Simple Variational Method Research Articles

Finite temperature variational analysis of the tunneling and localization in spin–phonon model

Temperature dependence of the effective tunneling frequency of the spin–phonon model for a few particular types of coupling has been studied within the framework of the simple variational method. Our analysis shows that for the Ohmic type of coupling, temperature drives the system towards delocalization. The same type of behavior has been noticed for super-Ohmic case, but in the so-called “adiabatic regime”, while in the nonadiabatic case we predict localization transition, analogous to that observed for Ohmic coupling, when temperature dependent coupling constant S ( T ) approaches critical value S ( T ) ∼ 1 / 2 . In contrast to these results, for super-Ohmic ( r = 3 ) case, there was no substantial difference with respect to zero-temperature case. Brief discussion of the validity of the method has been given.

Study of anharmonic singular potentials

A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix elements of H with respect to the eigenfunctions of a soluble singular problem with two free parameters A and B. The matrix eigenvalues are then optimized with respect to A and B for a given N. Applications, convergence rates, and comparisons with earlier work are discussed in detail.

Accuracy of Wind Fields Observed by a Bistatic Doppler Radar Network

The accuracy of wind vectors derived from bistatic dual-Doppler synthesis was investigated. The investigation was based on mathematical examinations and observation data analyses in both convective and stratiform cases. Accurate wind vectors were calculated within a range of 40 8, b , 1508, where b was the bistatic scatter angle. The accuracy is mainly governed by b as the first principle, while sidelobe contamination and the sensitivity of the low-gain bistatic antenna are practically the main obstacles in retrieving accurate wind fields in convective and stratiform echoes, respectively. The sidelobe contamination around strong convective echoes with large gradients of reflectivity can be eliminated by comparing the measured bistatic reflectivity and a clean bistatic radar reflectivity, which is derived from the measured transmitting radar reflectivity and a bistatic radar equation. The radar equation includes the bistatic resolution volume and a bistatic antenna pattern estimated by the longtime observation of stratiform echoes. The equation also leads to the distribution of minimum detectable reflectivity of the bistatic receiver. The multiple bistatic radar observation in stratiform echoes produced three kinds of horizontal wind vectors, which were almost coincident with each other, in the overdetermined region. The composite wind fields are calculated by a simple variational method.

Variational method for the generation of localized Wannier functions on the basis of Bloch functions

A simple and universal variational method for constructing localized Wannier functions from Bloch functions is proposed. The variational procedure is preceded by a symmetry analysis based on the induced representation theory and succeeded by a suitable orthogonalization procedure. The reliability of the method is demonstrated by computations of localized displacements in a one-dimensional diatomic lattice and a germanium lattice, of localized electronic states in a one-dimensional Kronig-Penney model, for the upper valence bands of Si and MgO crystals.

Effective-index increase, form birefringence and transition losses in UV-side-illuminated photosensitive fibers

We present a simple variational method for the analysis of UV-side-illuminated single-mode fibers. We use a shiftable, two-dimensional elliptical Gaussian function as a field trial for the fundamental-mode. By this method, the actual UV-induced peak refractive-index increase can be quantitatively related to the measured effective-index increase. The asymmetry of the UV-induced refractive-index profile due to the absorption of the writing UV light causes both form birefringence and transition losses between UV-illuminated and non-illuminated fiber sections. These characteristics are easily calculated from the results of the variational method. We show that UV-illumination of the fiber from two opposite sides reduces both the form birefringence and the transition losses.

Calculation of resonant frequencies of LS higher order modes in a dielectrically loaded grooved waveguide

AbstractA simple and efficient variation method is presented in this letter, which is employed to calculate the resonant frequencies of LS higher order modes in a dielectrically loaded grooved waveguide. Emphasis is placed on the calculation of the resonant frequencies of LSE11 and LSM11 modes since, certainly the first, and most probably the second will propagate in a practical device. The validity of this method is verified by experiments. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 442–446, 2001.

Two-dimensional electron systems in inversion layers of p-type Hg0.8Zn0.2Te metal-insulator-semiconductor structures

Strong oscillations on capacitance and conductance have been observed in p-type Hg0.8Zn0.2Te metal-insulator-semiconductor structures, made by using a recent process for the interface passivation. This behaviour is attributed to a two-dimensional electron gas in the n-inversion layer and the variation of the conductance maximums with temperature indicates that the dominant perpendicular transport mechanism for electrons is an incoherent two-step tunnelling through deep levels in the gap. Three models have been used to describe the quantum confinement: the simple variational method, the triangular potential approximation and the propagation matrix method. The later approach takes into account the non parabolicity of the conduction band structure and uses a finite height barrier at the insulator-semiconductor interface. A very good agreement between experimental and calculated values for the two lowest subband energy is obtained.

Tetraquarks with heavy flavors

In the framework of a simple nonrelativistic potential model, we have previously studied the stability of a system of two quarks and two antiquarks of identical light flavor. Here, we extend our analysis to quarks (antiquarks) of different masses and discuss the role of heavy flavors on the stability of the system. This analysis is performed by using a simple variational method which proved powerful in the treatment of other few-body systems. We compare our results with other results from the literature and single out a few characteristics of the spectrum of the tetraquarks.

A fast variation method for calculating the anisotropic magnetoexciton ground state

We have developed a fast and simple variation method for calculating the magnetoexciton ground state having anisotropic carrier masses. The exciton Hamiltonian is approximated into an isotropic form with an effective Coulomb interaction coefficient and is readily solved by using a standard variational method. The calculated results of this method are in good agreement with other numerical calculations for a wide range of mass anisotropy covering most semiconductors. For an application of the present theory, we determined the reduced mass of the anisotropic exciton in ordered InGaP 2 from the magnetic field dependence of the photoluminescence transition of the exciton ground state.

Mean-Field Theory of Photoinduced Formation of Surface Reliefs in Side-Chain Azobenzene Polymers

A mean-field model of photoinduced surface reliefs in dye containing side-chain polymers is presented. It is demonstrated that photoinduced ordering of dye molecules subject to anisotropic intermolecular interactions leads to mass transport even when the intensity of the incident light is spatially uniform. Theoretical profiles are obtained using a simple variational method and excellent agreement with experimental surface reliefs recorded under various polarization configurations is found. The polarization dependence of both period and shape of the profiles is correctly reproduced by the model.

A simple variational method for excited states of coupled anharmonic oscillators

A simple variational method for excited states is presented and extended to handle two-body Hamiltonians. The method is applied to coupled anharmonic oscillators with arbitrary coupling strength. Our results for the ground and excited states are in good agreement with other available results. Forn→∞, a simple but accurate analytical expression for the energy levels is obtained. Our method can also be used to calculate the excited states of other Hamiltonians.

Weakly bound three-body systems with no bound subsystems.

We investigate the domain of coupling constants which achieve binding for a 3-body system, while none of the 2-body subsystems is bound. We derive some general properties of the shape of the domain, and rigorous upper bounds on its size, using a Hall--Post decomposition of the Hamiltonian. Numerical illustrations are provided in the case of a Yukawa potential, using a simple variational method.

Excited states of hydrogenic impurities in quantum wells in magnetic fields

Quasi-two-dimensional hydrogenic impurity levels in quantum wells under the influence of magnetic fields are investigated. Experimentally, 1s to np (n=2, 3, 4) transition energies in quantum wells of various widths are measured by the photoconductivity technique for magnetic fields up to 9 T. Theoretically, these energies are calculated by a new variational method that is valid for the whole range of magnetic field strengths, from the zero-field limit to the high-field limit. Good agreement is achieved for every transition for well widths up to approximately 300 AA, for which the confinement effect is appreciable. Consistent discrepancies found for 450 AA are expected to be accounted for by including subband mixing because of the wide width and small subband separation. Our study demonstrates that the simple variational method can produce good results for highly excited levels in magnetic fields provided that the confinement due to the quantum well is sufficiently strong.

Variational analysis of diffused planar and channel waveguides and directional couplers

A simple and accurate analytical variational method is presented for studying the propagation characteristics of diffused planar and channel waveguides. The method gives accurate values of a normalized propagation constant for these waveguides. The method is also applied to the study of the dependence of coupling length on interwaveguide separation in diffused channel-waveguide directional couplers, and comparisons with other available theoretical results and experimental data are presented.

Fluid-dynamical approach to collective modes in metal clusters.

A simple variational method has recently been used to obtain the bulk-plasmon dispersion relation in a metal. In the present work we investigate the eigenmodes of the valence electrons in a metal cluster considering a semiclassical version of the method presented by And\ifmmode \bar{o}\else \={o}\fi{} and Nishizaki. As a variational function we consider the Slater determinant \ensuremath{\Vert}\ensuremath{\varphi}〉 which is related to the Slater determinant \ensuremath{\Vert}${\mathrm{\ensuremath{\varphi}}}_{0}$〉, describing the ground state, by means of the unitary transformation \ensuremath{\Vert}\ensuremath{\varphi}〉=${\mathit{e}}^{(\mathit{i}/\mathrm{\ensuremath{\Elzxh}})\mathit{S}}$\ensuremath{\Vert}${\mathrm{\ensuremath{\varphi}}}_{0}$〉, where S(x,p,t)=\ensuremath{\chi}(x,t)+1/2[p\ensuremath{\cdot}s(x,t)+s(x,t)\ensuremath{\cdot}p]. We use a polynomial approximation to determine the dynamical fields \ensuremath{\chi}(x,t) and s(x,t). It is shown that the eigensolutions satisfy the energy weighted sum rule and the cubic energy weighted sum rule. The spectrum of excited energies, as well as transition densities and currents are obtained for the sodium, aluminum, and silver.

Variational approach to the dynamics of electrons in metals

A simple variational method has recently been used to obtain the bulk plasmon dispersion relation. As a variational function a Slater determinant ”∣〉 has been considered, which is related to the Slater determinant ”∣ 0〉, describing the ground state, by the unitary transformation ”∣〉 = exp ((i/h)S)”∣ 0〉 , where S is a Hermitian operator of the form S = α( t) Q − β( t) P, with Q = Σ j cos( q · x j ) , and P = BΣ j[ p j · q sin ( q · x j) + sin( q · x j ) p j · q ] . The quantum mechanical action principle is used in the harmonic approximation to determine the equations of motion of the collective variables α and β. The method is here extended to the calculation of the dielectric function. The zero point energy of the collective degrees of freedom accounts for most of the correlation energy as obtained by modern techniques

Polarization rotation in periodic loaded rib waveguides

Polarization rotation in an asymmetric periodic loaded rib waveguide is analyzed by a scalar coupled-mode theory with vector correction. The scalar modes of the dielectric loaded rib waveguide are calculated by using a simple variational method. The polarization rotation is found to be caused by a geometric effect due to the asymmetric loading of the waveguide. By phase-matching the two polarized modes through the periodic loading, complete polarization rotation can be achieved. >

Dislocation Bound States in Compound Semiconductors

AbstractIn semiconductors, which have crystal structure without inversion symmetry, charge carriers interact with the long‐range strain field of dislocations through the deformation potential and the piezoelectric couplings. The ground state energy level of the one‐dimensional (1D) band in the potential, due to the long‐range strain field of an edge dislocation, is estimated theoretically, using simple variational and perturbational methods. The ground state energy levels of the 1D band in n‐type direct bandgap III–V and II–VI compound semiconductors are of the order of a few tens to one hundred meV. The contribution of the effect of the piezoelectric potential to the ground state energy level is relatively small, amounting to about 10 to 30% of the total energy. Finally the analogy of the 1D band associated with the dislocations with the 1D quantum well wire (QWW) is also pointed out.

Elementary Excitation in Solid Nuclear Matter

The effects of elementary excitations to the nature of dense solid nuclear matter are investigated using the Pandharipande·Smith (PS) potentials. A trial wave function embodying a simple cubic structure of nucleonic lattice leads to the Hamiltonian describing the dynamics of lattice vibrations (or phonons) spin·waves (or magnons) and isospin·waves (or 'isomagnons'). Magnons and isomagnons are treated as the Holstein·Primakoff bosons. In the density range from around 0.3 to 1 nucleons/fm 3 , the dynamics of phonons approximately reproduces the equations of state for PS's potentials 2 and 3. At the lowest order of perturbations, due to the tensor interaction, magnon has an energy gap of the order of 100 MeV at infinite wavelength, while isomagnon is gapless. The energy is lowered by 0(100 MeV /nucleon) in virtue of the zero·point fluctuation of spins. A simple variational method indicates that the ground state is likely to be realized by the simultaneous condensation of 7[±, 7[0 and of isomagnons, which further lowers the energy by 0(100 MeV /nucleon).

Elementary Excitations in a Solid Nuclear Matter

The effects of elementary excitations to the nature of dense solid nuclear matter are investigated using the Pandharipande·Smith (PS) potentials. A trial wave function embodying a simple cubic structure of nucleonic lattice leads to the Hamiltonian describing the dynamics of lattice vibrations (or phonons) spin·waves (or magnons) and isospin·waves (or 'isomagnons'). Magnons and isomagnons are treated as the Holstein·Primakoff bosons. In the density range from around 0.3 to 1 nucleons/fm 3 , the dynamics of phonons approximately reproduces the equations of state for PS's potentials 2 and 3. At the lowest order of perturbations, due to the tensor interaction, magnon has an energy gap of the order of 100 MeV at infinite wavelength, while isomagnon is gapless. The energy is lowered by 0(100 MeV /nucleon) in virtue of the zero·point fluctuation of spins. A simple variational method indicates that the ground state is likely to be realized by the simultaneous condensation of 7[±, 7[0 and of isomagnons, which further lowers the energy by 0(100 MeV /nucleon).