Complex Energy Method Research Articles

Resonant tunneling of electrons in biased symmetric triangular double barrier nanostructure triodes

The present work investigates the resonant tunneling of electrons in symmetric triangular double barrier triodes composed of GaAs-Ga1-yAlyAs nanostructures under a step bias voltage. This work employs the complex energy method to compute the resonant tunneling energy and the associated lifetimes. In the mathematical analysis of this work, the matching conditions are taken at specific points on both lateral sides of the triangular barrier. Results showed decreasing the resonant tunneling energies for both the lowest and excited states by applying step bias voltage and disappearing the lowest energy states at a specific applied bias voltage. The resonant tunneling lifetimes of the present structure exhibited nearly constant behavior at constant values of both well half-width and barrier half-thickness although the enhancement of the bias voltage. Moreover, the lifetimes of both the lowest and the first excited states increased nearly non-linearly by increasing the aluminum concentration, with the enhancement of the lowest resonant lifetimes over those values associated with the first excited states. The results showed considerable agreement with the data published in the literature for both magnitude and tendency. The present work highlights the importance of employing the mass-mismatch condition in studying heterostructures. It is found from the present study that resonant tunneling energies and their related lifetimes are more affected by the variations of the aluminum concentration in the barrier region, barrier thickness, and well width, which can be adjusted to improve the performance of the resonant tunneling triangular triodes and other nanostructure devices.

50 Years of Systems Analysis of Energy Development In The Ussr And Russia

This year replete with so many anniversaries related to the energy sector sees the centenary celebration of the GOELRO Plan. This event is remarkable for energy studies: a complex energy method that backed up the Plan development half a century later became one of the preconditions for the development of the methodology of systems analysis of the energy development. The groundwork of this methodology was laid at SEI/ESI SB RAS (Siberian Energy Institute. Melentiev Energy Systems Institute of the Siberian Branch of the Russian Academy of Sciences) founded by Academician L.A. Melentiev; the institute celebrates its 60th anniversary this year. Half a century ago, an 'off-site' department of the SEI was established in Moscow and 15 years later it was reorganized into ERI RAS (Energy Research Institute of the Russian Academy of Sciences) and GKNT (State Committee for Science and Technology). The paper focuses on the background of the development of the theory and methods of systems analysis of energy development, covers its main theoretical and applied contributions in two stages of social and economic development of the country, discusses evolution of this research area and its possible adoption in the alternative (mobilization-type and liberal) concepts of shaping 'the information society’ of the future.

The analysis of vibration characteristics of fiber metal laminated thin plate with partial constrained layer damping patches treatment

This study focuses on vibration characteristics analysis of fiber metal laminated thin plate (FMLTP) with partial constraint layer damping (CLD) patches treatment. Firstly, the overall stress–strain relationships of the viscoelastic layer, the constraint layer and the covered FMLTP are deduced to establish the theoretical model. Then, the classical laminates theory, orthogonal polynomial method, complex modulus method and energy method are employed to solve the natural frequencies, modal shapes, vibration responses and modal damping ratios. As an example to demonstrate the feasibility of the developed model, the experimental test of TA2/TC500 laminated thin plate treated with different sizes and shapes of stainless steel/Zn-33 CLD patches is implemented. The calculated and measured results show a good consistency. Moreover, the influences of different CLD treating positions and shapes on the vibration characteristics of FMLTP are investigated here.

A Λnnthree-body resonance

We solved the Faddeev equations in the Λ nn system J π = ½ + , T = 1). There is no bound state but found a resonance state. Complex Energy Method helps to find the location of the resonance energy in the complex Riemann sheet. We obtained a resonance energy E = 0.25 − 0.40 i MeV using the realistic NN and YN Nijmegen potential. As a preliminary result the recent Nijmegen YN potential (NSC97f) gives 0.60± 0.05 - (0.25 ± 0.05) i MeV. We discuss importance of an irreducible three-body force to make it bound.

Reactions in the four-nucleon system above breakup threshold

Microscopic calculations of four-body scattering become very challenging in the energy regime above the threshold for four free particles. We consider mixed-isospin four-nucleon reactions initiated by the proton-3 H, neutron-3 He, or deuteron-deuteron collisions. We solve the Alt, Grassberger, and Sandhas equations for the four-nucleon transition operators in the momentum-space framework. The complex-energy method with special integration weights is applied to deal with the complicated singularities in the kernel of AGS equations. Results for the differential cross section and spin observables in elastic, charge-exchange, transfer, and breakup reactions using realistic potentials are presented.

Calculation of proton-3He elastic scattering between 7 and 35 MeV

Background: Theoretical calculations of the four-particle scattering above the four-cluster breakup threshold are technically very difficult due to nontrivial singularities or boundary conditions. Further complications arise when the long-range Coulomb force is present.Purpose: We aim at calculating proton-${}^{3}$He elastic scattering observables above three- and four-cluster breakup threshold.Methods: We employ Alt, Grassberger, and Sandhas (AGS) equations for the four-nucleon transition operators and solve them in the momentum-space framework using the complex-energy method whose accuracy and practical applicability is improved by a special integration method.Results: Using realistic nuclear interaction models we obtain fully converged results for the proton-${}^{3}$He elastic scattering. The differential cross section, proton and ${}^{3}$He analyzing powers, spin correlation and spin transfer coefficients are calculated at proton energies ranging from 7 to 35 MeV. Effective three- and four-nucleon forces are included via the explicit excitation of a nucleon to a $\ensuremath{\Delta}$ isobar.Conclusions: Realistic proton-${}^{3}$He scattering calculations above the four-nucleon breakup threshold are feasible. There is quite good agreement between the theoretical predictions and experimental data for the proton-${}^{3}$He scattering in the considered energy regime. The most remarkable disagreements are the peak of the proton analyzing power at lower energies and the minimum of the differential cross section at higher energies. Inclusion of the $\ensuremath{\Delta}$ isobar reduces the latter discrepancy.

Four-Nucleon Scattering Above the Four-Body Breakup Threshold

The four-body equations of Alt, Grassberger and Sandhas are solved for the neutron-3H scattering at energies above the four-nucleon breakup threshold. The accuracy and practical applicability of the employed complex energy method is significantly improved by the use of integration with the special weights. This allows to obtain fully converged results with realistic nuclear interactions. A satisfactory description of the existing neutron-3H elastic scattering data is obtained.

3H production via neutron-neutron-deuteron recombination

We study the recombination of two neutrons and deuteron into neutron and ${}^3$H using realistic nucleon-nucleon potential models. Exact Alt, Grassberger, and Sandhas equations for the four-nucleon transition operators are solved in the momentum-space framework using the complex-energy method with special integration weights. We find that at astrophysical or laboratory neutron densities the production of ${}^3$H via the neutron-neutron-deuteron recombination is much slower as compared to the radiative neutron-deuteron capture. We also calculate neutron-${}^3$H elastic and total cross sections.

Neutron-3H scattering above the four-nucleon breakup threshold

The four-body equations of Alt, Grassberger and Sandhas are solved for the neutron-${}^3$H scattering at energies above the four-nucleon breakup threshold. The accuracy and practical applicability of the employed complex energy method is significantly improved by the use of integration with the special weights. This allows to obtain fully converged results with realistic nuclear interactions. A satisfactory description of the existing neutron-${}^3$H elastic scattering data is obtained.

The Complex Energy Method Applied to the Nd Scattering with a Model Three-Body Force

Using the complex energy method, the problem of nucleon-deuteron scattering is solved with a simple three-body force having a separable form. Our results are compared with the results of modern direct two-variable calculations and a good agreement is found. This forms a firm base for other applications of the complex energy method.

Complex energy method in four-body Faddeev-Yakubovsky equations

The Complex Energy Method [Prog. Theor. Phys. 109, 869L (2003)] is applied to the four-body Faddeev-Yakubovsky equations in the four-nucleon system. We obtain a well converged solution in all energy regions below and above the four-nucleon breakup threshold.

An analytical expression for quantum-well tunneling lifetimes

An analytical expression is presented for the tunneling-escape lifetime of an electron occupying a quantum state localized in a quantum well in a heterostructure, using the perturbation approach. In the present derivation, an orthogonal basis set of wave functions is used, and all the terms in the perturbation expansion are included. The present formulation is exact and free from the inconsistencies in the transfer Hamiltonian method found recently by Fransson et al. [Phys. Rev. B 64, 153403 (2001)]. The tunneling lifetimes obtained by the present formulation agree with those obtained by the complex energy method. The analytical expression is useful in modeling tunneling devices in the sequential tunneling picture. We find that coupling of quantum states outside the quantum well to excited states localized in the quantum well is very important, and including these terms changes the tunneling lifetime by about six orders of magnitude.

Complex Energy Method for Scattering Processes

A method for solving few-body scattering equations is proposed and examined. The solution of the scattering equations at complex energies is analytically continued to get scattering T-matrix with real positive energy. Numerical examples document that the method works well for two-nucleon scattering and three-nucleon scattering, if the set of complex energies is properly chosen.

Generalized WKB studies of shape resonance

Based on the generalized WKB and complex energy method, the authors study the atomic shape resonance in the IPA model, where the photoionization cross section shows maximum structure at resonance energies near the top of the barrier. Only f states of atoms around Xe and Rn have observable shape resonance structures.

On the evaluation of spin susceptibilities within multiple scattering theory

The authors develop two alternative reciprocal space methods applicable to the calculation of the spin susceptibility of transition metals. The first, a complex energy method, uses the tau matrices of scattering theory, while the second is based on the one-particle energy eigenvalues and the wavefunction coefficients. They demonstrate that both methods may be used to evaluate the non-interacting susceptibility by performing Brillouin zone integrations. As a second step the interacting quantities may be obtained using the methods described in previous work. Their applications to Pd yield a remarkable similarity between results gained in these different ways.

Further Calculations ofs-Wave Elastice−HScattering above the Ionization Threshold by the Complex-Energy Method

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Calculation of Ionization Amplitudes by the Complex-Energy Method

It is shown that, as the complex energy approaches its real physical value, the dominant part of the amplitude for ionization derived from the Faddeev equations is a product of a known singular factor and the physical scattering amplitude. This information suggests a method of calculating ionization amplitudes from the Faddeev equations. Corrections to the dominant term for this and another amplitude are discussed. Some numerical tests of the method as applied to a simple model are given.