Ground state energy of a bound piezoelectric polaron

The ground state energy of a piezoelectric polaron bound in a Coulomb potential is calculated analytically in the weak coupling limit.     

Ground state energy of the large polaron in a crystal with many LO phonon branches

The large polaron is studied in polyatomic crystals where more than one LO phonon branch is present. An upper bound to the ground state energy is obtained which is valid for all values of the electron-phonon coupling constants. For small coupling, we obtain the usual result that the ground state energy is the sum of the contributions of the different phonon branches. For large coupling, there is an extra contribution due to crossed terms between the different branches. Results are also given for intermediate coupling.     

Ground state of a bound polaron with a weak electron-phonon interaction

With the use of the integral representation of the Coulomb Green's function (3) the exact expression for the polaron shift of the ground state of the bound electron in the second order perturbation theory is obtained (5).     

Ground state and polaron and bipolaron excited states in polydiacetylene

The electronic properties of ground state and charged excited states of non-degenerate polydiacetylene were investigated by means of a tight-binding model. The parameters of the model were obtained by comparison of the experimental and other theoretical results. It was found that there is a stable dimerized structure of polydiacetylene in ground state and the doping induces the nonlinear excitations, such as polarons and bipolarons. In order to compare the stability of polaron and bipolaron, the creation energy and binding energy were separately defined. By neglecting the electron-electron Coulomb interaction, a bipolaron is more stable than two independent polarons.     

Ground and first excited state energies of impurity-bound polaron in a parabolic quantum dot

A Landau–Pekar variational theory is employed to obtain the ground and the first excited state binding energies of an electron bound to a Coulomb impurity in a polar semiconductor quantum dot (QD) with parabolic confinement in both two and three dimensions. It is found that the binding energy increase with increasing the Coulomb binding parameter and increase with the decrease in size of the QD and is much more pronounced with decreasing dimensionality.     

Mixed state in a superlattice

Presented in this paper is a theoretical calculation of the vortex solution in a chosen superlattice (Nb/NbZr) using the Gibbs free energy of an inhomogeneous superconductor. The eigenvalue obtained in this geometry from de Gennes-Werthamer proximity coupling theory is first examined according to a set of experimental data, while the correspondent eigenfunctions are then used to construct vortex solutions with either square lattice or triangle lattice symmetry. The Gibbs free energy is calculated in terms of the vortex solutions of both symmetries. The effective Ginzburg-Landau parameter,K _NS , for this superlattice is determined asK _NS =0.218 by requiring a consistency between the microscopic and macroscopic theoretical calculations. Of particular importance is a new mechanism revealed by this calculation that a highly localized state of superconducting condensate in its hosting layer, despite the spatially rapid varying characteristic of its correspondent nucleating order parameter, provides a lower eigenvalue state, which results in a dimensional crossover. A further examination of this mechanism is carried out in the mixed state calculation. Finally, a generalization of the present theoretical results to a large class of superlatices is discussed.     

Ground state energy of a many-particle boson system

A trial expression for the ground state energy of a system of many bosons interacting with strong forces is studied. Using an approximate expression for the pair-distribution function and applying the variational principle in an appropriate way, we obtain a non-linear integrodifferential equation for the correlation functionf(r). This equation is subsequently linearised and its behaviour for large separations is studied. It is also shown that for large separations an effective reduced mass of the pair can be defined. This is given by ^*=2, where=m/2 is the reduced mass of the pair.     

Ground state energies of neutral and negatively charged donors in nanowire superlattice

Using the Bastard-type trial function for the neutral donor and the Hylleraas-type trial function for the negatively charged donor, we investigate the effect of donor positions inside the cylindrical GaAs/Ga(Al)As nanowire superlattice on their ground state energies. Results of calculation, presented in the form of contour plots of the energies corresponding to different donor positions along a cross section through symmetry axis, show a close relationship between the energies of the neutral and negatively charged donors and the charge distributions in one- and two-electron nanowire superlattices, respectively, at the point of their locations. The higher the charge density resulting from the unbound electron at a point in the heterostructure, the lower are the ground state energies of the neutral and negatively charged donors located at this point.     

The polaron state of a crystal

The quantum mechanics of an electron-nuclear system with strong electron-phonon coupling is considered. First, a two-site model is treated in the adiabatic approximation. As the coupling constant increases, electron transfer undergoes qualitative changes; more specifically, a potential barrier forms in the adiabatic potential, the electron transfer becomes associated with the tunneling of nuclei through the barrier, and the level splitting in the system falls off exponentially. The properties of a similar crystal model are discussed. It is shown that electron transfer in a crystal in the case of strong coupling is likewise associated with the tunneling of nuclei through barriers in the deformation space. Strong coupling modifies the electron-electron interaction terms. The Hamiltonian (exchange) terms, which are not associated with electron transfer, are only weakly modified. At the same time, the terms involving transfer (the band terms) undergo exponential reduction and vanish in the limit as M → ∞ (M is the ion mass) and the carriers become small polarons. This reduction provides a basis for the natural mechanism of enhancement of the isotope effect.     

Ground state energy for a model gas in one dimension

Ground state energies of many-body systems in one dimension in the thermodynamic limit are calculated. We use relations between the ground state energy and the scattering phase, which are exact for a delta-function potential, and are fulfilled approximately for other interactions. This will be applied to a model of quantum field theory, for which theS-matrix can be calculated exactly by means of a property which is called factorization.     

Temperature-dependent polaron energy

Summary The temperature-dependent polaron energy is calculated by using the dispersion energy formalism. In this model the polaron energy is equated to the shift in the electromagnetic-field energy resulting from the electron-lattice interaction. The electronic as well as the lattice frequencies are renormalized as a result of the interaction and the energy content of each mode depends on the temperature through the Planck distribution. It is shown in this paper that the dispersion energy model predicts ionization of the polaron as the temperature goes to infinity.

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Riassunto L'energia polaronica dipendente dalla temperature è calcolata usando il formalismo dell'energia di dispersione. In questo modello l'energia polaronica è uguagliata alla variazione di energia del campo electtromagnetico risultante dall'interazione elettronereticolo. Le frequenze elettroniche e le frequenze reticolari sono rinormalizzate come risultato dell'interazione ed il contenuto in energia di ogni modo dipende dalla temperatura attraverso la distribuzione di Planck. Si mostra in questo lavoro che il modello dell'energia di dispersione prevede ionizzazione del polarone quando la temperatura tende ad infinito.

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Резюме Используя энергетический формализм диспесич вычифняется энергия понярона, завифящая от температуры. В этой модели энергия полярона равна сдвигу энергии электрмаглипного поля в результаце електрон-рэшеточлого взаимодей-ствия. В результате этого взаимодйствия перелормирыются электлонные, а также решеточные частоты. Энэргосодержание каждой моды зависит от температуры через распредение Планка. В этой статье показается, что энергетическая модель дисперсии иредсказываетт ионизацю полярона в том случае, корда температура стремится к бескнечности.

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To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Ground state energy of current carriers in graphene

The ground state energy of current carriers in graphene considered as a zero-gap semiconductor was calculated in the two-band approximation. The condition of the electronic (hole) system stability in graphene was obtained. The possibility of the zero-gap semiconductor—semimetal transition was discussed.     

Ground state energy of small electron-hole drops

The ground state energy of small electron-hole drops is calculated for droplets ranging in size from 10 to 10,000 pairs. A new value for the bending energy of $\text{1.1×10}{}^{\mathrm{?10}}\text{erg}\text{cm}$ is derived. We also give a simple highly accurate formula for the total energy per pair. The surface energy is extracted from the total energy and found to agree well with a previous self-consistent calculation. The density at the center of the drop remains essentially constant over the entire range of N, indicating that the drop is not dramatically compressed by the surface tension.     

Ground state energy of dilute magnetic alloys

The ground state energy of dilute magnetic alloys as described by thes-d-exchange Hamiltonian is calculated within the Nagaoka-Suhl theory. For integral impurity spinS it is shown that for positive coupling constantγ the energy is a holomorphic function ofγ. For negative coupling one obtains an additional singular contribution of the form (?1) ^s?1 e ^1/γ (γ<0). As this changes sign for different integral s-values, the interpretation of the singular part as a binding energy suggested previously does no longer hold. For half integral spin the energy is a singular function for bothγ>0. The singularities are not as elementary as in the case of integral spinS, but are rather related to those of the exponential integral function. In particular, forγ>0 the origin (γ=0) is a branch point. Earlier variational calculations are compared with our new results.     

Ground state energy of N Frenkel excitons

By using the composite many-body theory for Frenkel excitons we have recently developed, we here derive the ground state energy of N Frenkel excitons in the Born approximation through the Hamiltonian mean value in a state made of N identical Q = 0 excitons. While this quantity reads as a density expansion in the case of Wannier excitons, due to many-body effects induced by fermion exchanges between N composite particles, we show that the Hamiltonian mean value for N Frenkel excitons only contains a first order term in density, just as for elementary bosons. Such a simple result comes from a subtle balance, difficult to guess a priori, between fermion exchanges for two or more Frenkel excitons appearing in Coulomb term and the ones appearing in the N exciton normalization factor – the cancellation being exact within terms in 1/N_s where N_s is the number of atomic sites in the sample. This result could make us naively believe that, due to the tight binding approximation on which Frenkel excitons are based, these excitons are just bare elementary bosons while their composite nature definitely appears at various stages in the precise calculation of the Hamiltonian mean value.     

Magnon energy gap in a four-layer ferromagnetic superlattice

The magnon energy band in a four-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green＇s function technique. It is found that three modulated energy gaps exist in the magnon energy band along Kx direction perpendicular to the superlattice plane. The spin quantum numbers and the interlayer exchange couplings all affect the three energy gaps. The magnon energy gaps of the four-layer ferromagnetic superlattice are different from those of the three-layer one. For the four-layer ferromagnetic superlattice, the disappearance of the magnon energy gaps △ω12, △ω23 and △ω34 all correlates with the symmetry of this system. The zero energy gap △ω23 correlates with the symmetry of interlayer exchange couplings, while the vanishing of the magnon energy gaps △ω12 and △ω34 corresponds to a translational symmetry of x-direction in the lattice. When the parameters of the system deviate from these symmetries, the three energy gaps will increase.     

Binding energy of a polaron in asymmetric polar semiconductor heterostructures

By using a modified Lee-Low-Pines variational method, we have investigated the ground-state binding energy of a polaron confined in asymmetric single and step quantum wells (QWs) due to interface phonons, confined bulk-like LO phonons, and half-space LO phonons. The relative importance of the different phonon modes is analysed in detail. Our results show that the asymmetry and the well width of the QWs have a significant influence on the polaron energy. The polaron binding energy has an intimate relation to the potential parameters of QWs. The subband nonparabolicity has a little influence to the polaron binding energy. Comparing with the results calculated with perturbation theory, a good agreement is found.     

Ground-state energy and effective mass of a polaron in a two-dimensional surface layer

The energy and the effective mass of an electron interacting with the optical modes of a two-dimensional surface layer is evaluated using path integrals as introduced by Feynman for the bulk optical polaron.