Collective Excitation Frequencies Research Articles

Collective excitation frequencies of bosons in a parabolic potential with interparticle harmonic interactions

The fact that the ground-state first-order density matrix for bosons in a parabolic potential with interparticle harmonic interactions is known in exact form is here exploited to study collective excitations in the weak-coupling regime. Oscillations about the ground-state density are treated analytically by a linearized equation of motion which includes a kinetic energy contribution. We show that the dipole mode has the frequency of the bare trap, in accord with the Kohn theorem, and derive explicit expressions for the frequencies of the higher-multipole modes in terms of a frequency renormalized by the interactions.

Semiclassical Corrections to the Oscillation Frequencies of a Trapped Bose-Einstein Condensate

The oscillation frequencies of collective excitations of a trapped Bose-Einstein condensate, when calculated in the mean-field approximation and in the Thomas-Fermi limit, are independent of the scattering length $a$. We calculate the leading corrections to the frequencies from quantum fluctuations around the mean field. The semiclassical correction is proportional to ${N}^{1/5}{a}^{6/5}$, where $N$ is the number of atoms in the condensate. The correction is positive semidefinite and is zero for surface modes whose eigenfunctions have a vanishing Laplacian. The shift in the frequency of the lowest quadrupole mode for an axially symmetric trap is large enough that it should be measurable in future experiments.

Oscillation frequencies for a Bose condensate in a triaxial magnetic trap

We investigate the dynamics of a Bose condensate, interacting with either repulsive or attractive forces, confined in a fully anisotropic harmonic potential. The (3 + 1)-dimensional Gross-Pitaevskii equation is integrated numerically to derive the collective excitation frequencies, showing a good agreement with those calculated with a variational technique.

Excitations of a Bose-condensed gas in anisotropic traps

We investigate the zero-temperature collective excitations of a Bose-condensed atomic gas in anisotropic parabolic traps. The condensate density is determined by solving the Gross-Pitaevskii (GP) equation using a spherical harmonic expansion. The GP eigenfunctions are then used to solve the Bogoliubov equations to obtain the collective excitation frequencies and mode densities. The frequencies of the various modes, classified by their parity and the axial angular momentum quantum number, m, are mapped out as a function of the axial anisotropy. Specific emphasis is placed upon the evolution of these modes from the modes in the limit of an isotropic trap.

Approximate calculation of the collective excited states of a cytosine stack

Abstract Using the sum rules of oscillator strengths of different individual transitions of different symmetry, a simple algebraic equation for the frequency of the collective excitation of the π-system, of only the σ electrons, and finally for the whole valence electron system of a cytosine stack was derived. The input data (besides the geometry of DNA B and of the number of different types of electrons in cytosine) for the individual valence and core excitations were estimated on the basis of ab initio Hartree—Fock band structures of a cytosine stack. These bands were corrected for correlation at the MP2 level and the results of an intermediate exciton calculation were taken into account. The obtained frequencies of the different collective excitations (plasmons) are in fairly good agreement with the results of energy loss experiments.

Optical excitation in small ionized sodium clusters: closed-shell and open-shell systems

Photoabsorption cross-section profiles have been obtained for closed-shell and open-shell ionized size-selected sodium clusters Na + 9, Na + 21 and Na + 11. The spill-out of the valence electron cloud explains the red-shifted collective excitation frequency with regard to the Mie frequency. Quantum-mechanical calculations may give energy positions of the resonant structures consistent with the experiment. However, the absolute parameters of the profiles suggest that some oscillator strength is missing.

Elementary excitation spectrum of one-dimensional electron systems in confined semiconductor structures: Zero magnetic field.

We study theoretically the elementary excitation spectrum in various one-dimensional electron systems in the absence of a magnetic field. We first calculate the elementary excitations in a single quantum wire under the random-phase approximation. We find that the intersubband collective excitation frequency can be 5--6.5 times higher than the corresponding single-particle excitation energy due to a large depolarization shift. Next, we calculate the plasmon excitation energy of a double-layered quantum-wire system. Our result shows that the resonance peak splits due to the Coulomb interaction between electrons in different layers. We also study the elementary excitations in one-dimensional lateral quantum-wire superlattices. We include the Coulomb interaction between electrons in different wires and allow tunneling between neighboring wires. Finally, we calculate the spectral weights of the elementary excitations of both a single quantum wire and quantum-wire superlattices for various parameter values. We compare our results with recent experiments and find good agreement.

Plasmons in a superlattice with periodic defects.

The plasmon excitation spectrum for a multiple-quantum-well superlattice with rectangular defect barriers in each quantum well is calculated in the random-phase approximation. It is demonstrated that both the intersubband and the intrasubband plasma frequencies can be effectively tuned subject to variations of the parameters characterizing the defect barrier in the quantum well, such as the barrier width, its height, and its position in the quantum well. For example, by varying the defect barrier width from 0 to about 40 \AA{}, an order-of-magnitude increase is obtained in the intersubband plasma frequency, with corresponding changes in the intrasubband mode. It is shown that the variations of the collective excitation frequencies follow closely the electron energy subband structures and are therefore equally tunable via the defect barrier.

Optical effects of multipole interaction in aggregated structures: Rigorous scattering solution for a periodic chain of cylinders.

Recent experimental studies on the optical properties of gold colloidal aggregates have found interesting characteristics, such as double absorption peaks and enhanced depolarized scattering, that are not explainable in terms of traditional mean-field theories. Based on the observation that the aggregate clusters have a locally chainlike structure of touching spheres, a simple model for the calculation of their absorption and scattering characteristics is proposed that consists of a randomly oriented chain of cylindrical particles under the excitation of an electromagnetic field. The consideration of cylindrical geometry considerably simplifies the mathematics while retaining the essential physics of capacitive coupling between the particles. In the optical frequency regime, a rigorous scattering solution for the model shows that, besides the single-particle Mie resonance, there exists a low-frequency collective excitation arising from the anisotropic, high-multipole interactions between the metal particles. It results in a second absorption peak whose peak position is controlled by the capacitive coupling between the adjacent particles. Both the polarized and the depolarized scattering also show accompanying increases at the collective excitation frequency. Good agreement is found between the calculated results and the experimental observations.

Search for RPA instabilities in nuclear and neutron matter

Green’s function techniques are used to formulate the long-wavelength limit for the dispersion relation for collective excitation frequencies of a many-fermion system ground state in the random-phase approximation. Explicit account of spin and isospin degrees of freedom lead to four longitudinal modes: a spatial density fluctuation (which is essentially «zero sound»), a spin density variation, an isospin density one (the Goldhaber-Teller mode) and a coupled spin-isospin density mode. Their stability (reality of frequency) is studied for nuclear and neutron matter using several realistic \(\mathcal{N}--\bar {\mathcal{N}}\) potentials including the Reid soft-core potential, for which all modes turn out to be stable. Counter examples are given which prove instability where RPA predicts stability.