Perturbation theory of a bound piezoelectric polaron

The shift of the ground state energy of a piezoelectric polaron bound in a Coulomb potential is calculated, numerically, to second order in the electron-phonon interaction for arbitrary strengths of the Coulomb potential. The results obtained are discussed so that some comments on the previous communications of other authors are drawn.     

Perturbation theory for a bound polaron

Perturbation theory is applied suitably to obtain an expression, valid for all types of binding, for the shift in ground state energy of an electron bound to a coulomb impurity in a polar semiconductor.     

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.     

Perturbation theory for QED bound states

A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function.     

Excited states of a bound polaron

The results of the calculations of energies of states 2S and 2P of a bound electron interacting weakly with optical phonon field are presented.     

Excited states of a bound polaron

Expressions for the energies of the 3s, 3p and 3d states of a polaron, bound to a positively charged impurity ion in a polar crystal through a Coulomb potential, are obtained in analytic forms using perturbation theory. The values of these energies are calculated in several polar crystals.     

A bound polaron in a spherical quantum dot

The binding energy of a bound polaron in a spherical quantum dot has been investigated by using the variational method. The influence of LO and SO phonons have taken into consideration. Result shows that the phonon contribution to the binding energy is dependent on the size of the quantum dot as well as the position of the impurity in the quantum dot. Numerical calculation on the ZnSe quantum dot shows that such contribution is about 5% to 20% of the total binding energy. Received: 13 October 1997 / Revised: 4 March 1998 / Accepted: 26 May 1998     

Perturbation theory for a polarizing liquid

The thermodynamic perturbation theory is applied to polar polarizing liquids. A system of rigid dipoles is chosen as a basis, and the magnitude of the dipole moment is determined from the Gibbs-Bogolyubov variational principle. The equation of state obtained within the framework of the variational approach is used for calculating the free energy of a model system of polarizing dipolar solid spheres. Good agreement is obtained with results of computer experiment.     

Perturbation theory for kinds

In this paper we prove the validity of formal asymptotic results on perturbation theory for kind solutions of the sine-Gordon equation, originally obtained by McLaughlin and Scott. We prove that for appropriate perturbations, of size in an appropriate norm, slowly varying in time in the rest frame of the kink, the shape of the kink is unaltered in theL norm toO() for a time ofO(1/). The kink parameters, which represent its velocity and centre, evolve slowly in time in the way predicted by the asymptotics. The method of proof uses an orthogonal decomposition of the solution into an oscillatory part and a one-dimensional zero-mode term. The slow evolution of the kink parameters is chosen so as to suppress secular evolution of the zero-mode.Partially supported as a graduate student at Princeton University of NSF grant 215 6211     

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).     

Adiabatic approximation for a bound acoustic deformation potential polaron in a strong magnetic field

On the basis of the usual adiabatic scheme applied to a bound polaron in a strong magnetic field we observe an enhancement of the binding energy due to electron-lattice coupling via the deformation potential. This enhancement, being more pronounced with increasing field intensity, is, however, negligible for most common materials in experimentally interesting magnetic fields.     

A non-perturbative approach to the bound polaron

An iterative method, applied to the bound polaron hamiltonian, reduces it in successive steps. Lowest order results, valid for all types of bindings, are obtained and compared with available pertubation results.     

Perturbation theory for a hamiltonian linear in quasimomentum

Perturbation theory has been proposed to take into account small terms in the multiband Hamiltonian, which lead to significant changes such as the trigonal warping of the Fermi surface. The theory is similar to the “cross technique” and is reduced to the self-energy corrections to the matrix Green’s function. A particular application to graphite and a graphene bilayer has been given.     

Perturbation theory for a mixture of polarizable liquids

Thermodynamic perturbation theory developed for pure polar liquids with significant polarizability is applied to a mixture with polar and nonpolar polarizable components. Expressions for the average and unperturbed dipole moments of the components of the mixture are presented and the dipole and induced contributions to the thermodynamic functions of the mixture are calculated. The equation of state is obtained and used to calculate the excess properties of a binary mixture of particles interacting with a stockmeyer potential. It is shown that the induced dipole moments contribute significantly to the thermodynamic properties of this model solution and that their effects must be taken into account in predicting the properties of real liquid mixtures containing polar components.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 69–73, March, 1985.     

The bound one-dimensional “relativistic” polaron in a one-loop approximation

A quasirelativistic model of the narrow-gap semiconductor is considered. The interaction of the Dirac electron field with the non-dispersive phonon field in the short-range external potential (impurity) is taken into account. The classical solutions corresponding to the discrete spectrum are found. The fermion vacuum polarization effect is studied within the one-loop approximation.     

Perturbation theory for bending potentials

An efficient perturbative method is developed to facilitate the treatment of the anharmonicity of bending degrees of freedom. The Rosen-Morse and sec² potentials are transformed so that perturbation theory may be applied easily. For a model problem it is found that the difference between the energy levels obtained from perturbation theory and the exact energy levels is less than 0·1 cm^-1 for the first six energy levels.     

Perturbation theory for velocity-dependent potentials

In the presence of a velocity-dependent Kisslinger potential, the partial-wave, time-independent Schr?dinger equation with real boundary conditions is written as an equation for the probability density. The changes in the bound-state energy eigenvalues due to the addition of small perturbations in the local as well as the Kisslinger potentials are determined up to second order in the perturbation. These changes are determined purely in terms of the unperturbed probability density, the perturbing local potential, as well as the Kisslinger perturbing potential and its gradient. The dependence on the gradient of the Kisslinger potential stresses the importance of a diffuse edge in nuclei. Two explicit examples are presented to examine the validity of the perturbation formulas. The first assumes each of the local and velocity-dependent parts of the potential to be a finite square well. In the second example, the velocity-dependent potential takes the form of a harmonic oscillator. In both cases the energy eigenvalues are determined exactly and then by using perturbation theory. The agreement between the exact energy eigenvalues and those obtained by perturbation theory is very satisfactory. Received: 24 May 2002 / Accepted: 15 July 2002 / Published online: 3 December 2002 RID="a" ID="a"e-mail: mij@hu.edu.jo Communicated by V. Vento     

极性晶体膜中束缚极化子的有效质量

采用线性组合算符法和变分法,讨论了极性晶体膜中电子与SO声子耦合强,与LO声子耦合弱的电子-声子相互作用系统的有效质量.得出了束缚极化子的有效质量随膜厚的变化规律.对KCl材料进行数值计算的结果表明,不同支声子与电子相互作用对有效质量的贡献并不相同,而且由于束缚势的存在,使有效质量增大.