Terms Of Perturbation Theory Research Articles

Crosstalk- and charge-noise-induced multiqubit decoherence in exchange-coupled quantum dot spin qubit arrays

We determine the interqubit crosstalk- and charge-noise-induced decoherence time ${T}_{2}^{*}$ for a system of $L$ exchange-coupled electronic spin qubits in arrays of size $L=3$--14 for a number of different multiqubit geometries by directly calculating the return probability. We compare the behavior of the return probability to other quantities, namely, the average spin, the Hamming distance, and the entanglement entropy. In all cases, we use a starting state with alternating spins, $|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}=|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\cdots}\ensuremath{\rangle}$. We show that a power law behavior, ${T}_{2}^{*}\ensuremath{\propto}{L}^{\ensuremath{-}\ensuremath{\gamma}}$, is a good fit to the results for the chain and ring geometries as a function of the number of qubits and provide numerical results for the exponent $\ensuremath{\gamma}$. We find that ${T}_{2}^{*}$ depends crucially on the multiqubit geometry of the system. We also calculate the expectation value of one of the spins, the Hamming distance, and the entanglement entropy and show that they are good proxies for the return probability for measuring ${T}_{2}^{*}$. A key finding is that ${T}_{2}^{*}$ decreases with increasing $L$. We also demonstrate that these results may be understood in terms of perturbation theory and its breakdown.

Ground-state hyperfine structure of light muon-electron ions

The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.

Magnetoelastic anisotropy in Heusler-type Mn2−δCoGa1+δ films

Perpendicular magnetization is essential for high-density memory application using magnetic materials. High-spin polarization of conduction electrons is also required for realizing large electric signals from spin-dependent transport phenomena. Heusler alloy is a well-known material class showing the half-metallic electronic structure. However, its cubic lattice nature favors in-plane magnetization and thus minimizes the perpendicular magnetic anisotropy (PMA), in general. This study focuses on an inverse-type Heusler alloy, Mn$_{2-\delta}$CoGa$_{1+\delta}$ (MCG) with a small off-stoichiometry ($\delta$) , which is expected to be a half-metallic material. We observed relatively large uniaxial magnetocrystalline anisotropy constant ($K_\mathrm{u}$) of the order of 10$^5$ J/m$^3$ at room temperature in MCG films with a small tetragonal distortion of a few percent. A positive correlation was confirmed between the $c/a$ ratio of lattice constants and $K_\mathrm{u}$. Imaging of magnetic domains using Kerr microscopy clearly demonstrated a change in the domain patterns along with $K_\mathrm{u}$. X-ray magnetic circular dichroism (XMCD) was employed using synchrotron radiation soft x-ray beam to get insight into the origin for PMA. Negligible angular variation of orbital magnetic moment ($\Delta m_\mathrm{orb}$) evaluated using the XMCD spectra suggested a minor role of the so-called Bruno's term to $K_\mathrm{u}$. Our first principles calculation reasonably explained the small $\Delta m_\mathrm{orb}$ and the positive correlation between the $c/a$ ratio and $K_\mathrm{u}$. The origin of the magnetocrystalline anisotropy was discussed based on the second-order perturbation theory in terms of the spin--orbit coupling, claiming that the mixing of the occupied $\uparrow$- and the unoccupied $\downarrow$-spin states is responsible for the PMA of the MCG films.

Multi-channel Decay Partial Widths of <sup>1,3</sup>L° Autoionizing Levels of O<sup>6+</sup> Below N=5 Threshold

The motivation of the diagonalization method is to take into consideration the coupling between closed and opened channels in term of perturbation theory and to neglect the indirect coupling as well but also the autoionisation states through the opened channels. This procedure leads to a relatively simple mathematical problem consisting of solving a system of linear algebraic equations instead of a system of coupled differential equations or integro-differential equations. In this paper, we will focus on the Resonance positions, Partial and total widths for the autoionization into various decay channels of some ^1,3L° doubly excited states of helium-like oxygen ion O⁶⁺ converging on the N=5 hydrogenic thresholds are reported for L=1, 2, 3, 4, 5, 6 and 7. The calculation was made in the framework of the diagonalization method approximation in LS coupling scheme. The partial widths for multi-channel autoionizing levels to sublevels of O⁷⁺ are calculated by neglecting the direct coupling between the open channels. We were able to find results consistent with some in the literature. It is about the configuration P, D, F, G, H, I and K. We could see that the decays are relatively dependent on the ionization thresholds of the residual ion O⁷⁺. Some analyses are made on these resultast and only according to the level of decay focused in this paper then made a surplus in the framework of nuclear spectroscopy.

Near-BPS baby Skyrmions

We consider the baby-Skyrme model in the regime close to the so-called restricted baby-Skyrme model, which is a BPS model with area-preserving diffeomorphism invariance. The perturbation takes the form of the standard kinetic Dirichlet term with a small coefficient ϵ. Classical solutions of this model, to leading order in ϵ, are called restricted harmonic maps. In the BPS limit (ϵ → 0) of the model with the potential being the standard pion-mass term, the solution with unit topological charge is a compacton. Using analytical and numerical arguments we obtain solutions to the problem for topological sectors greater than one. We develop a perturbative scheme in ϵ with which we can calculate the corrections to the BPS mass. The leading order ( mathcal{O}left({upepsilon}^1right) ) corrections show that the baby Skyrmion with topological charge two is energetically preferred. The binding energy requires us to go to the third order in ϵ to capture the relevant terms in perturbation theory, however, the binding energy contributes to the total energy at order ϵ2. We find that the baby Skyrmions — in the near-BPS regime — are compactons of topological charge two, that touch each other on their periphery at a single point and with orientations in the attractive channel.

Dyakonov-like waveguide modes in an interfacial strip waveguide

We study Dyakonov surface waveguide modes in a waveguide represented by an interface of two anisotropic media confined between two air half-spaces. We analyze such modes in terms of perturbation theory in the approximation of weak anisotropy. We show that in contrast to conventional Dyakonov surface waves that decay monotonically with distance from the interface, Dyakonov waveguide modes can have local maxima of the field intensity away from the interface. We confirm our analytical results by comparing them with full-wave electromagnetic simulations. We believe that this work can bring new ideas in the research of Dyakonov surface waves.

Anharmonicity measure for materials

Theoretical frameworks used to qualitatively and quantitatively describe nuclear dynamics in solids are often based on the harmonic approximation. However, this approximation is known to become inaccurate or to break down completely in many modern functional materials. Interestingly, there is no reliable measure to quantify anharmonicity so far. Thus, a systematic classification of materials in terms of anharmonicity and a benchmark of methodologies that may be appropriate for different strengths of anharmonicity is currently impossible. In this work, we derive and discuss a statistical measure that reliably classifies compounds across temperature regimes and material classes by their "degree of anharmonicity". This enables us to distinguish "harmonic" materials, for which anharmonic effects constitute a small perturbation on top of the harmonic approximation, from strongly "anharmonic" materials, for which anharmonic effects become significant or even dominant and the treatment of anharmonicity in terms of perturbation theory is more than questionable. We show that the analysis of this measure in real and reciprocal space is able to shed light on the underlying microscopic mechanisms, even at conditions close to, e.g., phase transitions or defect formation. Eventually, we demonstrate that the developed approach is computationally efficient and enables rapid high-throughput searches by scanning over a set of several hundred binary solids. The results show that strong anharmonic effects beyond the perturbative limit are not only active in complex materials or close to phase transitions, but already at moderate temperatures in simple binary compounds.

The correlation function of (1, 1) and (2, 2) supersymmetric theories with Toverline{T} deformation

In the paper, we compute the correlation functions in 2D mathcal{N} = (1, 1) and mathcal{N} = (2, 2) superconformal field theories with Toverline{T} deformation up to the first order of the deformation in terms of perturbation theory. With the help of superconformal Ward identity in mathcal{N} = (1, 1) and mathcal{N} = (2, 2) theories and careful regularization, the correlation functions in the deformed theory can be obtained up to the first order perturbation. This study is the extension from previous bosonic Toverline{T} deformation to the supersymmetric one.

Resonance Parameters, Autoionisation of <sup>2S+1</sup>L<sup>o</sup> Doubly Excited N<sup>5+</sup> Ion States Associated with n=3 and 4, N<sup>6+</sup> Threshold

The motivation of the diagonalization method is to take into consideration the coupling between closed and opened channels in term of perturbation theory and to neglect the indirect coupling as well but also the autoionisation states through the opened channels. This procedure leads to a relatively simple mathematical problem consisting of solving a system of linear algebraic equations instead of a system of coupled differential equations or integro-differential equations. Diagonalization method under LS coupling scheme for the states ^1,3P^o; ^1,3D^o; ^1,3F^o; ^1,3G^o; ^1,3H^o was performed. The partial widths for multi-channel autoionizing levels to sublevels of N⁶⁺ were carried out by neglecting the direct coupling between opened channels. The calculations of total and partial widths of the (nln'l') ^1,3L^o (L=1, 2, 3, 4 and 5) multiple-decay-channel system N⁵⁺ were performed. From L=1 to 2, the (4l4l') ^1,3Lo states located under n=3 and the (3lnl') ^1,3Lo</sup> states follow the same rules. All the (4l4l') ^1,3Go and (4l4l') ^1,3H^o states located under n=3 observe the rule 1.

Computing Perturbations in the Two-Planetary Three-Body Problem with Masses Varying Non-isotropically at Different Rates

The classical problem of three bodies of variable masses is considered in the case when two of the bodies are protoplanets and all the masses vary non-isotropically at different rates. The problem is analyzed in the framework of the planetary perturbation theory in terms of the osculating elements of aperiodic motion on quasi-conic sections. An algorithm for symbolic computation of the disturbing function and its expansion into power series in terms of the eccentricities and inclinations is discussed in detail. Differential equations describing the long-term evolution of the orbital parameters are derived in the form of Lagrange’s planetary equations. All the relevant calculations are done with the computer algebra system Wolfram Mathematica.

Engineering effective Hamiltonians

In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilizes perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we provide a general framework for computing arbitrary time-dependent perturbation theory terms, as well as their gradients with respect to control variations, enabling the use of gradient methods for optimizing these terms. In particular, we show that effective Hamiltonian engineering is an instance of a bilinear control problem—the same general problem class as that of standard unitary design—and hence the same optimization algorithms apply. We demonstrate this method in various examples, including decoupling, recoupling, and robustness to control errors and stochastic errors. We also present a control engineering example that was used in experiment, demonstrating the practical feasibility of this approach.

Unusual square roots in the ghost-free theory of massive gravity

A crucial building block of the ghost free massive gravity is the square root function of a matrix. This is a problematic entity from the viewpoint of existence and uniqueness properties. We accurately describe the freedom of choosing a square root of a (non-degenerate) matrix. It has discrete and (in special cases) continuous parts. When continuous freedom is present, the usual perturbation theory in terms of matrices can be critically ill defined for some choices of the square root. We consider the new formulation of massive and bimetric gravity which deals directly with eigenvalues (in disguise of elementary symmetric polynomials) instead of matrices. It allows for a meaningful discussion of perturbation theory in such cases, even though certain non-analytic features arise.

Operator mixing in large N superconformal field theories on S4 and correlators with Wilson loops

We find a general formula for the operator mixing on the $\mathbb{S}^4$ of chiral primary operators (CPO) for the ${\cal N}=4$ theory at large $N$ in terms of Chebyshev polynomials. As an application, we compute the correlator of a CPO and a Wilson loop, reproducing an earlier result by Giombi and Pestun obtained from a two-matrix model proposal. Finally, we discuss a simple method to obtain correlators in general ${\cal N}=2$ superconformal field theories in perturbation theory in terms of correlators of the ${\cal N}=4$ theory.

Precision comparison of the power spectrum in the EFTofLSS with simulations

We study the prediction of the dark matter power spectrum at two-loop order in the Effective Field Theory of Large Scale Structures (EFTofLSS) using high precision numerical simulations. In our universe, short distance non-linear fluctuations, not under perturbative control, affect long distance fluctuations through an effective stress tensor that needs to be parametrized in terms of counterterms that are functions of the long distance fluctuating fields. We find that at two-loop order it is necessary to include three counterterms: a linear term in the overdensity, δ, a quadratic term, δ2, and a higher derivative term, ∂2δ. After the inclusion of these three terms, the EFTofLSS at two-loop order matches simulation data up to k ≃ 0.34 h Mpc−1 at redshift z = 0, up to k ≃ 0.55 h Mpc−1 at z = 1, and up to k ≃ 1.1 h Mpc−1 at z = 2. At these wavenumbers, the cosmic variance of the simulation is at least as small as 10−3, providing for the first time a high precision comparison between theory and data. The actual reach of the theory is affected by theoretical uncertainties associated to not having included higher order terms in perturbation theory, for which we provide an estimate, and by potentially overfitting the data, which we also try to address. Since in the EFTofLSS the coupling constants associated with the counterterms are unknown functions of time, we show how a simple parametrization gives a sensible description of their time-dependence. Overall, the k-reach of the EFTofLSS is much larger than previous analytical techniques, showing that the amount of cosmological information amenable to high-precision analytical control might be much larger than previously believed.

Topological charge using cooling and the gradient flow

The equivalence of cooling to the gradient flow when the cooling step $n_c$ and the continuous flow step of gradient flow $\tau$ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate $n_c$ and $\tau$ and show that the results for the topological charge become equivalent when rescaling $\tau \simeq n_c/({3-15 c_1})$ where $c_1$ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with $N_f=2+1+1$ twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling $\tau \simeq n_c/({3-15 c_1})$ leads to equivalent results.

Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators

The method of equations of motion for spin operators in the case of O(3) Heisenberg ferromagnet is systematically analyzed starting from the effective Lagrangian. It is shown that the random phase approximation and the Callen approximation can be understood in terms of perturbation theory for type B magnons. Also, the second order approximation of Kondo and Yamaji for one dimensional ferromagnet is reduced to the perturbation theory for type A magnons. An emphasis is put on the physical picture, i.e. on magnon–magnon interactions and symmetries of the Heisenberg model. Calculations demonstrate that all three approximations differ in manner in which the magnon–magnon interactions arising from the Wess–Zumino term are treated, from where specific features and limitations of each of them can be deduced.

Filtrations in Dyson–Schwinger equations: Next-to[formula omitted]-leading log expansions systematically

Dyson–Schwinger equations determine the Green functions Gr(α,L) in quantum field theory. Their solutions are triangular series in a coupling constant α and an external scale parameter L for a chosen amplitude r, with the order in L bounded by the order in the coupling.Perturbation theory calculates the first few orders in α. On the other hand, Dyson–Schwinger equations determine next-to{j}-leading log expansions, Gr(α,L)=1+∑j=0∞∑MpjMαjM(u). ∑M sums for any finite j a finite number of functions M in u. Here, u is the one-loop approximation to Gr, for example, for the (inverse) propagator in massless Yukawa theory, u=αL/2.The leading logs come then from the trivial representation, e.g. M(u)=1−1−2u in massless Yukawa theory. The respective period at j=0 is p0M(u)=1. All non-leading logs are organized by corresponding suppressions in powers αj.We describe an algebraic method to derive all next-to{j}-leading log terms from the knowledge of the first (j+1) terms in perturbation theory and their filtrations. This implies the calculation of the functions M(u) and periods pjM.In the first part of our paper, we investigate the structure of Dyson–Schwinger equations and develop a method to filter their solutions. Applying renormalized Feynman rules maps each filtered term to a certain power of α and L in the log-expansion.Based on this, the second part derives the next-to{j}-leading log expansions. Our method is general. Here, we exemplify it using the examples of the propagator in Yukawa theory and the photon self-energy in quantum electrodynamics. In particular, we give explicit formulas for the leading log, next-to-leading log and next-to-next-to-leading log orders in terms of at most three-loop Feynman integrals. The reader may apply our method to any (set of) Dyson–Schwinger equation(s) appearing in renormalizable quantum field theories.

Explaining the success of Kogelnik's coupled-wave theory by means of perturbation analysis: discussion.

The problem of diffraction of an electromagnetic wave by a thick hologram grating can be solved by the famous Kogelnik's coupled-wave theory (CWT) to a very high degree of accuracy. We confirm this finding by comparing the CWT and the exact result for a typical example and propose an explanation in terms of perturbation theory. To this end we formulate the problem of diffraction as a matrix problem following similar well-known approaches, especially rigorous coupled-wave theory (RCWT). We allow for a complex permittivity modulation and a possible phase shift between refractive index and absorption grating and explicitly incorporate appropriate boundary conditions. The problem is solved numerically exact for the specific case of a planar unslanted grating and a set of realistic values of the material's parameters and experimental conditions. Analogously, the same problem is solved for a two-dimensional truncation of the underlying matrix that would correspond to a CWT approximation but without the usual further approximations. We verify a close coincidence of both results even in the off-Bragg region and explain this result by means of a perturbation analysis of the underlying matrix problem. Moreover, the CWT is found not only to coincide with the perturbational approximation in the in-Bragg and the extreme off-Bragg cases, but also to interpolate between these extremal regimes.

Mechanism of Uniaxial Magnetocrystalline Anisotropy in Transition Metal Alloys

Magnetocrystalline anisotropy in transition metal alloys (FePt, CoPt, FePd, MnAl, MnGa, and FeCo) was studied using first-principles calculations to elucidate its specific mechanism. The tight-binding linear muffin-tin orbital method in the local spin-density approximation was employed to calculate the electronic structure of each compound, and the anisotropy energy was evaluated using the magnetic force theorem and the second-order perturbation theory in terms of spin-orbit interactions. We systematically describe the mechanism of uniaxial magnetocrystalline anisotropy in real materials and present the conditions under which the anisotropy energy can be increased. The large magnetocrystalline anisotropy energy in FePt and CoPt arises from the strong spin-orbit interaction of Pt. In contrast, even though the spin-orbit interaction in MnAl, MnGa, and FeCo is weak, the anisotropy energies of these compounds are comparable to that of FePd. We found that MnAl, MnGa, and FeCo have an electronic structure that is efficient in inducing the magnetocrystalline anisotropy in terms of the selection rule of spin-orbit interaction.

Pair correlations in a bidisperse ferrofluid in an external magnetic field: theory and computer simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole-dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole-dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation function g(r) − 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small-angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional composition of a ferrofluid, interparticle correlations, and external magnetic field.