Modified Perturbation Theory Research Articles

Two-particle density matrix calculation for atom by modified perturbation theory

The two-particle density matrix of hydrogen atoms moving in a solid film is calculated. The probability of surviving a bound state between electron and proton in the course of the atomic motion in the film is discussed. The surviving fraction of the initial beam possesses the increased energy of the Coulomb attraction and lowered energy losses. This fraction can be responsible for the observed number of Rydberg states in the exit beam.

Dynamical fidelity of a solid-state quantum computation.

In this paper we analyze the dynamics in a spin model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows us to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.

Modified perturbation theory approach for [formula omitted] production and decay

The modified perturbation theory (MPT), based on direct expansion of probabilities instead of amplitudes, allows one to avoid divergences in the phase–space integrals resulting from production and decay of unstable particles. In the present Letter the range of applicability of MPT is determined numerically in the case of the process e +e −→(γ,Z)→t t ̄ →W +bW − b ̄ . It is shown that with the complete expansion in powers of the coupling constant (without Dyson resummation) MPT operates best at the energies located near the maximum of the cross-section and slightly above the maximum. In this region the MPT expansion within the next-to-leading order considerably exceeds in accuracy well-known DPA approach.

Ferromagnetism and disorder: a dynamical mean-field study

We investigate ferromagnetism in the periodic Anderson model with diagonal disorder. Using dynamical mean-field theory in combination with the modified perturbation theory, the disorder can be included in the calculation consistently, which turns out to be equivalent to the coherent potential approximation method. Disorder generally reduces the Curie temperature and can for certain configurations completely suppress ferromagnetic order. This can be ascribed to the enhanced quasiparticle damping and the special structure of the density of states.

Electron scattering by nonspherically symmetric atoms: Zero-energy limit

A modified perturbation theory, previously introduced for the construction of asymptotic states accounting for a general class of long-range angle-dependent multipole potentials is developed in further detail. The threshold behavior of these states is presented in explicit form and these results are used, with the aid of a modified effective-range formulation, to determine the threshold energy dependence of the multichannel transition matrix. Unitarity properties are established formally and verified in the low-energy limit. A variational procedure for determining the parameters appearing in the modified effective-range expansion is described. The same procedure accounts for the presence of zero-energy bound states leading to resonant behavior that alters the threshold energy dependence.

Strong-coupling scenario of a metamagnetic transition

We investigate the periodic Anderson model in the presence of an external magnetic field, using dynamical mean-field theory in combination with the modified perturbation theory. A metamagnetic transition is observed which exhibits a massive change in the electronic properties. These are discussed in terms of the quasiparticle weight and densities of states. The results are compared with the experimental results of the metamagnetic transition in CeRu_2Si_2.

Finite width effects and gauge cancellations in W- and Z-boson production in the framework of modified perturbation theory

The processes of production and subsequent decay of W- and Z-bosons in $e^+ e^-$ collisions are considered in a recently proposed modified perturbation theory (PT), based on a direct expansion of probabilities instead of amplitudes. In such an approach the non-integrable singularities in the phase space, which are intrinsic in the conventional PT, appear as singularities in the coupling constant (with subsequent compensation by the decay factors of unstable particles). In the present paper the systematic investigation of the modified PT is carried out. The results are compared with the results of the conventional approach, based on calculation of the amplitude with Dyson resummation. A solution to the problem of the loss of one-loop PT order in the resonance region is found. On the basis of this solution the proof of gauge cancellations in any order of the modified PT is given. A simple generalization of the fermion-loop scheme is proposed which provides a complete description of W-pair production in next-to-leading order approximation.

Modified perturbation theory applied to the two-impurity Anderson model

Modified perturbation theory applied to the two-impurity Anderson model

Atomic motion in a two-mode laser field

A modified perturbation theory is developed for the calculation of the time-dependent wave function describing the propagation of an atom in a two-mode laser field. With the mode frequencies nearly equal, a first approximation is obtained that reproduces and extends known results, for both resonant and nonresonant transitions. This lowest-order solution sums terms that describe the absorption of a photon from one mode and emission into the other, leaving the total number of photons unchanged and shifting the momentum of the atom accordingly. Corrections are generated by expansion of a resolvent from which the nearly degenerate states have been projected out. These approximate solutions are used to construct asymptotic states in a formulation of atom-atom scattering in the two-mode field. In close analogy with the soft-photon approximation, a ``soft-pair'' approximation is developed based on the dominance of those asymptotic interactions in which the transfer of energy from the field to the atom is small, allowing one to relate the scattering amplitude in the presence of the field to the field-free amplitude. When the atomic ground state and an excited state are closely coupled by the field, the asymptotic wave function can have mixed parity allowing for long-range contributions to the effective potential. In addition to an enhancement of forward-scattering probabilities, this leads to a threshold anomaly that is analyzed here, in the resonant case, with the aid of a modified effective-range theory.

Dynamical mean-field study of ferromagnetism in the periodic Anderson model

The ferromagnetic phase diagram of the periodic Anderson model is calculated using dynamical mean-field theory in combination with the modified perturbation theory. Concentrating on the intermediate valence regime, the phase boundaries are established as a function of the total electron density, the position of the atomic level, and the hybridization strength. The main contribution to the magnetic moment stems from the f electrons. The conduction-band polarization is, depending on the system parameters, either parallel or antiparallel to the f magnetization. By investigating the densities of states, one observes that the change of sign of the conduction-band polarization is closely connected to the hybridization gap, which is only apparent in the case of almost complete polarization of the f electrons. Finite-temperature calculations are also performed, and the Curie temperature as function of electron density and f-level position are determined. In the intermediate-valence regime, the phase transitions are found to be of second order.

Ferromagnetism in the periodic Anderson model. A comparison of spectral density approximation (SDA), modified alloy analogy (MAA) and modified perturbation theory (MPT)

We compare different approximation schemes for investigating ferromagnetism in the periodic Anderson model. The use of several approximations allows for a detailed analysis of the implications of the respective methods, and also of the mechanisms driving the ferromagnetic transition. For the Kondo limit, our results confirm a previously proposed mechanism leading to ferromagnetic order, namely an RKKY exchange mediated via the formation of Kondo screening clouds in the conduction band. The contrary case is found in the intermediate-valence regime. Here, the bandshift correction ensuring a correct high-energy expansion of the self-energy is essential. Inclusion of damping effects reduces stability of the ferromagnetic phase.

Investigation of the Two-Particle-Self-Consistent Theory for the Single-Impurity Anderson Model and an Extension to the Case of Strong Correlation

The two-particle-self-consistent theory is applied to the single-impurity Anderson model. It is found that it cannot reproduce the small energy scale in the strong correlation limit. A modified scheme to overcome this difficulty is proposed by introducing an appropriate vertex correction explicitly. Using the same vertex correction, the self-energy is investigated, and it is found that under certain assumptions it reproduces the result of the modified perturbation theory which interpolates the weak and the strong correlation limits.

Extended coherent states and modified perturbation theory

An extended coherent state for describing a system of two interacting quanum objects is considered. A modified perturbation theory based on using the extended coherent states is formulated.

Kondo screening and exhaustion in the periodic Anderson model

We investigate the paramagnetic periodic Anderson model using the dynamical mean-field theory in combination with the modified perturbation theory which interpolates between the weak and strong coupling limits. For the symmetric PAM, the ground state is always a singlet state. However, as function of the hybridization strength, a crossover from collective to local Kondo screening is found. Reducing the number of conduction electrons, the local Kondo singlets remain stable. The unpaired f-electrons dominate the physics of the system. For very low conduction electron densities, a large increase of the effective mass of the quasiparticles is visible, which is interpreted as the approach of the Mott-Hubbard transition.

Periodic Anderson model: magnetic properties

We investigate the periodic Anderson model using dynamical mean-field theory. The effective impurity problem is solved by means of the modified perturbation theory. Our focus is on the possibility of ferromagnetic order, and on the properties of the ferromagnetic phase. Within the ferromagnetic phase, the coupling between f- and s-electrons changes from anti- to ferromagnetic depending on the total number of electrons.

Modified Perturbation Theory Applied to Kondo-Type Transport through a Quantum Dot under a Magnetic Field

Linear conductance through a quantum dot is calculated under a finite magnetic field using the modified perturbation theory. The method is based on the second-order perturbation theory with respect to the Coulomb repulsion, but the self-energy is modified to reproduce the correct atomic limit and to fulfill the Friedel sum rule exactly. Although this method is applicable only to zero temperature in a strict sense, it is approximately extended to finite temperatures. It is found that the conductance near electron-hole symmetry is suppressed by the application of the magnetic field at low temperatures. Positive magnetoconductance is observed in the case of large electron-hole asymmetry.

The asymmetric single-impurity Anderson model – the modified perturbation theory

We investigate the single-impurity Anderson model by means of the recently introduced modified perturbation theory. This approximation scheme yields reasonable results away from the symmetric case. The agreement with exactly known results for the symmetric case is checked, and results for the non-symmetric case are presented. With decreasing conduction band occupation, the breakdown of the screening of the local moment is observed. In the crossover regime between Kondo limit and mixed-valence regime, an enhanced zero-temperature susceptibility is found.

Magnetic Field Effects on Transport Properties of a Quantum Dot Studied by Modified Perturbation Theory

A new scheme is proposed for calculating excitation spectrum of a quantum dot expressed by the impurity Anderson model. It is based on the second order perturbation theory with respect to the Coulomb repulsion, but is modified so as to reproduce the correct atomic limit and to fulfil the Friedel sum rule. The magnetic field dependence of both the excitation spectra and the transport properties of a quantum dot is investigated. It is found that the zero bias peak in differential conductance splits under external magnetic field and that negative magnetoresistance will be observed at zero bias voltage in case of electron-hole asymmetry.

Non-darcian effects on double diffusive convection in a sparsely packed porous medium

The linear and non-linear stability of double diffusive convection in a sparsely packed porous layer is studied using the Brinkman model. In the case of linear theory conditions for both simple and Hopf bifurcations are obtained. It is found that Hopf bifurcation always occurs at a lower value of the Rayleigh number than one obtained for simple bifurcation and noted that an increase in the value of viscosity ratio is to delay the onset of convection. Non-linear theory is studied in terms of a simplified model, which is exact to second order in the amplitude of the motion, and also using modified perturbation theory with the help of self-adjoint operator technique. It is observed that steady solutions may be either subcritical or supercritical depending on the choice of physical parameters. Nusselt numbers are calculated for various values of physical parameters and representative streamlines, isotherms and isohalines are presented.

Stability of gravitational andelectromagnetic geons

Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate time-averaged fields, is used to test the requirement of quasi-stability. It is found that the modified perturbation theory results in an internal inconsistency. The time-scale of evolution is found to be of the same order of magnitude as the period of the comprising waves. This contradicts the requirement of slow evolution. Thus not all of the requirements for the existence of electromagnetic or gravitational geons are met though perturbation theory. From this result it cannot be concluded that an electromagnetic or a gravitational geon is a viable entity. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.