL(N,\mathbb R))$, $(GL(M,\mathbb C), GL(N,\mathbb C))$, $(U^*(2M), U^*(2N))$, $(U(M_+,M_-), U(N_+,N_-))$, $(O(N_+,N_-),Sp(2M,\mathbb R))$, $(O(N,\mathbb C), Sp(2M,\mathbb C))$ and $(O^*(2N), Sp(M_+,M_-))$. Then, we decompose the Fock space into irreducible representations of each group in the dual pairs for the cases where one member of the pair is compact as well as the first non-trivial cases of where it is non-compact. We discuss the relevance of these representations in several physical applications throughout this analysis. In particular, we discuss peculiarities of their branching properties. Finally, closed-form expressions relating all Casimir operators of two groups in a pair are established

Coulomb-Volkov approach of ionization by extreme ultraviolet laser pulses in the subfemtosecond regime

In conditions where the interaction betweeen an atom and a short high-frequency extreme ultraviolet laser pulse is a perturbation, we show that a simple theoretical approach, based on Coulomb-Volkov-type states, can make reliable predictions for ionization. To avoid any additional approximation, we consider here a standard case : the ionization of hydrogen atoms initially in their ground state. For any field parameter, we show that the method provides accurate energy spectra of ejected electrons, including many above threshold ionization peaks, as long as the two following conditions are simultaneously fulfilled : (i) the photon energy is greater than or equal to the ionization potential ; (ii) the ionization process is not saturated. Thus, ionization of atoms or molecules by the high order harmonic laser pulses which are generated at present may be addressed through this Coulomb-Volkov treatment.Comment: 19 pages including 5 figures and figure caption

Odorants of Capsicum spp. dried fruits as candidate attractants for Lasioderma serricorne F. (Coleoptera: Anobiidae)

The cigarette beetle, Lasioderma serricorne F. (Coleoptera: Anobiidae) is an important food storage pest affecting the tobacco industry and is increasingly impacting museums and herbaria. Monitoring methods make use of pheromone traps which can be implemented using chili fruit powder. The objective of this study was to assess the response of L. serricorne to the volatile organic compounds (VOCs) from different chili powders in order to identify the main semiochemicals involved in this attraction. Volatiles emitted by Capsicum annuum, C. frutescens, and C. chinense dried fruit powders were tested in an olfactometer and collected and analyzed using SPME and GC-MS. Results indicated that C. annuum and C. frutescens VOCs elicit attraction toward L. serricorne adults in olfactometer, while C. chinense VOCs elicit no attraction. Chemicals analysis showed a higher presence of polar compounds in the VOCs of C. annuum and C. frutescens compared to C. chinense, with α-ionone and β-ionone being more abundant in the attractive species. Further olfactometer bioassays indicated that both α-ionone and β-ionone elicit attraction, suggesting that these compounds are candidates as synergistic attractants in pheromone monitoring traps for L. serricorne

Multiplicity Studies and Effective Energy in ALICE at the LHC

In this work we explore the possibility to perform ``effective energy'' studies in very high energy collisions at the CERN Large Hadron Collider (LHC). In particular, we focus on the possibility to measure in $pp$ collisions the average charged multiplicity as a function of the effective energy with the ALICE experiment, using its capability to measure the energy of the leading baryons with the Zero Degree Calorimeters. Analyses of this kind have been done at lower centre--of--mass energies and have shown that, once the appropriate kinematic variables are chosen, particle production is characterized by universal properties: no matter the nature of the interacting particles, the final states have identical features. Assuming that this universality picture can be extended to {\it ion--ion} collisions, as suggested by recent results from RHIC experiments, a novel approach based on the scaling hypothesis for limiting fragmentation has been used to derive the expected charged event multiplicity in $AA$ interactions at LHC. This leads to scenarios where the multiplicity is significantly lower compared to most of the predictions from the models currently used to describe high energy $AA$ collisions. A mean charged multiplicity of about 1000-2000 per rapidity unit (at $\eta \sim 0$) is expected for the most central $Pb-Pb$ collisions at $\sqrt{s_{NN}} = 5.5 TeV$.Comment: 12 pages, 19 figures. In memory of A. Smirnitski

Spin picture of the one-dimensional Hubbard model: Two-fluid structure and phase dynamics

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schroedinger equations, whereas near half-filling the model is described by two coupled Josephson junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed point equation of the simpler among them, we show that the standard one-band ground state phase space is found.Comment: 10 pages, 1 figure, to appear on Phys. Rev.

Assessing the Potential of Intra-specific Biodiversity towards Adaptation of Irrigated and Rain-fed Italian Production Systems to Future Climate

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Ferromagnetism in a hard-core boson model

The problem of ferromagnetism -- associated with a ground state with maximal total spin -- is discussed in the framework of a hard-core model, which forbids the occupancy at each site with more than one particle. It is shown that the emergence of ferromagnetism on finite square lattices crucially depends on the statistics of the particles. Fermions (electrons) lead to the well-known instabilities for finite hole densities, whereas for bosons (with spin) ferromagnetism appears to be stable for all hole densities.Comment: 8 pages, 7 figures, RevTex

Definizione di mappe georeferenziate di dose da esposizioni per contaminazione da radionuclidi rilasciati nell'ambiente atmosferico in seguito ad un ipotetico evento incidentale

Il sistema di calcolo CALMET-CALPUFF è stato utilizzato per lo studio del trasporto a lunga distanza e la deposizione di diverse specie radioattive a seguito di un ipotetico incidente nella centrale nucleare di Gösgen, situata presso il Canton Soletta, Svizzera. CALPUFF è un modello gaussiano a puff in grado di descrivere la dispersione atmosferica di inquinanti multi-specie su scale che vanno dalla decina alle centinaia di chilometri dalla sorgente. I dati meteorologici sono stati simulati con il codice di calcolo 3D CALMET. I risultati in termini di concentrazioni dell’inquinante radioattivo in aria e deposizione al suolo sono stati elaborati con il software GRADO (GRid_in Air of specific effective DOse), messo a punto dal gruppo di ricerca per la definizione di mappe georeferenziate di dose da esposizione utilizzando i coefficienti di conversione riportati nelle pubblicazioni ICRP. L’analisi dei risultati mostra che il pacchetto software integrato CALMET-CALPUFF-GRADO può risultare uno strumento utile nelle strategie di gestione dell’emergenza in caso di eventi incidentali come quello oggetto di studio

A geometric theory for 2-D systems including notions of stabilisability

In this paper we consider the problem of internally and externally stabilising controlled invariant and output-nulling subspaces for two-dimensional (2-D) Fornasini–Marchesini models, via static feedback. A numerically tractable procedure for computing a stabilising feedback matrix is developed via linear matrix inequality techniques. This is subsequently applied to solve, for the first time, various 2-D disturbance decoupling problems subject to a closed-loop stability constraint