Surface effect on two nanocracks emanating from an electrically semi-permeable regular 2n-polygon nanohole in one-dimensional hexagonal piezoelectric quasicrystals under anti-plane shear

In this paper, the conformal mapping from a regular 2[Formula: see text]-polygon hole with two collinear asymmetric cracks into a circle is constructed. Based on the Gurtin–Murdoch surface/ interface model and complex potential theory, two collinear asymmetric nanocracks emanating from an electrically semi-permeable regular 2[Formula: see text]-polygon nanohole embedded in an infinite one-dimensional hexagonal piezoelectric quasicrystals with surface effect are investigated. The size-dependent stress intensity factors of phonon field and phason field, electric displacement intensity factor at the nanocrack tip are derived for electrically semi-permeable boundary condition. Numerical examples are illustrated to show that the size of the hole, mechanical load, electric load, cracks relative size change with stress intensity factor of phonon field and electric displacement intensity factor. Also analyzed the change of the electric displacement intensity factor with different electric permeability at the nanocrack tip and the dimensionless intensity factor with [Formula: see text].

Microscopic Model to Take into Account Complex Configurations for Pygmy and Giant Resonances

A microscopic model for taking into account quasiparticle–phonon interaction in magic nuclei is considered within nuclear quantum many-body theory. This model is of interest for constructing a microscopic theory of pygmy and giant multipole resonances—first of all, a description of their fine structure. This article reports on a continuation and development of our earlier study [1]. Basic physics results of that study are confirmed here, and new results are obtained: (i) exact (not approximate, as in [1]) expressions for the first and second variations of the vertex in the phonon field are found and employed; (ii) a new equation involving, in addition to the known effective interaction, the total amplitude for particle–hole interaction is derived for the vertex, which is the main ingredient in the theory of finite Fermi systems; (iii) the required two-phonon configurations are obtained owing to the last result. The new equation for the vertex now contains complex configurations such as $$1p1h\otimes\textrm{phonon}$$ and two-phonon ones, along with numerous ground-state correlations.

Translation-Invariant Excitons in a Phonon Field

Large-radius excitons in polar crystals are considered. It is shown that translation invariant description of excitons interacting with a phonon field leads to a nonzero contribution of phonons into the exciton ground state energy only in the case of weak or intermediate electron-phonon coupling. A conclusion is made that self-trapped excitons cannot exist in the limit of strong coupling. Peculiarities of the absorption and emission spectra of translation invariant excitons in a phonon field are discussed. Conditions when the hydrogen-like exciton model remains valid in the case of electron-phonon interaction are found.

Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit

We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

Antiplane Fracture Problem of Three Nanocracks Emanating from an Electrically Permeable Hexagonal Nanohole in One-Dimensional Hexagonal Piezoelectric Quasicrystals

Based on the Gurtin-Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the electrically permeable boundary condition with surface effect is established, and the antiplane fracture problem of three nanocracks emanating from a hexagonal nanohole in one-dimensional hexagonal piezoelectric quasicrystals with surface effect is studied. The exact solutions of the stress intensity factor of the phonon field and the phason field, the electric displacement intensity factor, and the energy release rate are obtained under the two electrically permeable and the electrically impermeable boundary conditions. The numerical examples show the influence of surface effect on the stress intensity factors of the phonon field and the phason field, the electric displacement intensity factor, and the energy release rate under the two boundary conditions. It can be seen that the surface effect leads to the coupling of the phonon field, phason field, and electric field, and with the decrease of cavity size, the influence of surface effect is more obvious.

The Symmetry of Pairing and The Electromagnetic Properties of A Superconductor with A Four-Fermion Attraction at Zero Temperature

Properties of a fermion system at zero temperature are investigated. The physical system is described by a Hamiltonian containing the BCS interaction and an attractive four-fermion interaction. The four-fermion potential is caused by attractions between Cooper pairs mediated by the phonon field. In this paper, the BCS interaction is assumed to be negligible and the four-fermion potential is the only one that acts in the system. The effect of the pairing symmetry used in the four-fermion potential on some zero-temperature properties is studied. This especially concerns the electromagnetic response of the system to an external magnetic field. It turns out that, in this instance, there are serious differences between the conventional BCS system and the one investigated in this paper.

Superconducting gap anisotropy and d-wave pairing in YBa2Cu3O7−δ

Considering Born–Mayer–Huggins potential as a most suitable potential to study the dynamical properties of high-temperature superconductors (HTS), the many-body quantum dynamics to obtain phonon Green’s functions has been developed via a Hamiltonian that incorporates the contributions of harmonic electron and phonon fields, phonon field anharmonicities, defects and electron–phonon interactions without considering BCS structure. This enables one to develop the quasiparticle renormalized frequency dispersion in the representative high-temperature cuprate superconductor YBa2Cu3O[Formula: see text]. The superconducting gap shows substantial changes with increased doping. The in-plane gap study revealed a [Formula: see text]-shape gap with a nodal point along [Formula: see text] direction for optimum doping ([Formula: see text] = 0.16) and the nodal point vanished in underdoped and overdoped regimes. The d[Formula: see text] pairing symmetry is observed at optimum doping with the presence of s or d[Formula: see text] components ([Formula: see text] 3%) in underdoped and overdoped regimes.

Interacting Electron–Hole–Phonon System

Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting electron-hole-phonon system. The coupled Fermion Green’s function equations involve five interactions (electron-electron, hole-hole, electron-hole, electron-phonon, and hole-phonon). Starting with quantum Hamilton equations of motion for the various electron/hole creation/annihilation operators and their nonequilibrium average/expectation values, variational differentiation with respect to particle sources leads to a chain of coupled Green’s function equations involving differing species of Green’s functions. For example, the 1-electron Green’s function equation is coupled to the 2-electron Green’s function (as earlier), also to the 1-electron/1-hole Green’s function, and to the Green’s function for 1-electron propagation influenced by a nontrivial phonon field. Similar remarks apply to the 1-hole Green’s function equation, and all others. Higher order Green’s function equations are derived by further variational differentiation with respect to sources, yielding additional couplings. Chapter 11 also introduces the 1-phonon Green’s function, emphasizing the role of electron coupling in phonon propagation, leading to dynamic, nonlocal electron screening of the phonon spectrum and hybridization of the ion and electron plasmons, a Bohm-Staver phonon mode, and the Kohn anomaly. Furthermore, the single-electron Green’s function with only phonon coupling can be rewritten, as usual, coupled to the 2-electron Green’s function with an effective time-dependent electron-electron interaction potential mediated by the 1-phonon Green’s function, leading to the polaron as an electron propagating jointly with its induced lattice polarization. An alternative formulation of the coupled Green’s function equations for the electron-hole-phonon model is applied in the development of a generalized shielded potential approximation, analysing its inverse dielectric screening response function and associated hybridized collective modes. A brief discussion of the (theoretical) origin of the exciton-plasmon interaction follows.

Exponentially Correlated Gaussians for Simulating Of Localized and Autolocalized States in Polar Media

Localized and autolocalized states and their simplest two-electron complexes in polar media are considered in the continuum approximation. The electron-phonon interaction is taken into account in the Pekar-Fröhlich approximation. The exponentially correlated Gaussian basis is used for the calculation of the energy spectrum of two-electron systems in phonon field. Analytical expressions for effective functionals of paramagnetic centers and their simplest two-electron complexes are presented. Numerical examples are given for the calculations of the energy spectrum of localized and self-localized states in metal-ammonia solutions.