Oscillation collective

When the size of metals is comparable or smaller than the electron mean free path, for example in metal nanoparticles, then the motion of electrons becomes limited by the size of the nanoparticle and interactions are expected to be mostly with the surface. This gives rise to surface plasmon resonance effects, in which the optical properties are determined by the collective oscillation of conduction electrons resulting from the interaction with light. Plasmonic metal nanoparticles and nanostructures are known to absorb light strongly, but they typically are not or only weakly luminescent [22-24]. 

When a metallic probe, which has a nanometric tip, is illuminated with an optical field, conductive free electrons collectively oscillate at the surface of the metal (Figure 10.3). The quantum of the induced oscillation is referred to as surface plas-mon polariton (SPP) (Raether 1988). The electrons (and the positive charge) are concentrated at the tip apex and strongly generate an external electric field. Photon energy is confined in the local vicinity of the tip. Therefore, the metallic tip works as a photon reservoir. 

Vp(fO is peaked at the surface. Many collective oscillations manifest themselves as predominantly surface modes. As a result, already one separable term generating by (74) usually delivers a quite good description of collective excitations like plasmons in atomic clusters and giant resonances in atomic nuclei. The detailed distributions depends on a subtle interplay of surface and volume vibrations. This can be resolved by taking into account the nuclear interior. For this aim, the radial parts with larger powers and spherical Bessel functions can be used, much similar as in the local RPA [24]. This results in the shift of the maxima of the operators (If), (12) and (65) to the interior. Exploring different conceivable combinations, one may found a most efficient set of the initial operators. 

Note that there is no bulk absorption band in aluminum corresponding to the prominent extinction feature at about 8 eV. Indeed, the extinction maximum occurs where bulk absorption is monotonically decreasing. This feature arises from a resonance in the collective motion of free electrons constrained to oscillate within a small sphere. It is similar to the dominant infrared extinction feature in small MgO spheres (Fig. 11.2), which arises from a collective oscillation of the lattice ions. As will be shown in Chapter 12, these resonances can be quite strongly dependent on particle shape and are excited at energies where the real part of the dielectric function is negative. For a metal such as aluminum, this region extends from radio to far-ultraviolet frequencies. So the... 

Ions in the lattice of a solid can also partake in a collective oscillation which, when quantized, is called a phonon. Again, as with plasmons, the presence of a boundary can modify the characteristics of such lattice vibrations. Thus, the infrared surface modes that we discussed previously are sometimes called surface phonons. Such surface phonons in ionic crystals have been clearly discussed in a landmark paper by Ruppin and Englman (1970), who distinguish between polariton and pure phonon modes. In the classical language of Chapter 4 a polariton mode is merely a normal mode where no restriction is made on the size of the sphere pure phonon modes come about when the sphere is sufficiently small that retardation effects can be neglected. In the language of elementary excitations a polariton is a kind of hybrid excitation that exhibits mixed photon and phonon behavior. 

It is theoretically predicted that the formation of the breather is accompanied by the collective oscillation of the bond-length, which can be detected in the pump-probe experiment as modulation of the instantaneous vibrational frequencies. The simulation of a frequency distribution of the vibrational frequencies and a spectrogram was made with a modulation period of 44-fs and a modulation duration time of 50-fs. The evidence of the modulation appears in the spectrogram in the shape of satellite-bands S , S and D , D on both sides of the main vibrational modes S and D, respectively with the same separation. These sidebands do not appear in cis-rich samples. These results clearly suggests that the unidentified... 

Here p is the frequency of plasmon oscillations in a system of free electrons (3.7). The oscillator strengths ft introduced previously differ from the usual fm (see Section IV) in their normalization (Efl, / = 1). A method for calculating the thus defined oscillator strengths from experimental values of e2 is presented in Ref. 89. Since the energy range essential for collective oscillations is ho> < 30 eV, the electrons of inner atomic shells can be disregarded. Thus, the value of ne is determined by the density of valence electrons only, and only the transitions of these electrons should be taken into account in the sum over i in formula (3.15). A convenient formula for calculating the frequencies molecular liquids is presented in ref. 89 ... 

As an example, let us consider liquid water (Fig. 8). The highest oscillator strength, fx = 0.43, corresponds to the transition ha>x = 13.5 eV. The peak the energy-loss function Im [-l/e(w)] has around 21 eV is of plasmon nature, that is, corresponds to longitudinal collective oscillations... 

As far back as 1960, Fano299 had pointed out the two possible reasons for delocalization of the energy absorbed by a medium. The first one has to do with the quantum-mechanical nature of microparticles the second one is connected with the possibility of excitation of plasmon-type collective oscillations.92... 

As for delocalization due to collective oscillations, the very existence of the latter in molecular media has been the subject of discussion for quite a long time (see Refs. 4 and 25). Later it was established that, in a molecular medium, too, fast moving charged particles can induce states of collective nature (see Section III.C). Let us now consider both of these reasons in more detail. 

Analytical results are possible if we assume collective oscillations of the peptide elements, e.g., F(t) = Acos(interaction center undergoes local thermal fluctuations, represented by mutually uncorrelated white noise of intensity a2 fi(t) = where = u2[Pg.379]

In order to interpret the results of our experiments, optimal-control calculations were performed where a GA controlled 40 independent degrees of freedom in the laser pulses that were used in a molecular dynamics simulation of the laser-cluster interactions for Xejv clusters with sizes ranging from 108 to 5056 atoms/cluster. These calculations, which are reported in detail elsewhere [67], showed optimization of the laser-cluster interactions by a sequence of as many as three laser pulses. Detailed inspection of the simulations revealed that the first pulse in this sequence initiates the cluster ionization and starts the expansion of the cluster, while the second and third pulse optimize two mechanisms that are directly related to the behaviour of the electrons in the cluster. We consistently observe that the second pulse in the three-pulse sequence arrives a time delay where the conditions for enhanced ionization are met. In other words, the second pulse arrives at a time where the ionization of atoms is assisted by the proximity of surrounding ions. The third peak is consistently observed at a delay where the collective oscillation of the quasi-free electrons in the cluster is 7t/2 out of phase with respect to the driving laser field. For a driven and damped oscillator this phase-delay represents an optimum for the energy transfer from the driving force to the oscillator. 

This detector is based on the collective oscillations of the free electron plasma at a metal surface. Typically a prism is coated with a metal film and the film coated with a chemically selective layer. The surface is illuminated by a laser and the amount of material adsorbed by the coating affects the angle of the deflected beam. This platform is theoretically similar in sensitivity to a quartz crystal microbalance. This is another platform whose selectivity is based on the coating. The typical coating is using bound antibodies thus, this device becomes a platform for immuno-sensors (12). 

Although this is phrased in the language of a single oscillating particle, it is equivalent to the equation for normal modes, where kh, bd, me, and e are effective quantities describing entire collective oscillations. There are several special cases of e2/(/ch - i(obi — co2me) for certain further idealized forms of response. 

The vibronic exciton is a collective oscillation of the crystal where vibronic molecular states (e.g. electronic and molecular excitations) stay on the same site. To the first order of the perturbations Jnm the vibron dispersion is given by... 

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