EMC 2008 14th European Microscopy Congress 1–5 September 2008, Aachen, Germany
ABSTRACT In this communication we show results on the angular dependence of scattering for plasmo... more ABSTRACT In this communication we show results on the angular dependence of scattering for plasmons excitations (bulk) in the case of an interacting electron gas, which can serve as a model system for simple metals. We make use of energy filtered diffraction pattern from TEM to collect the signal as a function of momentum transfer. Figure 1 shows the scattering profile at energy loss centered on the bulk plasmon in aluminum. A first cutoff at θ E, due to the dominant Lorentzian term in the angular part, and a second smooth cut-off at θ C are visible. The second cut-off is due to the damping of the plasmon by particle-hole excitations [1]. Figure 1 shows the enhancement in the visibility of θ C by removing the quasi-elastic scattering by means of a deconvolution with a diffraction pattern filtered around the zero loss peak.
Some illustrative examples are given of the use of vectorization in practical circumstances, with... more Some illustrative examples are given of the use of vectorization in practical circumstances, with working subroutines and programs, taken from existing scalar programs of general use. Despite the lack of a vector variable in the standard FORTRAN language, several examples are given of global vectorization, which is beyond the capability of any autovectorizer.
On the basis of the Hohenberg‐Kohn theorem, an effective exchange and correlation potential is de... more On the basis of the Hohenberg‐Kohn theorem, an effective exchange and correlation potential is derived for nearly free electron metals. Using the one particle approach, derived by Kohn and Sham, on variational grounds, an expansion of the total energy with respect to deviations from the uniform density allows for calculating the effective potential.
The ground-state energy of a three-dimensional polaron gas in a magnetic field is investigated. A... more The ground-state energy of a three-dimensional polaron gas in a magnetic field is investigated. An upper bound for the ground-state energy is derived within a variational approach which is based on a many-body generalization of the Lee-Low-Pines transformation. The basic contributing ingredients found are the ground-state energy and the static structure factor of the homogeneous electron gas in a magnetic field. Both these quantities are derived in the Hartree-Fock approximation. The resulting ground-state energy of the polaron gas is analyzed as a function of the electron density and of the magnetic field strength.
The ground state energy of an N-polaron system confined to a quantum dot with a neutralizing back... more The ground state energy of an N-polaron system confined to a quantum dot with a neutralizing background charge is investigated within an all-coupling many-body path-integral variational principle taking into account both Fermi statistics of polarons and the electron-electron interaction. The treatment of the ground-state energy is performed for both closed-shell and open-shell systems. The electron-phonon contribution to the ground-state energy as a function of the number of fermions demonstrates a trend to a constant value when increasing N. For a finite number of polarons, the dependencies of the ground-state energy and of the polaron contribution on the parameter rs^*, which determines the average fermion density in a quantum dot, are very similar to those for a polaron gas in bulk. Herefrom, we can conclude that the ground-state properties of a polaron gas in bulk can be qualitatively described using a model of a finite number of polarons in a confinement potential provided by a...
The onset of Bose-Einstein condensation in a 2D gas of bosons in a parabolic confinement potentia... more The onset of Bose-Einstein condensation in a 2D gas of bosons in a parabolic confinement potential is investigated. For such a system of non-interacting bosons, both the grand-canonical and the canonical partition function are calculated. The canonical partition function of a system of harmonically interacting bosons in 2D is obtained analytically. Both in the case of interacting and of non-interacting bosons, a distinct peak in the specific heat is found at a critical temperature and the dependence of this critical temperature on the number of particles and on the interparticle interaction strength is investigated.
We propose a conceptually easy and relatively straigthforward numerical method for calculating th... more We propose a conceptually easy and relatively straigthforward numerical method for calculating the groundstate properties of many-particle systems based on the Hohenberg-Kohn theorems. In this "density-functional Monte Carlo" method a direct numerical minimization of the energy functional is performed by a Monte Carlo algorithm in which the density is simulated by a distribution of Bernoulli walkers. The total number of particles is conserved by construction, unlike for other implementations of density-functional theory. The feasibility of the method is illustrated by applying it to a nanoshell.
F. BROSENS (a), J. CORNELIS (b), D. C. WALLACE (a), and J. T. DEVREESE (a)4) I n the central pote... more F. BROSENS (a), J. CORNELIS (b), D. C. WALLACE (a), and J. T. DEVREESE (a)4) I n the central potential approximation, the first and second derivative of the two-body potential for metals in the atom positions can be calculated by inverting the eigenvalue equations for the phonons. The potential is obtained from a straightforward integration procedure. Explicit results for Na are reported, which fully reproduce the experimental phonon spectrum. In der Zentralfeldnaherung lassen sich die ersten und zweiten Ableitungen des Zwei-Korperpotentials fur Metalle in den Atomlagen durch Inversion der Eigenwertgleichungen fur die Phononen berechnen. Das Potential wird am einem einfachen Integrationsverfahren erhalten. Explizite Ergebnisse werden fur Na mitgeteilt, die das experimentelle Phononenspektrum vollstandig wiedergeben.
The dynamical exchange decoupling method for including exchange in the dielectric function of the... more The dynamical exchange decoupling method for including exchange in the dielectric function of the electron gas is applied to one-dimensional systems with a tight-binding energy band. Depending on the bandwidth and the position of the Fermi energy in the band, dynamical exchange effects are shown to have appreciable effects on the plasmon dispersion. For propagation of the plasmon along the strand axis, and in the long-wavelength limit, exchange effects drastically lower the slope of the plasmon dispersion. For non-parallel incidence, the exchange effects are less pronounced, and extended over a smaller wave vector region. Die dynamische Austauschentkopplungsmethode fur die Einbeziehung des Austauschs in die dielektrische Funktion des Elektronengases wird auf eindimensionale Systeme mit einem ,,tightbinding"-Energieband angewendet. Es wird gezeigt, daI3 abhjingig von der Breite der Binder und der Lage der Fermienergie im Band die dynamischen Austauscheffekte einen betrichtlichen Ein-flu13 auf die Plasmonendispersion haben. Fur die Ausbreitung eines Plasmons in Richtung der ,,Strand"-Achse und im Grenzfall lsnger Wellen erniedrigen die Austauscheffekte drastisch den h s t i e g der Plasmonendispersion. Fur nichtparallelen Einfall sind die Austauscheffekte geringer ausgepragt und uber einen kleineren Bereich des Wellenvektors ausgedehnt.
We find for the first time the ground state energy and the optical absorption spectra for N elect... more We find for the first time the ground state energy and the optical absorption spectra for N electrons (holes) interacting with each other and with the longitudinal optical (LO) phonons at an arbitrary electron-phonon coupling strength α in a parabolic confinement potential. A recently developed path integral formalism for identical particles is used in order to account for the fermion statistics. The approach is applicable to closed and open shells. Using an extension of the Jensen-Feynman variational principle, the ground state energy of the N-polarons system in a parabolic confinement potential is analyzed as a function of N and α. A ferromagnetic-to-nonmagnetic transition is shown to occur between states with different total spin of the system in the case of strong electron-phonon interaction. This transition is manifested through the optical absorption spectra and should be experimentally observable. Strong mixing between zero-phonon and one-phonon states is revealed in the optical absorption spectrum, when the confinement frequency parameter is in resonance with the LO phonon frequency ("confinement-phonon resonance"). Moments of the optical absorption spectra are calculated for a N-polaron system in a parabolic quantum dot.
The inequality derived by Ferrell for the ground-state energy of a Hamotonian depending linearly ... more The inequality derived by Ferrell for the ground-state energy of a Hamotonian depending linearly on a parameter is generalized for an arbitrary dependence on that parameter. It is shown that this inequality is satisfied under certain conditions for wave functions calculated by a variational principle. Using the generalized inequality, the ground-state energy of the bound Frohlich polaron is studied and regions in the plane of coupling constant (a,P) where the inequality is violated, are determined.
EMC 2008 14th European Microscopy Congress 1–5 September 2008, Aachen, Germany
ABSTRACT In this communication we show results on the angular dependence of scattering for plasmo... more ABSTRACT In this communication we show results on the angular dependence of scattering for plasmons excitations (bulk) in the case of an interacting electron gas, which can serve as a model system for simple metals. We make use of energy filtered diffraction pattern from TEM to collect the signal as a function of momentum transfer. Figure 1 shows the scattering profile at energy loss centered on the bulk plasmon in aluminum. A first cutoff at θ E, due to the dominant Lorentzian term in the angular part, and a second smooth cut-off at θ C are visible. The second cut-off is due to the damping of the plasmon by particle-hole excitations [1]. Figure 1 shows the enhancement in the visibility of θ C by removing the quasi-elastic scattering by means of a deconvolution with a diffraction pattern filtered around the zero loss peak.
Some illustrative examples are given of the use of vectorization in practical circumstances, with... more Some illustrative examples are given of the use of vectorization in practical circumstances, with working subroutines and programs, taken from existing scalar programs of general use. Despite the lack of a vector variable in the standard FORTRAN language, several examples are given of global vectorization, which is beyond the capability of any autovectorizer.
On the basis of the Hohenberg‐Kohn theorem, an effective exchange and correlation potential is de... more On the basis of the Hohenberg‐Kohn theorem, an effective exchange and correlation potential is derived for nearly free electron metals. Using the one particle approach, derived by Kohn and Sham, on variational grounds, an expansion of the total energy with respect to deviations from the uniform density allows for calculating the effective potential.
The ground-state energy of a three-dimensional polaron gas in a magnetic field is investigated. A... more The ground-state energy of a three-dimensional polaron gas in a magnetic field is investigated. An upper bound for the ground-state energy is derived within a variational approach which is based on a many-body generalization of the Lee-Low-Pines transformation. The basic contributing ingredients found are the ground-state energy and the static structure factor of the homogeneous electron gas in a magnetic field. Both these quantities are derived in the Hartree-Fock approximation. The resulting ground-state energy of the polaron gas is analyzed as a function of the electron density and of the magnetic field strength.
The ground state energy of an N-polaron system confined to a quantum dot with a neutralizing back... more The ground state energy of an N-polaron system confined to a quantum dot with a neutralizing background charge is investigated within an all-coupling many-body path-integral variational principle taking into account both Fermi statistics of polarons and the electron-electron interaction. The treatment of the ground-state energy is performed for both closed-shell and open-shell systems. The electron-phonon contribution to the ground-state energy as a function of the number of fermions demonstrates a trend to a constant value when increasing N. For a finite number of polarons, the dependencies of the ground-state energy and of the polaron contribution on the parameter rs^*, which determines the average fermion density in a quantum dot, are very similar to those for a polaron gas in bulk. Herefrom, we can conclude that the ground-state properties of a polaron gas in bulk can be qualitatively described using a model of a finite number of polarons in a confinement potential provided by a...
The onset of Bose-Einstein condensation in a 2D gas of bosons in a parabolic confinement potentia... more The onset of Bose-Einstein condensation in a 2D gas of bosons in a parabolic confinement potential is investigated. For such a system of non-interacting bosons, both the grand-canonical and the canonical partition function are calculated. The canonical partition function of a system of harmonically interacting bosons in 2D is obtained analytically. Both in the case of interacting and of non-interacting bosons, a distinct peak in the specific heat is found at a critical temperature and the dependence of this critical temperature on the number of particles and on the interparticle interaction strength is investigated.
We propose a conceptually easy and relatively straigthforward numerical method for calculating th... more We propose a conceptually easy and relatively straigthforward numerical method for calculating the groundstate properties of many-particle systems based on the Hohenberg-Kohn theorems. In this "density-functional Monte Carlo" method a direct numerical minimization of the energy functional is performed by a Monte Carlo algorithm in which the density is simulated by a distribution of Bernoulli walkers. The total number of particles is conserved by construction, unlike for other implementations of density-functional theory. The feasibility of the method is illustrated by applying it to a nanoshell.
F. BROSENS (a), J. CORNELIS (b), D. C. WALLACE (a), and J. T. DEVREESE (a)4) I n the central pote... more F. BROSENS (a), J. CORNELIS (b), D. C. WALLACE (a), and J. T. DEVREESE (a)4) I n the central potential approximation, the first and second derivative of the two-body potential for metals in the atom positions can be calculated by inverting the eigenvalue equations for the phonons. The potential is obtained from a straightforward integration procedure. Explicit results for Na are reported, which fully reproduce the experimental phonon spectrum. In der Zentralfeldnaherung lassen sich die ersten und zweiten Ableitungen des Zwei-Korperpotentials fur Metalle in den Atomlagen durch Inversion der Eigenwertgleichungen fur die Phononen berechnen. Das Potential wird am einem einfachen Integrationsverfahren erhalten. Explizite Ergebnisse werden fur Na mitgeteilt, die das experimentelle Phononenspektrum vollstandig wiedergeben.
The dynamical exchange decoupling method for including exchange in the dielectric function of the... more The dynamical exchange decoupling method for including exchange in the dielectric function of the electron gas is applied to one-dimensional systems with a tight-binding energy band. Depending on the bandwidth and the position of the Fermi energy in the band, dynamical exchange effects are shown to have appreciable effects on the plasmon dispersion. For propagation of the plasmon along the strand axis, and in the long-wavelength limit, exchange effects drastically lower the slope of the plasmon dispersion. For non-parallel incidence, the exchange effects are less pronounced, and extended over a smaller wave vector region. Die dynamische Austauschentkopplungsmethode fur die Einbeziehung des Austauschs in die dielektrische Funktion des Elektronengases wird auf eindimensionale Systeme mit einem ,,tightbinding"-Energieband angewendet. Es wird gezeigt, daI3 abhjingig von der Breite der Binder und der Lage der Fermienergie im Band die dynamischen Austauscheffekte einen betrichtlichen Ein-flu13 auf die Plasmonendispersion haben. Fur die Ausbreitung eines Plasmons in Richtung der ,,Strand"-Achse und im Grenzfall lsnger Wellen erniedrigen die Austauscheffekte drastisch den h s t i e g der Plasmonendispersion. Fur nichtparallelen Einfall sind die Austauscheffekte geringer ausgepragt und uber einen kleineren Bereich des Wellenvektors ausgedehnt.
We find for the first time the ground state energy and the optical absorption spectra for N elect... more We find for the first time the ground state energy and the optical absorption spectra for N electrons (holes) interacting with each other and with the longitudinal optical (LO) phonons at an arbitrary electron-phonon coupling strength α in a parabolic confinement potential. A recently developed path integral formalism for identical particles is used in order to account for the fermion statistics. The approach is applicable to closed and open shells. Using an extension of the Jensen-Feynman variational principle, the ground state energy of the N-polarons system in a parabolic confinement potential is analyzed as a function of N and α. A ferromagnetic-to-nonmagnetic transition is shown to occur between states with different total spin of the system in the case of strong electron-phonon interaction. This transition is manifested through the optical absorption spectra and should be experimentally observable. Strong mixing between zero-phonon and one-phonon states is revealed in the optical absorption spectrum, when the confinement frequency parameter is in resonance with the LO phonon frequency ("confinement-phonon resonance"). Moments of the optical absorption spectra are calculated for a N-polaron system in a parabolic quantum dot.
The inequality derived by Ferrell for the ground-state energy of a Hamotonian depending linearly ... more The inequality derived by Ferrell for the ground-state energy of a Hamotonian depending linearly on a parameter is generalized for an arbitrary dependence on that parameter. It is shown that this inequality is satisfied under certain conditions for wave functions calculated by a variational principle. Using the generalized inequality, the ground-state energy of the bound Frohlich polaron is studied and regions in the plane of coupling constant (a,P) where the inequality is violated, are determined.
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