GCM analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of ²⁰⁸Pb. In this study, we rely on a coherent approach based on the Generator Coordinate Method (GCM) including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF + BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations. Received: 31 May 2001 / Accepted: 23 August 2001     

Interband collective electronic excitations in resonant Raman scattering of two-subband quantum wires

Using the bosonization technique, a theory for the collective excitations of the interacting electrons in quantum wires with two subbands occupied is developed. The dispersion relations for the inter-subband charge and spin density excitations are determined. The results are used to interpret the features observed in recent measurements of the Raman spectra of AlGaAs/GaAs quantum wires, particularly for photon energies near band gap resonance. It is shown that peaks previously identified as “single particle excitations” are signatures of higher order collective spin density excitations. Predictions about the observability of the interband modes are made. Received 8 February 1999     

SU(2) gauge theory of the Hubbard model: emergence of an anomalous metallic phase near the Mott critical point

We propose one possible mechanism for an anomalous metallic phase appearing frequently in two spatial dimensions, that is, local pairing fluctuations. Introducing a pair-rotor representation to decompose bare electrons into collective pairing excitations and renormalized electrons, we derive an SU(2) gauge theory of the Hubbard model as an extended version of its U(1) gauge theory. Since our effective SU(2) gauge theory admits two kinds of collective bosons corresponding to pair excitations and density fluctuations, respectively, an intermediate phase appears naturally between the spin liquid Mott insulator and Fermi liquid metal of the U(1) gauge theory, characterized by softening of density-fluctuation modes as the Fermi liquid, but gapping of pair-excitation modes. We show that this intermediate phase is identified with an anomalous metallic phase because there are no electronlike quasiparticles although it is metallic.     

Collective surface plasmon resonance coupling in silver nanoshell arrays

Collective surface plasmon resonance (SPR) excitations in an ordered array of silver nanoshells have been theoretically studied using generalized Mie theory. Near- and far-field radiative coupling between the nanoshells in the array result in a non-monotonic shift of the collective SPR band. When the distance between the shells in the array approaches that of the collective SPR wavelength, we observe narrowing of the collective SPR band due to constructive interference between the scattered electric field from the particles in the array. Further increase of the distance between the nanoshells in the array leads to destructive interference and broadening of the collective SPR band.     

Collective electronic excitations in a semiconductor superlattice in the Landau and Wannier-Stark ladder regime

Using a mean-field approximation, we have developed a systematic treatment of collective electronic modes in a semiconductor superlattice (SL) in the presence of strong electric and magnetic fields parallel to the SL axis. The spectrum of collective modes with zero wavevector along the SL axis is shown to consist of a principle magnetoplasmon mode and an infinite set of Bernstein-like modes. For non-zero wavevector along the SL axis, in addition to the cyclotron modes, extra collective modes are found at the frequencies |Nω _c±Mω _s|, which we call cyclotron-Stark modes (ω _c and ω _s are respectively the cyclotron and Stark frequencies, N and M are integer numbers). The frequencies of the modes propagating in “oblique” direction with respect to the SL axis show oscillatory behavior as a function of electric field strength. All the modes considered have very weak spatial dispersion and they are not Landau damped. The specific predictions made for the dispersion relations of the collective excitations should be observable in resonant Raman scattering experiments. Received 29 August 2002 / Received in final form 25 February 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: 612033@inbox.ru     

Superfluid-Mott-Insulator Phase Transition Phases of Bosons in an and Collective Fluctuations in both Optical Lattice

The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean t~eld theory based on a constraint SU（3） pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mort phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.     

Dielectric properties of multiband electron systems II. Collective modes

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (q → 0), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In insulators there are only inter-band charge oscillations. If atomic dipolar transitions are allowed, the corresponding collectivemodes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak on-site interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent inter-band electron-hole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail. In conductors the intra-band charge fluctuations give rise to plasmons. If the atomic dipolar transitions are forbidden, the coupling of inter-band collective modes and plasmons tends to zero as q → 0. On the contrary, in dipolar conductors this coupling is strong and nonperturbative, due to the long range monopole-dipole interactions between intra-band and inter-band charge fluctuations. The resulting collective modes are hybrids of intra-band plasmons and inter-band dipolar oscillations. It is shown that the frequency of the lower hybridized longitudinal mode is proportional to the frequency of the transverse dipolar mode when the latter is small. The dielectric instability in a multi-band conductor is therefore characterized by the simultaneous softening of a transverse and a longitudinal mode, which is an important, directly measurable consequence of the present theory.     

Nuclear compressibilities

We discuss the relation between the compressibility of nuclear matter and the frequencies of the collective monopole vibrations of nuclei. We analyse some of the problems which arise when one extrapolates from properties of finite nuclei to those of infinite nuclear matter. The best way to perform this extrapolation is to use a theory capable of describing both systems on the same footing. Self-consistent calculations using phenomenological effective interactions realize such a program. The general properties of these effective interactions are discussed. The theory we used is described; we emphasize that it accounts for both the properties of the ground states of nuclei and the small amplitude collective vibrations. Simple models of compression modes in infinite nuclear matter and in nuclei are presented; they illustrate various features of the collective modes in both systems. In particular we discuss the role of the shell structure and the effects of the nuclear surface. Results of extensive self-consistent calculations of the breathing mode of nuclei are presented and many features of the mode are analyzed. The role of the single particle spectrum on the frequencies of the collective modes is studied. Finally we briefly review the experimental situation on the monopole excitations of nuclei.We show that experimental data are compatible with a well defined value of the compression modulus of nuclear matter: K_∞ = 210±30 MeV.     

Collective excitations in fast ion conductor superlattices

Within the framework of the electromagnetic theory, the collective modes in the superlattice system composed of superionic conductors and ionic crystals are studied. The superionic conductor is described by the hydrodynamical model in which the anion cage is immersed in the cation liquid. The behavior of the modes are analysed in terms of the coupling strength between excitations pertaining to different layers. The coupling strength is controlled by varying the slab thicknesses. An interesting behavior in which the diffusion mode transforms to the relaxation mode when the coupling strength is varied from strong to weak is obtained. Also, the effect of the coupling strength on the acoustical and optical modes are shown.     

On the contribution of nearly critical spin and charge collective modes to the Raman spectra of high-Tc cuprates

We discuss how Raman spectra are affected by nearly critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We show that specific fingerprints of nearly critical collective modes can indeed be observed in Raman spectra and that the selectivity of Raman spectroscopy in momentum space may also be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-T_c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover, spin modes should be more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuate with high frequency.     

Landau Damping of Collective Modes in a Disc-Shaped Bose-Einstein Condensate

We investigate the Landau damping of collective modes in an anisotropic Bose Einstein condensate （BEC）, Based on divergence-free analytical solutions for the ground state wavefunction of the condensate and all eigenvalues and eigenfunctions for thermal excited quasiparticles, we make a detailed analytical calculation on coupling matrix elements. We evaluate the Landau damping of a quadrupole collective mode in the BEC with a disc-shaped trap and discuss its dependence on temperature and particle number of the system.     

The role of layer-thickness deviation in dispersion and structure of plasmons in finite superlattices

We study the effects of layer thickness variations on the collective plasmon excitation modes of finite superlattices. Unlike other symmetry lowering mechanisms, thickness variation does not strongly localize the surface modes. We find that the reason for this insensitivity lies in the fact that the collective modes of a given finite structure must evolve continuously from the single-finite-superlattice at zero thickness deviation into modes of a pair of uncoupled finite structures at large thickness variation. We also show that this behavior is analogous to the evolution of molecular orbitals from atomic orbitals as the internuclear separation is reduced, in contrast to the analogy of the superlattice modes as a stack of coupled quantum wells. This emphasizes the difference between the electromagnetic symmetry of the finite superlattice and the structural symmetry. Received 16 April 2001 and Received in final form 6 July 2001     

Towards a theory of superconductivity based on collective Cooper pairs

Superconductivity could be seen as a Bose-Einstein condensation (BEC) of Cooper pairs. However, the creation and annihilation operators of Cooper pairs do not satisfy the bosonic commutation relations and then, the mentioned viewpoint has a weakness in its foundation. In this work, we introduce the concept of collective Cooper pairs (CCP) as linear combinations of Cooper pairs and prove their bosonic nature at the dilute limit. This bosonic nature is given rise from their diffuse character on the Cooper pairs, which permits the accumulation of many collective pairs at a single quantum state. Moreover, the superconducting ground state proposed by Bardeen, Cooper and Schrieffer (BCS) can be written in terms of these collective Cooper pairs, which means that the BCS theory is consistent with a possible BEC theory of superconductivity based on collective Cooper pairs. Finally, we calculate the energy spectra and the BEC critical temperature of CCP.     

Spectroscopy of soft modes and quantum phase transitions in coupled electron bilayers

Strongly correlated two-dimensional electrons in coupled semiconductor bilayers display remarkable broken symmetry many-body states under accessible and controllable experimental conditions. In the case of continuous quantum phase transitions (QPTs), soft collective modes drive the transformations that link distinct ground states of the electron double layers. In this paper we consider results showing that resonant inelastic light scattering methods detect soft collective modes of the double layers and probe their evolution with temperature and magnetic field. The light scattering experiments offer venues of research of fundamental interactions and continuous QPTs in low-dimensional electron liquids.     

Dynamical response functions in correlated fermionic systems

Response functions in nuclear matter at finite temperature are considered beyond the usual Hartree-Fock plus random phase approximation (RPA) scheme. The contributions due to the propagator for the dressed nucleons and the corresponding vertex corrections are treated in a consistent way. For that purpose a semi-realistic Hamiltonian is developed with parameters adjusted to reproduce the nucleon self-energy as derived from realistic nucleon-nucleon interactions. For a scalar residual interaction the resulting response functions are very close to the RPA response functions. However, the collective modes, if present, get an additional width due to the coupling to multi-pair configurations. For isospin-dependent residual interactions we find strong modifications of isospin response functions due to multi-pair contributions in the response function. Such a modification can lead to the disappearance of collective spin or isospin modes in a correlated system and shall have an effect on the absorption rate of neutrinos in nuclear matter.     

Quantization Scheme of Surface Plasmon Polaritons in Two-Dimensional Helical Liquids

The collective modes of two-dimensional helical electron gases interacting with light have been studied in an extended random phase approximation.An inverse operator transformation that interprets electron oscillations and photons with quasi particles is developed.Because photons are initially included in the model,one can directly derive and compare the static and radiation(or vector)Helds for the excited collective modes.Unlike the traditional quantization scheme that the electron oscillation's contribution is totally hidden in the dielectric function,we can directly investigate their roles when the collective modes interact with other particles.As an example,we find an additional term which plays an important role at small distance arising from electron exchanging effect when the collective modes couple to emitters.     

Spin-one color superconductors: Collective modes and effective Lagrangian

We investigate the collective excitations in spin-one color superconductors. We classify the Nambu–Goldstone modes by the pattern of spontaneous symmetry breaking, and then use the Ginzburg–Landau theory to derive their dispersion relations. These soft modes play an important role for the low-energy dynamics of the system such as the transport phenomena and hence are relevant for late-stage evolution of neutron stars. In the case of the color-spin-locking phase, we use a functional technique to obtain the low-energy effective action for the physical Nambu–Goldstone bosons that survive after gauging the color symmetry.     

Structural-scale transitions in solids with defects and symmetry aspects of field theory

Relaxation and failure mechanisms in solids with mesoscopic defects are considered in the context of a specific class of critical phenomena—structural-scaling transitions. The association of collective modes in mesodefect ensembles with gauge invariance in string theory is discussed. Statistical and thermodynamic properties of deformed solids are studied in relation to dynamics of collective modes of defects.