On the application of Brillouin—Wigner perturbation theory to multireference configuration mixing

A posteriori corrections to state specific multireference configuration interaction are proposed which restore linear scaling with particle number. The corrections are based on an analysis of the Brillouin-Wigner perturbation theory, using a Lippmann-Schwinger-like equation.     

Soliton perturbation theory of Biswas–Milovic equation

This paper studies the perturbed Biswas–Milovic equation by the aid of soliton perturbation theory. The adiabatic variation of the soliton parameters is derived from the modified integrals of motion. The velocity of the soliton is also obtained when these perturbation terms are turned on. There are four types of nonlinear media that are taken into consideration.     

Decay width of positronium. O(α2) correction in second-order perturbation theory

Corrections ² to the decay width of parapositronium and orthopositronium are calculated to second order in perturbation theory using the local quasipotential equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 3–7, October, 1994.     

Analytical energy gradients for local second-order Møller-Plesset perturbation theory using intrinsic bond orbitals

ABSTRACT

We present the theory and an implementation for PAO-LMP2 analytical energy gradients (local second-order Møller-Plesset perturbation theory with domains of projected atomic orbitals), using intrinsic bond orbitals (IBOs). The accuracy of optimised LMP2 geometry parameters relative to canonical MP2 and CCSD(T) ones is benchmarked for more than 100 small- to medium-sized molecules. Using augmented triple-ζ basis sets, the deviations of computed LMP2 bond lengths and bond angles from the corresponding MP2 ones are small and quickly decrease with increasing domain sizes. For small domains, a systematic compensation between the intrinsic error of MP2 and the errors due to the local approximations is found, so that the LMP2 results deviate less from CCSD(T) than the MP2 ones. On the other hand, with extended domains, the differences between LMP2 and MP2 geometry parameters become negligible.     

Modified thermodynamic perturbation theory for fused–sphere dimer fluids

Wertheim's thermodynamic perturbation theory of first order (TPT1) is based on the approximation that the monomer–monomer distribution functions can be approximated by the reference fluid distribution functions regardless of the amount of bonding. This is remarkably accurate for chains formed by tangent spheres, but no longer valid for chains of fused spheres. This constitutes the reason for the inadequacy of TPT1 for fused sphere chains. We present a systematic modification of TPT1, the path integral perturbation method, that takes into account the variations of the distribution functions with extent of bonding. We demonstrate the accuracy of the theory for mixtures of hard spheres and diatomics over a range of extent of bonding (pure monomers to pure dimers) and degree of fusion (bond length 0–1). We found that the choice of reference fluid was decisive for the accuracy of the model's predictions. The proposed theory can accurately predict the properties of mixtures of hard spheres and diatomics, and of the pure fused diatomic fluids. The results from the path integral theory are in excellent agreement with simulation results, and compare favourably with the results from the Tildesley–Streett and the Boublík–Nezbeda equations of state.     

Accurate nucleon–nucleon potential based upon chiral perturbation theory

We present an accurate nucleon–nucleon (NN) potential based upon chiral effective Lagrangians. The model includes one- and two-pion exchange contributions up to chiral order three. We show that a quantitative fit of the NN D-wave phase shifts requires contact terms (which represent the short range force) of order four. Within this framework, the NN phase shifts below 300 MeV lab. energy and the properties of the deuteron are reproduced with high-precision. This chiral NN potential represents a reliable starting point for testing the chiral effective field theory approach in exact few-nucleon and microscopic nuclear many-body calculations. An important implication of the present work is that the chiral 2π exchange at order four is of crucial interest for future chiral NN potential development.     

Convergent perturbation theory for a q–deformed anharmonic oscillator

A q–deformed anharmonic oscillator is defined within the framework of q–deformed quantum mechanics. It is shown that the Rayleigh–Schr?dinger perturbation series for the bounded spectrum converges to exact eigenstates and eigenvalues, for q close to 1. The radius of convergence becomes zero in the undeformed limit. Received: 6 August 1998 / Published online: 16 September 1998     

K → πππγ in chiral perturbation theory

We present a complete analysis K → 3ππγ decays to (p ⁴) in the low-energy expansion of the Standard Model. We employ the notion of “generalized bremsstrahlung” to take full advantage of experimental information on the corresponding non-radiative K → 3π decays     

“Phonon” scattering beyond perturbation theory

Searching and designing materials with intrinsically low lattice thermal conductivity(LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical-bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T~(-1) relationship(T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.     

K→ππγ and chiral perturbation theory

Weak radiative decaysK _L,S →π⁺π^?γ andK ⁺→π⁺π⁰γ are reexamined. The electromagnetic form factors and long-distance contributions to the direct photon emission are evaluated using the higher order effective chiral Lagrangian. We find that (1) the naive soft-pion theorem cannot be applied to the magnetic-type transition amplitude, (2) the shortdistance contribution toK _L →π⁺π^?γ is comparable to or even bigger than the long-distance one, (3) the ΔI=1/2 enhancement persists in the decayK ⁺→π⁺π⁰γ, (4) to the order of 1/Λ _χ ² (Λ _χ being the chiral-symmetry breaking scale) the direct photon emission amplitude does not receive a contribution from penguin operators, and (5) the 1/N _c expansion improves the discrepancy between theory and experiment.     

The Schrödinger equation and canonical perturbation theory

LetT ₀(, )+V be the Schrödinger operator corresponding to the classical HamiltonianH ₀()+V, whereH ₀() is thed-dimensional harmonic oscillator with non-resonant frequencies =(₁, ... , _d ) and the potentialV(q ₁, ... ,q _d) is an entire function of order (d+1)^–1. We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schrödinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schrödinger series near any eigenvalue ofT ₀(, ) admits a convergent expansion in powers of of initial point the corresponding term of the classical Birkhoff expansion. Moreover ifV is an even polynomial, the above result and the KAM theorem show that all eigenvalues _n (, ) ofT ₀+V such thatn coincides with a KAM torus are given, up to order , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in .     

The Lipatov argument for φ 3 4 perturbation theory

We extend to ₃ ⁴ the work of S. Breen on the leading behavior at large order of ₂ ⁴ perturbation theory. Using a phase space expansion to obtain new estimates on the high energy behavior of ₃ ⁴ Feynman graphs, and a rigorous semiclassical expansion, we prove that the radius of convergence of the Borel transform of the pertubative series for ₃ ⁴ Euclidean field theory is the one computed by the Lipatov method.     

A tunable multi-wavelength Brillouin–erbium fiber laser with fourfold Brillouin frequency spacing

We have experimentally demonstrated a tunable multi-wavelength Brillouin–erbium fiber laser with over 40 GHz spacing utilizing two cascaded double Brillouin-frequency-spacing cavities. In this laser configuration, two segments of 25 km-long single-mode fibers are used as Brillouin gain medium in each ring cavity, and a segment of 8 m-long erbium-doped fiber with 980 nm pump is employed to amplify Brillouin pump (BP). At BP wavelength of 1550 nm, BP power of 8.3 dBm (6.8 mW) and the maximum 980 nm pump power of 27.78 dBm (600 mW), seven output channels with fourfold Brillouin-frequency spacing, and the tuning range of 15 nm from 1545 to 1560 nm are achieved. The proposed multi-wavelength Brillouin–erbium fiber laser has wide applications, such as in microwave signal generation and optical communications.     

Rayleigh-Schrödinger-Goldstone variational perturbation theory for many Fermion systems

We present a Rayleigh-Schrödinger-Goldstone perturbation formalism for many Fermion systems. Based on this formalism, variational perturbation scheme which goes beyond the Gaussian approximation is developed. In order to go beyond the Gaussian approximation, we identify a parent Hamiltonian which has an effective Gaussian vacuum as a variational solution and carry out further perturbation with respect to the renormalized interaction using Goldstones expansion. Perturbation rules for the ground state wavefunctional and energy are found, thus, opening a way for general use of the Schrödinger picture method for many Fermion systems. Useful commuting relations between operators and the Gaussian wavefunctional are also found, which could reduce the calculational efforts substantially. As examples, we calculate the first order correction to the Gaussian wavefunctional and the second order correction to the ground state of an electron gas system with the Yukawa-type interaction.     

High orders of perturbation theory. Are renormalons significant?

According to Lipatov [Sov. Phys. JETP 45, 216 (1977)], the high orders of perturbation theory are determined by saddle-point configurations, i.e., instantons, which correspond to functional integrals. According to another opinion, the contributions of individual large diagrams, i.e., renormalons, which, according to t’Hooft [The Whys of Subnuclear Physics: Proceedings of the 1977 International School of Subnuclear Physics (Erice, Trapani, Sicily, 1977), A. Zichichi (Ed.), Plenum Press, New York (1979)], are not contained in the Lipatov contribution, are also significant. The history of the conception of renormalons is presented, and the arguments in favor of and against their existence are discussed. The analytic properties of the Borel transforms of functional integrals, Green’s functions, vertex parts, and scaling functions are investigated in the case of ϕ ⁴ theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou-Zinn-Justin hypothesis [Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B 21, 3976 (1980)] is proved. It rules out the existence of the renormalon singularities pointed out by t’Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of ϕ ⁴ theory. Zh. éksp. Teor. Fiz. 116, 369–389 (August 1999)     

The hierarchicalφ 4-trajectory by perturbation theory in a running coupling and its logarithmby perturbation theory in a running coupling and its logarithm

We compute the hierarchical ⁴- in terms of perturbation theory in a running coupling. In the three-dimensional case we resolve a singularity due to resonance of power counting factors in terms of logarithms of the running coupling. Numerical data are presented and the limits of validity explored. We also compute moving eigenvalues and eigenvectors on the trajectory as well as their fusion rules.