Lowest-order Corrections Research Articles

Spin–orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals

Spin–orbit coupling of electrons with the crystal lattice plays a crucial role in materials without inversion symmetry, lifting spin degeneracy of the Bloch states and endowing the resulting nondegenerate bands with complex spin textures and topologically nontrivial wavefunctions. We present a detailed symmetry-based analysis of the spin–orbit coupling and the band degeneracies in noncentrosymmetric metals. We systematically derive the semiclassical equations of motion for fermionic quasiparticles near the Fermi surface, taking into account both the spin–orbit coupling and the Zeeman interaction with an applied magnetic field. Some of the lowest-order quantum corrections to the equations of motions can be expressed in terms of a fictitious “magnetic field” in the momentum space, which is related to the Berry curvature of the band wavefunctions. The band degeneracy points or lines serve as sources of a topologically nontrivial Berry curvature. We discuss the observable effects of the wavefunction topology, focusing, in particular, on the modifications to the Lifshitz–Onsager semiclassical quantization condition and the de Haas-van Alphen effect in noncentrosymmetric metals.

Limitations of the ocular wavefront correction with contact lenses

We analyze theoretically, by means of both computer simulations and laboratory experiments, the limitations of correcting aberrations with ideal customized contact lenses. Four experiments are presented: In the first one, we have analyzed the limitations of a static correction on the dynamic wavefront. In the second one, we studied the rotations of a contact lens on the eye using an optical method. The third one researched the limitations of the wavefront correction, focusing on a group of normal and highly aberrated eyes, when the correction suffers from a permanent rotation or translation. The fourth one estimates, under a simple approximation, the error made when applying on the corneal plane the correction corresponding to the wavefront measured at the entrance-pupil plane. Results show that a static correction of the wavefront leaves a residual aberration of 0.15–0.25 μm for a 5 mm pupil. Rotation of the contact lens (up to ±4°) diminishes the effectiveness of the correction. Horizontal or vertical translations of 0.5 mm could generate a high-order-aberration RMS that is higher than the remaining one after a standard low-order correction. In particular, the group of eyes having normal values of high-order aberrations are more sensitive to translations than the one having higher values. Most of the results could be applied to other methods of aberration correction, such as refractive surgery or correction by means of intraocular lenses.

High-Precision Calculations of the Hyperfine Constants for the Low-Lying Excited 2S States of Be+

High-precision Hylleraas-type calculations of the hyperfine constants for the four lowest excited 3 (2)S, 4 (2)S, 5 (2)S, and 6 (2)S states of the (9)Be(+) ion are reported. Small adjustments to the hyperfine constants arising from effects that include the finite nuclear mass, the magnetization density distribution over the nucleus, the Breit-Rosenthal correction for finite nuclear size, and lowest-order relativistic and quantum electrodynamic corrections are considered. The final values obtained for the hyperfine constants for the n (2)S states were: -158.78, -62.43, -30.66, and -17.29 MHz for n = 3, 4, 5, and 6, respectively.

Tunneling in two-dimensional systems using a higher-order Herman–Kluk approximation

A principal weakness of the Herman-Kluk (HK) semiclassical approximation is its failure to provide a reliably accurate description of tunneling between different classically allowed regions. It was previously shown that semiclassical corrections significantly improve the HK treatment of tunneling for the particular case of the one-dimensional Eckart system. Calculations presented here demonstrate that the lowest-order correction also substantially improves the HK description of tunneling across barriers in two-dimensional systems. Numerical convergence issues either do not arise or are easily overcome, so that the calculations require only a moderate number of ordinary, real, classical trajectories.

Lower order terms in the 1-level density for families of holomorphic cuspidal newforms

The Katz-Sarnak density conjecture states that, in the limit as the conductors tend to infinity, the behavior of normalized zeros near the central point of families of L-functions agree with the N -> oo scaling limits of eigenvalues near 1 of subgroups of U(N). Evidence for this has been found for many families by studying the n-level densities; for suitably restricted test functions the main terms agree with random matrix theory. In particular, all one-parameter families of elliptic curves with rank r over Q(T) and the same distribution of signs of functional equations have the same limiting behavior. We break this universality and find family dependent lower order correction terms in many cases; these lower order terms have applications ranging from excess rank to modeling the behavior of zeros near the central point, and depend on the arithmetic of the family. We derive an alternate form of the explicit formula for GL(2) L-functions which simplifies comparisons, replacing sums over powers of Satake parameters by sums of the moments of the Fourier coefficients lambda_f(p). Our formula highlights the differences that we expect to exist from families whose Fourier coefficients obey different laws (for example, we expect Sato-Tate to hold only for non-CM families of elliptic curves). Further, by the work of Rosen and Silverman we expect lower order biases to the Fourier coefficients in families of elliptic curves with rank over Q(T); these biases can be seen in our expansions. We analyze several families of elliptic curves and see different lower order corrections, depending on whether or not the family has complex multiplication, a forced torsion point, or non-zero rank over Q(T).

Superfluid density near the critical temperature in the presence of random planar defects

The superfluid density near the superconducting transition is investigated in the presence of spatial inhomogeneity in the critical temperature. Disorder is accounted for by means of a random ${T}_{c}$ term in the conventional Ginzburg-Landau action for the superconducting order parameter. Focusing on the case where a low density of randomly distributed planar defects is responsible for the variation in ${T}_{c}$, we derive the lowest-order correction to the superfluid density in powers of the defect concentration. The correction is calculated assuming a broad Gaussian distribution for the strengths of the defect potentials. Our results are in a qualitative agreement with the superfluid density measurements in the underdoped regime of high-quality YBCO crystals by Broun and co-workers.

Relationship between preoperative aberrations and postoperative refractive error in enhancement of previous laser in situ keratomileusis with the LADARVision system

To identify factors leading to inaccuracy of spherical correction in wavefront-guided enhancement treatments. Department of Ophthalmology, University of California, Irvine, California, USA. This retrospective outcomes analysis comprised 23 eyes (20 patients) having wavefront-guided flap-lift (19 eyes) or photorefractive keratectomy (4 eyes) enhancements after conventional non-wavefront-guided laser in situ keratomileusis (LASIK) for correction of residual myopia with a minimum follow-up of 1 month. Main outcomes measures were changes in lower-order aberrations and higher-order aberrations (HOAs) related to predictability of the refractive outcome. The enhancement procedures reduced HOAs. Because of a hyperopic shift, however, uncorrected visual acuity (UCVA) improved 2 or more Snellen lines in 3 of 9 eyes (33.3%) treated without a surgeon offset compared with 9 of 14 (64.3%) when a surgeon offset was incorporated into the treatment plan. The quantitative amount of preoperative HOAs correlated with the amount of hyperopic shift, particularly strongly for spherical aberration (r(2) = 0.446, P = .0005). The amount of hyperopic shift was related in a linear manner to the amount of HOAs (for spherical aberrations, Y = 1.31X - 0.30, where Y is the postoperative manifest refraction spherical equivalent and X is the wavefront error in microns root mean square). Wavefront-guided enhancements can reduce levels of HOAs. Although UCVA improved in many patients, some with high levels of preenhancement spherical aberration had worse UCVA. Adjusting the nomogram for the amount of preenhancement HOAs may improve the accuracy of the lower-order correction in wavefront-guided enhancements.

Fluctuation-induced quantum interactions between compact objects and a planemirror

The interaction of compact objects with an infinitely extended mirror plane due toquantum fluctuations of a scalar or electromagnetic field that scatters off the objects isstudied. The mirror plane is assumed to obey either Dirichlet or Neumann boundaryconditions or to be perfectly reflecting. Using the method of images, we generalize arecently developed approach for compact objects in unbounded space to show that theCasimir interaction between the objects and the mirror plane can be accuratelyobtained over a wide range of separations in terms of charge and current fluctuationsof the objects and their images. Our general result for the interaction dependsonly on the scattering matrices of the compact objects. It applies to scalar fieldswith arbitrary boundary conditions and to the electromagnetic field coupled todielectric objects. For the experimentally important electromagnetic Casimirinteraction between a perfectly conducting sphere and a plane mirror we presentthe first results that apply at all separations. We obtain both an asymptoticlarge-distance expansion and the two lowest-order correction terms to the proximity forceapproximation. The asymptotic Casimir–Polder potential for an atom and a mirror isgeneralized to describe the interaction between a dielectric sphere and a mirror,involving higher-order multipole polarizabilities that are important at sub-asymptoticdistances.

2γ and 3γ annihilation as calibration processes for high energy e + e − colliders

Born differential cross sections and the lowest-order radiative correction to them are obtained in the kinematics of large-angle final photon emissions in high-energy electron-positron annihilation processes. Taking into account the possible emission of real soft and hard photons in collinear kinematics, we show the validity of the Drell-Yan form of the differential cross section with the nonsinglet structure functions of the initial leptons. The leading and next-to-leading contribution to the cross sections is obtained. The relevant numerical estimations are presented.

Breakdown of Migdal–Eliashberg Theory via Catastrophic Vertex Divergence at Low Phonon Frequency

We investigate the applicability of Migdal–Eliashberg (ME) theory by revisiting Migdal’s analysis within the dynamical mean-field theory framework. First, we compute spectral functions, the quasi-particle weight, the self energy, renormalised phonon frequency and resistivity curves of the half-filled Holstein model. We demonstrate how ME theory has a phase-transition-like instability at intermediate coupling, and how the Engelsberg–Schrieffer (ES) picture is complicated by low-energy excitations from higher order diagrams (demonstrating that ES theory is a very weak coupling approach). Through consideration of the lowest-order vertex correction, we analyse the applicability of ME theory close to this transition. We find a breakdown of the theory in the intermediate coupling adiabatic limit due to a divergence in the vertex function. The region of applicability is mapped out, and it is found that ME theory is only reliable in the weak coupling adiabatic limit, raising questions about the accuracy of recent analyses of cuprate superconductors which do not include vertex corrections.

Completeα2relativistic corrections to the pure vibrational non-Born-Oppenheimer energies ofHeH+

We report the implementation of the complete set of the lowest-order relativistic corrections of the order of ${\ensuremath{\alpha}}^{2}$ (where $\ensuremath{\alpha}$ is the fine structure constant) for calculating vibrational states of diatomic molecular systems within the framework that does not assume the Born-Oppenheimer approximation. To test the accuracy of the approach we have performed calculations for all rotationless vibrational states (also called pure vibrational states or $S$ states) of the ${\text{HeH}}^{+}$ ion in the ground electronic state. For the lowest transitions, where very precise experimental results are available, an excellent agreement with the experimental values has been achieved.

Application of the multiscale singular perturbation method to nonparaxial beam propagations in free space

Starting from the vector Maxwell's equations and applying the multiscale singular perturbation method, the nonparaxial beam propagation is studied in free space. Two new equations have been derived for transverse and longitudinal electric fields of an arbitrary polarized electromagnetic wave even in the case of tightly focused nonparaxial laser beams. By using the analogy of the optical beam in the space domain and the optical pulse in the time domain, the higher-order diffraction term is introduced. For strongly nonparaxial beams that are characterized by large values of the perturbative parameter, our correction solutions yield an accurate description of the field in the near-field region and are consistent with all other correction results obtained by others in the far-field region. For weakly nonparaxial beams, our correction solutions can be expressed in a very simple form that is proved to be exactly consistent with the solutions obtained by Cao and Deng [J. Opt. Soc. Am. A15, 1144 (1998)]. In addition, the lowest-order correction to the paraxial approximation can be found to be in good agreement with the results of Lax et al. [Phys. Rev. A11, 1365 (1975)] and Seshadri [J. Opt. Soc. Am. A19, 2134 (2002)].

An efficient method for multi-band plane wave CI calculations in semiconductor QD's

A method for the calculation of a large number of Coulomb integrals among quantum dot states given in the envelope function plane wave representation was presented. The efficiency of the method was achieved by performing a calculation in k -space. The degree of accuracy can be systematically improved by increasing the embedding box that defines the k -space grid or by introducing the several lowest order corrections in the multipole expansion of the Coulomb integral.

Geometric phase in a composite system subjected to decoherence

In this paper, we investigate the geometric phase of a composite system which is composed of two spin-\(\frac{1}{2}\) particles driven by a time-varying magnetic field. Firstly, we consider the special case that only one subsystem driven by time-varying magnetic field. Using the quantum jump approach, we calculate the geometric phase associated with the adiabatic evolution of the system subjected to decoherence. The results show that the lowest order corrections to the phase in the no-jump trajectory is only quadratic in decoherence coefficient. Then, both subsystem driven by time-varying magnetic field is considered, we show that the geometric phase is related to the exchange-interaction coefficient and polar angle of the magnetic field.

Born-Oppenheimer expansion at constant energy

The well-known Born-Oppenheimer procedure considers molecular properties in the limit of large values of the nuclear mass M (in units of electronic mass), with quantum numbers held constant. It is shown that the lowest-order correction to the molecular wave function is proportional to M(-34). Here we consider the same expansion, but with energy held constant instead of quantum numbers. We show that, if the singular coupling term near a conical intersection is removed via a quasidiabatic transformation, the lowest-order remaining correction is proportional to M(-12).

The effect of surface tension (Kelvin effect) on the equilibrium radius of a hygroscopic aqueous aerosol particle

The effect of surface tension (the Kelvin effect) on the equilibrium radius of an aqueous solution drop at fractional relative humidity h less than unity is analyzed mathematically. Expressions for the lowest-order corrections to the equilibrium radius and radius ratio (relative to the volume-equivalent dry radius r dry ) due to the Kelvin effect are presented and compared with data for solution drops of ammonium sulfate and sodium chloride. To lowest order the decrease in equilibrium radius resulting from the Kelvin effect is independent of the amount of solute in the drop and is approximated to good accuracy by Δ r / nm = - ( h / 3 ) / ( 1 - h ) , with only weak dependences on solute and temperature. The importance of the Kelvin effect on drop radius is further quantified in several ways. The value of the volume-equivalent dry radius below which the Kelvin effect results in more than a 5% decrease in the equilibrium radius of a solution drop at given h is approximately r dry , 5 % / nm = 8 h / ( 1 - h ) 2 / 3 . The decrease in the hygroscopic growth factor g of an aqueous solution drop between a low relative humidity and h = 0.9 resulting from the Kelvin effect is given approximately by Δ g = - ( 3 nm ) / r dry , again with only weak dependences on solute and temperature. These approximations compare well with measurements of growth factors of ammonium sulfate solution drops for dry radius as low as 10 nm. These findings, all of which are presented for fractional relative humidity as the independent variable, allow the magnitude of the Kelvin effect and its consequences on the properties of an aqueous solution drop to be readily assessed.

The effect of intersubsystem coupling on the geometric phase in a composite system driven by decohering quantized fields

We investigate the behaviour of the geometric phase of a bipartite system with intersubsystem coupling via a quantum jump approach, where one of the subsystems is driven by a one- or two-mode quantized field which is also subjected to decoherence. The results show that the first correction due to the decohering field is only quadratic in decaying rate λ when the evolution of the system is adiabatic, and the lowest order correction is related to the first order in λ when the evolution of the system is non-adiabatic. Moreover, an interesting interpretation of this phenomenon is given.

Effective Hamiltonian for the pyrochlore antiferromagnet: Semiclassical derivation and degeneracy

In the classical pyrochlore lattice Heisenberg antiferromagnet, there is a macroscopic continuous ground-state degeneracy. We study the semiclassical limit of large spin length $S$, keeping only the lowest-order (in $1∕S$) correction to the classical Hamiltonian. We perform a detailed analysis of the spin-wave modes, and using a real-space loop expansion, we produce an effective Hamiltonian, in which the degrees of freedom are Ising variables representing fluxes through loops in the lattice. We find a family of degenerate collinear ground states, related by gaugelike ${Z}_{2}$ transformations, and provide bounds for the order of the degeneracy. We further show that the theory can readily be applied to determine the ground states of the Heisenberg Hamiltonian on related lattices and to field-induced collinear magnetization plateau states.

Electroweak Radiative Corrections to Parity-Violating Asymmetry in Møller Scattering

We have computed the lowest-order electroweak radiative corrections (sans vacuum polarization contribution) to parity-violating observables in polarized Møller scattering. A covariant method of removing infrared divergences is applied, which allows to compute the corrections without introducing any unphysical parameters. When applied to the kinematics of SLAC E158 experiment, the considered radiative corrections reduce the parity-violating asymmetry by about 13%.

Relativistic Correction to the Helium Dimer Interaction Energy

The lowest-order relativistic correction to the helium-helium interaction energy has been calculated for the first time, using two independent methods based on expansions in explicitly correlated Gaussian functions. At the equilibrium interatomic distance of 5.6 bohr, this correction amounts to +15.4 +/- 0.6 mK. As a by-product, a new upper bound of -10.9985 K for the nonrelativistic Born-Oppenheimer interaction energy has been obtained.