First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

Gaussian operator bases for correlated fermions

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus allows first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness of the basis and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anticommuting Grassmann variables. Furthermore, because of the overcompleteness of the basis, the phase-space distribution can always be chosen positive. This has important consequences for the sign problem in fermion physics.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behavior in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

One-dimensional interacting anyon gas: Low-energy properties and haldane exclusion statistics

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.

Noninertial observers in special relativity and clock synchronization debates

Selleri's arguments that a consideration of noninertial reference frames in the framework of special relativity identify absolute simultaneity as being Nature's choice of synchronization are considered. In the case of rectilinearly accelerating rockets, it is argued by considering two rockets which maintain a fixed proper separation rather than a fixed separation relative to the inertial frame in which they start from rest, that what seems the most natural choice for a simultaneity convention is problem-dependent and that Einstein's definition is the most natural (though still conventional) choice in this case. In addition, the supposed problems special relativity has with treating a rotating disk, namely how a pulse of light traveling around the circumference of the disk can have a local speed of light equal to c everywhere but a global speed not equal to c, and how coordinate transformations to the disk can give the Lorentz transformations in the limit of large disk radius but small angular velocity, are addressed. It is shown that the theory of Fermi frames solves both of these problems. It is also argued that the question of defining simultaneity relative to a uniformly rotating disk does riot need to be resolved in order to resolve Ehrenfest's paradox.

Strong electronic correlations in superconducting organic charge transfer salts

We review the role of strong electronic correlations in quasi-two-dimensional organic charge transfer salts such as (BEDT-TTF)(2)X, (BETS)(2)Y, and beta'-[Pd(dmit)(2)](2)Z. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerized and is described by a half-filled Hubbard model; the second class is not strongly dimerized and is described by a quarter-filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-filled quasi-two-dimensional organic charge transfer salts, focusing on the metallic and superconducting phases. We review work showing that the metallic phase, which has both Fermi liquid and 'bad metal' regimes, is described both quantitatively and qualitatively by dynamical mean field theory (DMFT). The phenomenology of the superconducting state is still a matter of contention. We critically review the experimental situation, focusing on the key experimental results that may distinguish between rival theories of superconductivity, particularly probes of the pairing symmetry and measurements of the superfluid stiffness. We then discuss some strongly correlated theories of superconductivity, in particular the resonating valence bond (RVB) theory of superconductivity. We conclude by discussing some of the major challenges currently facing the field. These include parameterizing minimal models, the evidence for a pseudogap from nuclear magnetic resonance (NMR) experiments, superconductors with low critical temperatures and extremely small superfluid stiffnesses, the possible spin- liquid states in kappa-(ET)(2)Cu-2(CN)(3) and beta'-[Pd(dmit)(2)](2)Z, and the need for high quality large single crystals.

Spesa pubblica in Sanità, Istruzione e Ricerca: efficienza, efficacia e determinanti

La ricerca intende analizzare l’efficacia della spesa pubblica, l’efficienza e le loro determinanti nei settori della Sanità, dell’Istruzione e della Ricerca per 33 paesi dell’area OCSE. L’analisi ha un duplice obiettivo: da un lato un confronto cross country e dall’altro un confronto temporale, prendendo in considerazione il periodo che va dal 1992 al 2011. Il tema della valutazione dell’efficacia e dell’efficienza della spesa pubblica è molto attuale, soprattutto in Europa, sia perché essa incide di quasi il 50% sul PIL, sia a causa della crisi finanziaria del 2008 che ha spinto i governi ad una riduzione dei bugdet e ad un loro uso più oculato. La scelta di concentrare il lavoro di analisi nei settori della Sanità, dell’Istruzione e della Ricerca e Sviluppo deriva da un lato dalla loro peculiarità di attività orientate al cliente (scuole, ospedali, tribunali) dall’altro dal ruolo strategico che essi rappresentano per lo sviluppo economico di un paese. Il lavoro è articolato in tre sezioni: 1. Rassegna dei principali strumenti metodologici utilizzati in letteratura per la misurazione della performance e dell’efficienza della spesa pubblica nei tre settori. 2. Valutazione e confronto dell’efficienza e della performance della spesa pubblica dal punto di vista sia temporale sia cross-country attraverso la costruzione di indicatori di performance e di efficienza della spesa pubblica (per approfondire l'indice dell'efficienza ho applicato la tecnica DEA "bootstrap output oriented" con indicatori di output ed input non simultanei mentre l’evoluzione dell’efficienza tra i periodi 2011-2002 e 2001-1992 è stata analizzata attraverso il calcolo dell’indice di Malmquist). 3. Analisi delle variabili esogene che influenzano l’efficienza della spesa pubblica nei settori Salute, Istruzione e Ricerca e Sviluppo attraverso una regressione Tobit avente come variabile dipendente i punteggi di efficienza DEA output oriented e come variabili esogene alcuni indicatori scelti tra quelli presenti in letteratura: l’Indicatore delle condizioni socioeconomiche delle famiglie (costruito e applicato da OCSE PISA per valutare l’impatto del background familiare nelle performance dell’apprendimento), l’Indicatore di fiducia nel sistema legislativo del paese, l’Indicatore di tutela dei diritti di proprietà, l’Indicatore delle azioni di controllo della corruzione, l’Indicatore di efficacia delle azioni di governo, l’Indicatore della qualità dei regolamenti, il PIL pro-capite. Da questo lavoro emergono risultati interessanti: non sempre alla quantità di risorse impiegate corrisponde il livello massimo di performance raggiungibile. I risultati della DEA evidenziano la media dei punteggi di efficienza corretti di 0,712 e quindi, impiegando la stessa quantità di risorse, si produrrebbe un potenziale miglioramento dell’output generato di circa il 29%. Svezia, Giappone, Finlandia e Germania risultano i paesi più efficienti, più vicini alla frontiera, mentre Slovacchia, Portogallo e Ungheria sono più distanti dalla frontiera con una misura di inefficienza di circa il 40%. Per quanto riguarda il confronto tra l’efficienza della spesa pubblica nei tre settori tra i periodi 1992-2001 e 2002-2011, l’indice di Malmquist mostra risultati interessanti: i paesi che hanno migliorato il loro livello di efficienza sono quelli dell’Est come l’Estonia, la Slovacchia, la Lituania mentre Paesi Bassi, Belgio e Stati Uniti hanno peggiorato la loro posizione. I paesi che risultano efficienti nella DEA come Finlandia, Germania e Svezia sono rimasti sostanzialmente fermi con un indice di Malmquist vicino al valore uno. In conclusione, i risultati della Tobit contengono indicazioni importanti per orientare le scelte dei Governi. Dall’analisi effettuata emerge che la fiducia nelle leggi, la lotta di contrasto alla corruzione, l’efficacia del governo, la tutela dei diritti di proprietà, le condizioni socioeconomiche delle famiglie degli studenti OECD PISA, influenzano positivamente l’efficienza della spesa pubblica nei tre settori indagati. Oltre alla spending review, per aumentare l’efficienza e migliorare la performance della spesa pubblica nei tre settori, è indispensabile per gli Stati la capacità di realizzare delle riforme che siano in grado di garantire il corretto funzionamento delle istituzioni.

A study of the electrical and optical properties of unhydrogenated neon-sputtered amorphous silicon

Films of amorphous silicon (a-Si) were prepared by r.f. sputtering in a Ne plasma without the addition of hydrogen or a halogen. The d.c. dark electrical conductivity, he optical gap and the photoconductivity of the films were investigated for a range of preparation conditions, the sputtering gas pressure, P, the target-substrate spacing, d, the self-bias voltage, Vsb, on the target and the substrate temperature, Ts. The dependence of the electrical and optical properties on these conditions showed that various combinations of P, d and Vsb, at a constant Ts, giving the same product (Pd/V sb) result in films with similar properties, provided that P, d and Vsb remain vithin a certain range. Variation of Pd/Vsb between about 0.2 and 0.8 rrTorr.cm!V varied the dark conductivity over about 4 orders of magnitude, the optical gap by 0.5 eV and the photoconductivity over 4-5 orders of magnitude. This is attributed to controlling the density-of-states distribution in the mobility gap. The temperature-dependence of photoconductivity and the photoresponse of undoped films are in support of this conclusion. Films prepared at relatively high (Pd/Vsb) values and Ts=300 ºc: exhibited low dark-conductivity and high thermal activation energy, optical gap and photoresponse, characteristic properties of a 'low density-of-states material. P-type doping with group-Ill elements (Al, B and Ga) by sputtering from a composite target or from a predoped target (B-.doped) was investigated. The systematic variation of room-temperature conductivity over many orders of magnitude and a Fermi-level shift of about 0.7 eV towards the valence-band edge suggest that substitutional doping had taken place. The effects of preparation conditions on doping efficiency were also investigated. The post-deposition annealing of undoped and doped films were studied for a temperature range from 250 ºC to 470 ºC. It was shown that annealing enhanced the doping efficiency considerably, although it had little effect on the basic material (a-Si) prepared at the optimum conditions (Pd/Vsb=0.8 mTorr.cm/V and Ts=300 $ºC). Preliminary experiments on devices imply potential applications of the present material, such as p-n and MS junctions.

Effect of electron-phonon coupling on transmission through Luttinger liquid hybridized with resonant level

We show that electron-phonon coupling strongly affects transport properties of the Luttinger liquid hybridized with a resonant level. Namely, this coupling significantly modifies the effective energy-dependent width of the resonant level in two different geometries, corresponding to the resonant or antiresonant transmission in the Fermi gas. This leads to a rich phase diagram for a metal-insulator transition induced by the hybridization with the resonant level.

Impurity scattering in a Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations, which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in a rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Quantum wire hybridized with a single-level impurity

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, T(epsilon), and a local density of states, nu(epsilon) at low energies epsilon. In particular, we have found that the antiresonance in T(epsilon) has a generalized Breit-Wigner shape with the effective width Gamma(epsilon) which diverges at the Fermi level.

Impurity scattering in Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Bose-Einstein condensate in a quartic potential:static and dynamic properties

In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.

Catching transcriptional regulation by thermostatistical modeling

Gene expression is frequently regulated by multiple transcription factors (TFs). Thermostatistical methods allow for a quantitative description of interactions between TFs, RNA polymerase and DNA, and their impact on the transcription rates. We illustrate three different scales of the thermostatistical approach: the microscale of TF molecules, the mesoscale of promoter energy levels and the macroscale of transcriptionally active and inactive cells in a cell population. We demonstrate versatility of combinatorial transcriptional activation by exemplifying logic functions, such as AND and OR gates. We discuss a metric for cell-to-cell transcriptional activation variability known as Fermi entropy. Suitability of thermostatistical modeling is illustrated by describing the experimental data on transcriptional induction of NF?B and the c-Fos protein.

Seminar 1 impurity in the tomonaga-luttinger model:a functional integral approach

This chapter explains a functional integral approach about impurity in the Tomonaga–Luttinger model. The Tomonaga–Luttinger model of one-dimensional (1D) strongly correlates electrons gives a striking example of non-Fermi-liquid behavior. For simplicity, the chapter considers only a single-mode Tomonaga–Luttinger model, with one species of right- and left-moving electrons, thus, omitting spin indices and considering eventually the simplest linearized model of a single-valley parabolic electron band. The standard operator bosonization is one of the most elegant methods developed in theoretical physics. The main advantage of the bosonization, either in standard or functional form, is that including the quadric electron–electron interaction does not substantially change the free action. The chapter demonstrates the way to develop the formalism of bosonization based on the functional integral representation of observable quantities within the Keldysh formalism.