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.     

Corrosion and erosion monitoring in plates and pipes using constant group velocity Lamb wave inspection

Recent improvements in tomographic reconstruction techniques generated a renewed interest in short-range ultrasonic guided wave inspection for real-time monitoring of internal corrosion and erosion in pipes and other plate-like structures. Emerging evidence suggests that in most cases the fundamental asymmetric A₀ mode holds a distinct advantage over the earlier market leader fundamental symmetric S₀ mode. Most existing A₀ mode inspections operate at relatively low inspection frequencies where the mode is highly dispersive therefore very sensitive to variations in wall thickness. This paper examines the potential advantages of increasing the inspection frequency to the so-called constant group velocity (CGV) point where the group velocity remains essentially constant over a wide range of wall thickness variation, but the phase velocity is still dispersive enough to allow accurate wall thickness assessment from phase angle measurements. This paper shows that in the CGV region the crucial issue of temperature correction becomes especially simple, which is particularly beneficial when higher-order helical modes are also exploited for tomography. One disadvantage of working at such relatively high inspection frequency is that, as the slower A₀ mode becomes faster and less dispersive, the competing faster S₀ mode becomes slower and more dispersive. At higher inspection frequencies these modes cannot be separated any longer based on their vibration polarization only, which is mostly tangential for the S₀ mode while mostly normal for the A₀ at low frequencies, as the two modes become more similar as the frequency increases. Therefore, we propose a novel method for suppressing the unwanted S₀ mode based on the Poisson effect of the material by optimizing the angle of inclination of the equivalent transduction force of the Electromagnetic Acoustic Transducers (EMATs) used for generation and detection purposes.     

Superfluidity and collective modes in Rashba spin–orbit coupled Fermi gases

We present a theoretical study of the superfluidity and the corresponding collective modes in two-component atomic Fermi gases with s$s$-wave attraction and synthetic Rashba spin–orbit coupling. The general effective action for the collective modes is derived from the functional path integral formalism. By tuning the spin–orbit coupling from weak to strong, the system undergoes a crossover from an ordinary BCS/BEC superfluid to a Bose–Einstein condensate of rashbons. We show that the properties of the superfluid density and the Anderson–Bogoliubov mode manifest this crossover. At large spin–orbit coupling, the superfluid density and the sound velocity become independent of the strength of the s$s$-wave attraction. The two-body interaction among the rashbons is also determined. When a Zeeman field is turned on, the system undergoes quantum phase transitions to some exotic superfluid phases which are topologically nontrivial. For the two-dimensional system, the nonanalyticities of the thermodynamic functions and the sound velocity across the phase transition are related to the bulk gapless fermionic excitation which causes infrared singularities. The superfluid density and the sound velocity behave nonmonotonically: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The three-dimensional system is also studied.     

Microscopic theory on the Raman spectra of transition metal dichalcogenides in CDW state

Microscopic mechanisms are clarified for Raman scattering of collective modes, i.e., amplitude and phase modes in the charge density wave (CDW) state of transition metal dichalcogenides. We study three phonon process in triple CDW state and effects of $\text{partial}$ destruction of the Fermi surface due to the phase transition. It has then been understood how both phase and amplitude modes are given Raman activity and how A-E splittings of both modes and the commensurability pinning of the phase mode are related to the three phonon process. We can also explain change of Raman intensity of the originally Raman active A_1g phonon mode at phase transition as interference between paramagnetic and diamagnetic contributions for 2HTaSe₂ as well as other materials.     

Collective mode dispersions of organic chain compounds

We investigate the collective mode dispersions for the tight-binding dielectric matrix with two one-dimensional electron bands per donor and acceptor chains, and the three-dimensional long-range Coulomb electron-electron interaction within the random phase approximation. The hybridized collective modes are the result of the strong coupling between the intraband plasmon and the interband dipolar modes due to strong dipole Coulomb interactions. Our calculations show the existence of the low-energy renormalized plasmon mode above the electron-hole quasi-continuum in the long wavelength limit. The obtained modes are brought into correspondence with the optical data of quasi-one-dimensional organic conductor tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ). Namely, the renormalized plasmon and the dipolar mode are assigned to the observed excitations at respective energy scales of roughly 10 meV and 0.75 eV, explaining why lower excitation is eliminated while higher excitation persists below the temperature of the Peierls phase transition.     

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.     

Elastic anomaly in K2ZnCl4 around the normal-incommensurate-commensurate phase transition points

The ultrasonic velocities in K₂ZnCl₄ were measured as functions of temperature. At the incommensurate-commensurate phase transition point the velocity of the c₅₅ mode showed a clear anomaly, whereas anomalies were hardly observable in all other modes. The results are analyzed in terms of a phenomenological theory.     

Spin-charge fluctuations in itinerant helical magnets

Using a generalized random phase approach quantum fluctuations beyond the helical mean-field states of the Hubbard model off half filling are discussed. The collective mode spectrum is shown to exhibit spin-charge mixing and is found to be strongly renormalized by coupling to low-energy incoherent particle-hole excitations. Results for the collective mode dispersion which displays a significant anisotropy are presented for selected helical phases. Moreover phase space regions of ‘missing’ modes are identified with a finite wave length instability of the helical states suggesting novel inhomogeneous phases of the doped Hubbard model. P.A.C.S. : 71.27.+a, 75.30.Fv, 75.40.Gb     

Dynamics of the collective spontaneous emission of two three-level atoms in a cavity

Based on the master equation for the density matrix, the collective spontaneous emission of two A-type three-level atoms interacting with two modes of a quantum electromagnetic field in a finite-Q cavity is studied. The evolution of the emission intensity for each mode is found for the case where both atoms are initially in the excited state.     

Variety of c-axis collective excitations in layered multigap superconductors

We present a dynamical theory for the phase differences along a stacked direction of intrinsic Josephson junctions (IJJ's) in layered multigap superconductors, motivated by the discovery of highly anisotropic iron-based superconductors with thick perovskite-type blocking layers. The dynamical equations describing ac and dc intrinsic Josephson effects peculiar to multigap IJJ's are derived, and collective Leggett mode excitations in addition to the Josephson plasma established in single-gap IJJ's are predicted. The dispersion relations of their collective modes are explicitly displayed, and the remarkable peculiarity of the Leggett mode is demonstrated.     

Collective motion of active Brownian particles in one dimension

We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with numerical simulations of the microscopic model.     

Very-short-wavelength collective modes in fluids

The existence of very-short-wavelength collective modes in fluids is discussed. These collective modes are the extensions of the five hydrodynamic (heat, sound, viscous) modes to wavelengths of the order of the mean free path in a gas or to a fraction of the molecular size in a liquid. They are computed here explicitly on the basis of a model kinetic equation for a hard sphere fluid. At low densities all five modes are increasingly damped with decreasing wavelength till each ceases to exist at a cutoff wavelength. At high densities the extended heat mode softens very appreciably for wavelengths of the order of the size of the particles and becomes a diffusion-like mode that persists till much shorter wavelengths than the other modes. Except for the shortest wavelengths these collective modes and in particular the heat mode dominate the dynamical structure factorS(k, ) for all densities. The agreement of the theory with experimentalS(k, ) of liquid Ar seems to imply that very-short-wavelength collective modes also occur in real fluids.     

Resonance attenuation of ultrasonic waves in a superconductor with a moving vortex structure

Equations describing the interaction of ultrasonic waves with a moving vortex structure are derived. The addition to attenuation and the relative change in the velocity of longitudinal ultrasonic waves due to this interaction are calculated. It is found that when a longitudinal ultrasonic wave propagates along the direction of motion of the vortex structure and the velocity V of the structure is equal to half the velocity of the wave, then anomalous acoustic attenuation occurs and the contribution from the ultrasound-vortex interaction to the velocity of the ultrasonic wave vanishes. It is shown that if the vortex structure moves at a sufficiently high velocity, then (in contrast to the case of the structure at rest) a weakly damping collective mode propagating with velocity 2V arises in the structure. It is this mode that is responsible for anomalous attenuation of longitudinal ultrasonic waves.     

Collective modes in asymmetric ultracold Fermi systems

We derive the long wavelength effective action for the collective modes in systems of fermions interacting via a short-range s-wave attraction, featuring unequal chemical potentials for the two fermionic species (asymmetric systems). As a consequence of the attractive interaction, fermions form a condensate that spontaneously breaks the U(1) symmetry associated with total number conservation. Therefore at sufficiently small temperatures and asymmetries, the system is a superfluid. We reproduce previous results for the stability conditions of the system as a function of the four-fermion coupling and asymmetry. We obtain these results analyzing the coefficients of the low energy effective Lagrangian of the modes describing fluctuations in the magnitude (Higgs mode) and in the phase (Nambu-Goldstone, or Anderson-Bogoliubov, mode) of the difermion condensate. We find that for certain values of parameters, the mass of the Higgs mode decreases with increasing mismatch between the chemical potentials of the two populations, if we keep the scattering length and the gap parameter constant. Furthermore, we find that the energy cost for creating a position dependent fluctuation of the condensate is constant in the gapped region and increases in the gapless region. These two features may lead to experimentally detectable effects. As an example, we argue that if the superfluid is put in rotation, the square of the radius of the outer core of a vortex should sharply increase on increasing the asymmetry, when we pass through the relevant region in the gapless superfluid phase. Finally, by gauging the global U(1) symmetry, we relate the coefficients of the effective Lagrangian of the Nambu-Goldstone mode with the screening masses of the gauge field.     

Guided wave dispersion curves for a bar with an arbitrary cross-section,a rod and rail example

Theoretical and experimental issues of acquiring dispersion curves for bars of arbitrary cross-section are discussed. Since a guided wave can propagate over long distances in a structure, guided waves have great potential for being applied to the rapid non-destructive evaluation of large structures such as rails in the railroad industry. Such fundamental data as phase velocity, group velocity, and wave structure for each guided wave mode is presented for structures with complicated cross-sectional geometries as rail. Phase velocity and group velocity dispersion curves are obtained for bars with an arbitrary cross-section using a semi-analytical finite element method. Since a large number of propagating modes with close phase velocities exist, dispersion curves consisting of only dominant modes are obtained by calculating the displacement at a received point for each mode. These theoretical dispersion curves agree in characteristic parts with the experimental dispersion curves obtained by a two-dimensional Fourier transform technique.     

Dual squeezed states in an atom-photon cluster and their manifestations

The general kinetic equation for an isolated two-level atom and a high-Q cavity mode in a heat bath exhibiting quantum correlations (entangled bath) is applied to the analysis of the squeezed states of the collective system. Two types of collective operators are introduced for the analysis: one is based on bosonic commutation relations, and the other, on the commutation relations of the algebra obtained by a polynomial deformation of the angular momentum algebra. On the basis of these relations, formulas for observables are constructed that identify squeezed states in the system. It is shown that, under certain conditions, the collective system exhibits dual squeezing within the relations for boson operators, as well as for the operators constructed from the angular momentum algebra. Such squeezing is demonstrated under a projective measurement of an atom and for an entanglement swapping protocol. In the latter case, when measuring two initially independent atomic systems, depending on the type of measurement, two cavity modes collapse into a nonseparable state, which is described either by a nonseparability relation based on boson operators or by a relation based on the operators of the algebra of the quasimomentum of the collective system consisting of these two modes.     

On the thermodynamics of phase transitions in metal hydrides

Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a particular phase transition in TiH _x , which can approximately be described as a second-order phase transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the density of H⁺ ions and of the distance between adjacent H⁺ ions. Moreover, as the system approaches the transition and the correlation radius increases, we show -with the help of statistical mechanics-that the statistical weight of modes involving a large number of H⁺ ions (‘collective modes’) increases sharply, in spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, the interaction of the H⁺ ions with collective modes makes a tiny suprathermal fraction of the H⁺ population appear. Our results hold for similar transitions in metal deuterides, too. A violation of an -insofar undisputed-upper bound on hydrogen loading follows.     

Spectral signatures of critical charge and spin fluctuations in cuprates

We discuss how Raman spectra of high temperature superconducting cuprates are affected by nearly critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We find that specific fingerprints of nearly critical collective modes can be observed and that the selectivity of Raman spectroscopy in momentum space may 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 have larger masses and are more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuating with high frequency.     

谱有限元数值分析各向异性复合板中导波色散特性

提出谱有限元方法研究层状各向异性复合板中导波的色散特性和波结构。基于三维弹性动力学方程,用有限元方法离散波导截面,波传播方向的位移用简谐波表示,得到了导波色散的特征方程。分析了单层和双层复合板中导波沿不同方向传播的色散特性和波结构,讨论了双层复合板中层厚比对相速度的影响。数值研究结果表明:导波的对称模态沿纤维方向传播时在较宽的频率范围内保持弱色散状态。双层复合板中导波基本模态的相速度在低频时受层厚比的影响较明显,随着频率的增加趋向于相速度较低的材料。数值模拟结果为导波用于复合材料定量无损检测和性能评价提供理论依据。