Search results for "Fermi"
showing 10 items of 1388 documents
Electrons on a spherical surface: Physical properties and hollow spherical clusters
2012
We discuss the physical properties of a noninteracting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential, and its electric static polarizability. All these properties are discussed analytically as functions of the number $N$ of electrons. The trends obtained with increasing $N$ are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasispherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the definition of a scale-invariant distribution of magic n…
Dynamically screened vertex correction to $GW$
2020
Diagrammatic perturbation theory is a powerful tool for the investigation of interacting many-body systems, the self-energy operator $\mathrm{\ensuremath{\Sigma}}$ encoding all the variety of scattering processes. In the simplest scenario of correlated electrons described by the $GW$ approximation for the electron self-energy, a particle transfers a part of its energy to neutral excitations. Higher-order (in screened Coulomb interaction $W$) self-energy diagrams lead to improved electron spectral functions (SFs) by taking more complicated scattering channels into account and by adding corrections to lower order self-energy terms. However, they also may lead to unphysical negative spectral f…
Variation of physical constants and electron–positron oscillations: Zitterbewegung in a plane wave
2021
The space and time dependence of physical constants is currently a debated issue for experimental findings, and theoretical reasons seem to indicate that this is not a mere speculative possibility. The paper provides a relativistic description of a free fermion evolving under the assumption of temporal variation of the physical constants. The assumed generalisation of the Dirac equation is particularly simple and permits a grouping of the constants in one single parameter and a consequent agile treatment of the problem. The form of the equations suggests a rescaling of the temporal coordinate $$x^0=ct$$ which allows a plane wave solution. Two are the main results of the treatment. First, th…
Exchange and correlation energy functionals for two-dimensional open-shell systems
2009
We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation holes, respectively, and assuming proportionality between their characteristic sizes. The electron current and spin are explicitly taken into account, so that the resulting functionals are suitable to deal with systems exhibiting orbital currents and/or spin polarization. Our numerical results show that in finite systems the proposed functionals outperform the standard two-dimensional local spin-density approximation, still performing well also in the importa…
Non-cooperative Equilibria of Fermi Systems With Long Range Interactions
2019
We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, we give a first answer to an old open problem in mathematical physics - first addressed by Ginibre in 1968 within a different context - about the validity of the so-called Bogoliubov approximation on the level of states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, our method provides a systematic way to study all its correlation functions and can thus be used to analyze the physics of long range interactions. Furthermore, we show tha…
Simultaneous time-optimal control of the inversion of two spin-12particles
2010
We analyze the simultaneous time-optimal control of two-spin systems. The two noncoupled spins, which differ in the value of their chemical offsets, are controlled by the same magnetic fields. Using an appropriate rotating frame, we restrict the study to the case of opposite shifts. We then show that the optimal solution of the inversion problem in a rotating frame is composed of a pulse sequence of maximum intensity and is similar to the optimal solution for inverting only one spin by using a nonresonant control field in the laboratory frame. An example is implemented experimentally using nuclear magnetic resonance techniques.
Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics
1997
Density-functional theory is applied to compute the ground-state energies of quantum hard-sphere solids. The modified weighted-density approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis and the Feynman approximation, connecting the static structure factor and the linear response function. The Fermi liquid is treated by the Wu-Feenberg cluster expansion, which approximately accounts for the effects of antisymmetry. Liquid-solid transitions for both systems are obtained with no adjustment of input data. Limited …
Future $\nu_\tau$ Oscillation Experiments and Present Data
1995
Our goal in this paper is to examine the discovery potential of laboratory experiments searching for the oscillation $\nu_\mu(\nu_e) \rightarrow \nu_\tau$, in the light of recent data on solar and atmospheric neutrino experiments, which we analyse together with the most restrictive results from laboratory experiments on neutrino oscillations. In order to explain simultaneously $all$ present results we use a four-neutrino framework, with an additional sterile neutrino. Our predictions are rather pessimistic for the upcoming experiments NOMAD and CHORUS, which, we find, are able to explore only a small area of the oscillation parameter space. On the other hand, the discovery potential of futu…
The leading disconnected contribution to the anomalous magnetic moment of the muon
2014
The hadronic vacuum polarization can be determined from the vector correlator in a mixed time-momentum representation. We explicitly calculate the disconnected contribution to the vector correlator, both in the $N_f = 2$ theory and with an additional quenched strange quark, using non-perturbatively $O(a)$-improved Wilson fermions. All-to-all propagators are computed using stochastic sources and a generalized hopping parameter expansion. Combining the result with the dominant connected contribution, we are able to estimate an upper bound for the systematic error that arises from neglecting the disconnected contribution in the determination of $(g-2)_\mu$.
Evidence for Strange-Quark Contributions to the Nucleon’s Form Factors atQ2=0.108 (GeV/c)2
2005
We report on a measurement of the parity violating asymmetry in the elastic scattering of polarized electrons off unpolarized protons with the A4 apparatus at MAMI in Mainz at a four momentum transfer value of ${Q}^{2}=0.108\text{ }(\mathrm{GeV}/c{)}^{2}$ and at a forward electron scattering angle of $30\ifmmode^\circ\else\textdegree\fi{}l{\ensuremath{\theta}}_{e}l40\ifmmode^\circ\else\textdegree\fi{}$. The measured asymmetry is ${A}_{LR}(\stackrel{\ensuremath{\rightarrow}}{e}p)=[\ensuremath{-}1.36\ifmmode\pm\else\textpm\fi{}0.29(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.13(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. The expectation from the standard model as…