States of intermediate charge symmetry as low-lying, 0 collective excitations of medium weight nuclei

A method for calculating the states of the charge-independent pairing hamiltonian that have intermediate charge symmetry is presented. The states are shown to be collective 0⁺ excitations with energies that fall well within the gap in the single-particle spectrum.     

Green's function approach to the quantum many-body theory of the solid state

TheGreen's function approach is used to develop a quantum many-body theory of the solid state which should work at low temperatures as well as in the neighbourhood of phase transition points. The theory is applicable also in those cases where the traditional expansion of the potential in powers of the atomic displacements is entirely inadequate (crystalline helium). The starting point of our approach is the concept of broken symmetry since the invariance of the equilibrium ensemble under the continuous group of infinitesimal translations is reduced in a crystalline solid to the invariance under finite translations through a lattice vector. A homogeneous integral equation is derived which has nontrivial solutions in the crystalline state. By this equation it is shown that the umklapp phonons are the symmetry restoring collective modes expected due to a general theorem ofGoldstone. The single particle excitations and the structure of the Dyson mass operator in the crystalline state are discussed. It is further shown that the homogeneous Bethe-Salpeter equation for the linear response to an external disturbance possesses symmetry breaking solutions which are connected to the lattice dynamics of the solid state. These collective excitations (phonons) are exhibited in RPA and tight-binding approximation for monoatomic cubic crystals with a Bravais lattice in order to demonstrate how the present theory reproduces well-known results.     

Parametric conversion and maximally entangled photon pair via collective excitations in a cycle atomic ensemble

We study the propagation of two quantized optical fields via considering the collective effects of photonic emissions and excitations of a three-level cyclic-type system (such as atomic ensemble with symmetry broken, or the chiral molecular gases, or manual “atomic” array with symmetry broken), where the quantum transitions is driven by two quantized fields and a classical one. The results show that the parametric conversion and maximally entangled photon pair generation can be achieved by means of the collective excitation of the two upper energy levels induced by the classic optical field. This investigation may be used for the generated coherent short-wavelength quantum radiation and quantum information processing.     

U(3) symmetry: a link between nuclear models and phenomena

Light nuclei show evidence for aU(3) symmetry. This symmetry appears in all of the basic models of these nuclei, such as the shell, collective and cluster model. It has a microscopic origin which is related to the shell structure and to the nature of the effective two-nucleon forces, but it determines macroscopic characteristics as well, such as the amount of quadrupole deformation, moment of inertia, etc. We show that this symmetry also serves as a basis for interrelating various cluster configurations of the same (compound) nucleus, offering a natural link between seemingly unrelated phenomena, like nuclear molecular resonances and excitations in the low-lying nuclear spectra.     

Electric-field-induced plasmon in AA-stacked bilayer graphene

The collective excitations in AA-stacked bilayer graphene for a perpendicular electric field are investigated analytically within the tight-binding model and the random-phase approximation. Such a field destroys the uniform probability distribution of the four sublattices. This drives a symmetry breaking between the intralayer and interlayer polarization intensities from the intrapair band excitations. A field-induced acoustic plasmon thus emerges in addition to the strongly field-tunable intrinsic acoustic and optical plasmons. At long wavelengths, the three modes show different dispersions and field dependence. The definite physical mechanism of the electrically inducible and tunable mode can be expected to also be present in other AA-stacked few-layer graphenes.     

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.     

Giant Gamow-Teller resonance in neutron-rich nuclei

The giant Gamow-Teller resonance and other branches of collective nuclear excitations are described on the basis of the theory of finite Fermi systems. A connection between the Gamow-Teller resonance and Wigner SU(4) symmetry is proven. The beta-decay strength function and processes accompanying the β ⁻ decay of neutron-rich nuclei are described. The effect of the satellites of the Gamow-Teller resonance on the decay properties of neutron-rich nuclei is analyzed.     

Soft fermi surfaces and breakdown of Fermi-liquid behavior

Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi-liquid behavior over the whole surface except at the Brillouin zone diagonal.     

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.     

Rotational bands on few-particle excitations of very high spin

An RPA formalism is developed to investigate the existence and properties of slow collective rotation around a non-symmetric axis, when there already exists a large angular momentum K along the symmetry axis built up by aligned single-particle spins. Both repeatability and E2 collectivity are required to distinguish the collective rotational-like solutions from the others, which may come lower in energy. First the formalism is applied to bands on high-K isomers in the well-deformed nucleus ¹⁷⁹Hf, where the rotational-model picture is reproduced for intermediate K-values in agreement with experiment. At high K the collectivity is suppressed even more than the diminishing vector-coupling coefficient of the rotational model would suggest, but the repeatability actually improves. The moment of inertia is predicted to remain substantially smaller than the rigid-body value, so the bands slope up steeply from the yrast line at spins where pairing effects are gone. A second application is to the initially spherical nucleus ²¹²Rn, which is believed to acquire an oblate deformation that increases steadily with K due to the oblate shape of the aligned orbitals. In this case the rotational-like excitations also exist but are still less favoured than in ¹⁷⁶Hf, even at comparable deformations. Some collective states may come closer to the average yrast trend, but they have lower repeatability because they are more like dressed single-particle excitations. The main differences between the two nuclei studied is interpreted as a general consequence of their different shell structure.     

Dynamics of nematics with conformational degrees of freedom

On the basis of Hamilton approach the dynamics of the biaxial nematics is considered. All hydrodynamic parameters, connected with broken symmetry, are introduced in terms of the distortion tensor. The equations of ideal hydrodynamics are obtained and the three spectra of collective excitations of biaxial nematics are considered, taking into account the rod-shape of molecules.     

Collective coordinates in Fermi systems

The problem of developing a consistent perturbation theory for a Fermi system in the case in which the unperturbed system exhibits dynamical symmetry breaking is discussed, by using collective coordinate methods. By adapting to this problem the methods used in the quantization of gauge theories, it is shown how to deal with composite zero-frequency excitations in such a way that the resulting perturbation theory is free of infrared divergencies. Explicit calculations are carried out in the case of a simple quantum mechanical model representing a superfluid Fermi system.     

Effects of symmetry breaking in finite quantum systems

The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose–Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.     

A comparative study of optic phonon-like excitations in liquid mixtures and molten salts

We report a study of collective excitations in an equimolar Lennard–Jones liquid mixture KrAr and a molten salt NaCl within the parameter-free generalized collective modes (GCM) approach. It is shown that the high-frequency propagating modes in liquid KrAr and molten NaCl correspond to optic phonon-like excitations, caused by fast mass-concentration (charge in NaCl) fluctuations. Dispersion curves for optic collective excitations are discussed.     

ModifiedT-matrix approximation in itinerant ferromagnets

In this paper we investigate the effect of spin wave excitations on the one-particle energy spectrum of an itinerant ferromagnet. A modifiedT-matrix approximation is developed which takes into account also the effect of other collective modes. In the case of a completely polarized system we obtain a new type of quasi-particle at low excitation energy, and a large damping of the usual one-particle excitations.     

Scale invariance and viscosity of a two-dimensional Fermi gas

We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.