Nonperturbative Treatment Research Articles

Heat-kernel expansion and counterterms of the Faddeev–Popov determinant in Coulomb and Landau gauge

The Faddeev-Popov determinant of Landau gauge in d dimensions and Coulomb gauge in d+1 dimensions is calculated in the heat-kernel expansion up to next-to-leading order. The UV-divergent parts in d=3,4 are isolated and the counterterms required for a non-perturbative treatment of the Faddeev-Popov determinant are determined.

RKKY coupling in graphene

We study the carrier-mediated exchange interaction, the so-called Ruderman-Kittel-Kasuya-Yoshida (RKKY) coupling, between two magnetic impurity moments in graphene using exact diagonalization on the honeycomb lattice. By using the tight-binding nearest-neighbor band structure of graphene we also avoid the use of a momentum cutoff which plagues perturbative results in the Dirac continuum model formulation. We extract both the short and long impurity-impurity distance behavior and show on a qualitative agreement with earlier perturbative results in the long-distance limit but also report on a few new findings. In the bulk the RKKY coupling is proportional to $1/{|\mathbf{R}|}^{3}$ and displays $[1+\text{cos}(2{\mathbf{k}}_{D}\ensuremath{\cdot}\mathbf{R})]$ -type oscillations. A-A sublattice coupling is always ferromagnetic whereas A-B subattice coupling is always antiferromagnetic and three times as large. We also study the effect of edges in zigzag graphene nanoribbons (ZGNRs). We find that for impurities on the edge the RKKY coupling decays exponentially because of the localized zero-energy edge states and we also conclude that a nonperturbative treatment is essential for these edge impurities. For impurities inside a ZGNR the bulk characteristics are quickly regained.

Exact master equations for the non-Markovian decay of a qubit

Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. Employing the exact solution for the model we determine analytical expressions for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows a detailed investigation and comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, we find that the structure of widely used phenomenological master equations with memory kernel may be incompatible with a non-perturbative treatment of the underlying microscopic model. We discuss several physical implications of our results on the microscopic analysis and the phenomenological modelling of non-Markovian quantum dynamics of open systems.

Photoassociation spectra and the validity of the dipole approximation for weakly bound dimers

Photoassociation (PA) of ultracold metastable helium to the $2s2p$ manifold is theoretically investigated using a nonperturbative close-coupled treatment in which the laser coupling is evaluated without assuming the dipole approximation. The results are compared with our previous study [D. G. Cocks and I. B. Whittingham, Phys. Rev. A 80, 023417 (2009)], which makes use of the dipole approximation. The approximation is found to strongly affect the PA spectra because the photoassociated levels are weakly bound, and a similar impact is predicted to occur in other systems of a weakly bound nature. The inclusion of the approximation does not affect the resonance positions or widths; however, significant differences are observed in the background of the spectra and the maximum laser intensity at which resonances are discernible. Couplings not satisfying the dipole selection rule $|J\ensuremath{-}1|\ensuremath{\leqslant}{J}^{\ensuremath{'}}\ensuremath{\leqslant}|J+1|$ do not lead to observable resonances.

Nonperturbative treatment of single ionization ofH2by fast highly-charged-ion impact

We present a detailed analysis of the interference effects observed for ionization in collisions of fast highly charged projectiles with molecular hydrogen. We propose a nonperturbative semiclassical approach to describe the process under consideration by solving the time-dependent Schroedinger equation fully numerically on a 3D spatial grid. We present results for Kr{sup 34+}-H{sub 2} collisions at 63 MeV/u impact energy and discuss different structures observed experimentally in doubly differential cross sections. The presence of Young-type minima and the absence of high-frequency oscillations are especially addressed. We also report unexpected interference patterns which can be observed for fixed-in-space molecular targets.

Ionization of molecular hydrogen and deuterium by frequency-doubled Ti:sapphire laser pulses

A theoretical study of the intense-field single ionization of molecular hydrogen or deuterium oriented either parallel or perpendicular to a linear-polarized laser pulse (400 nm) is performed for different internuclear separations and pulse lengths in an intensity range of $(2--13)\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{W}\text{ }{\text{cm}}^{\ensuremath{-}2}$. The investigation is based on a nonperturbative treatment that solves the full time-dependent Schr\"odinger equation of both correlated electrons within the fixed-nuclei and the dipole approximations. The results for various internuclear separations are used to obtain the ionization yields of molecular hydrogen and deuterium in their ground vibrational states. An atomic model is used to identify the influence of the intrinsic diatomic two-center character of the problem.

Non-perturbative treatment of the attractive Hubbard model

We have used a Hubbard–Stratonovich transformation to convert the quartic Hubbard problem of interacting electrons into more tractable quadratic problem of non-interacting electrons coupled to a Bose field. The Dyson and the Bethe-Salpeter (BS) equations for the corresponding Green functions are derived by applying a functional derivative technique combined with the method of Legendre transform. This approach allows us to obtain exact relations between single- and two-particle quantities. We have compared the self-consistent relationship between mass operator and two-particle Green function with the similar relationship in the two-particle self-consistent (TPSC) approximation, and came up with the conclusion that the accuracy of the TPSC approximation is questionable because: (i) if equal-time pair-correlation function is set to one, the mass operator in TPSC approximation differs significantly from the exact mass operator; and (ii) the TPSC approximation does not take into account the Hartree part of the mass operator. The latter results in missing exchange interaction in the BS equation. A generalized random-phase approximation is applied to demonstrate the important role of the exchange interaction when BS equation is used to study collective excitation spectrum of the attractive Hubbard model.

Nonperturbative Treatment of Double Compton Backscattering in Intense Laser Fields

The emission of a pair of entangled photons by an electron in an intense laser field can be described by two-photon transitions of laser-dressed, relativistic Dirac-Volkov states. In the limit of a small laser field intensity, the two-photon transition amplitude approaches the result predicted by double Compton scattering theory. Multiexchange processes with the laser field, including a large number of exchanged laser photons, cannot be described without the fully relativistic Dirac-Volkov propagator. The nonperturbative treatment significantly alters theoretical predictions for future experiments of this kind. We quantify the degree of polarization correlation of the photons in the final state by employing the well-established concurrence as a measure of the entanglement.

Theoretical study of orientation-dependent multiphoton ionization of polyatomic molecules in intense ultrashort laser fields: A new time-dependent Voronoi-cell finite difference method

We present a new grid-based time-dependent method to investigate multiphoton ionization (MPI) of polyatomic molecules in intense ultrashort laser fields. The electronic structure of polyatomic molecules is treated by the density-functional theory (DFT) with proper long-range potential and the Kohn–Sham equation is accurately solved by means of the Voronoi-cell finite difference method on non-uniform and highly adaptive molecular grids utilizing geometrical flexibility of the Voronoi diagram. This method is generalized to the time-dependent problems with the split-operator time-propagation technique in the energy representation, allowing accurate and efficient non-perturbative treatment of attosecond electronic dynamics in strong fields. The new procedure is applied to the study of MPI of N 2 and H 2O molecules in intense linearly-polarized and ultrashort laser fields with arbitrary field–molecule orientation. Our results demonstrate that the orientation dependence of MPI is determined not just by the highest-occupied molecular orbital (HOMO) but also by the symmetries and dynamics of other contributing molecular orbitals. In particular, the inner orbitals can show dominant contributions to the ionization processes when the molecule is aligned in some specific directions with respect to the field polarization. This feature suggests a new way to selectively probe individual orbitals in strong-field electronic dynamics.

Laser-intensity dependence of photoassociation in ultracold metastable helium

Photoassociation of spin-polarized metastable helium to the three lowest rovibrational levels of the J=1, $0_u^+$ state asymptoting to 2$s {}^{3}$S$_{1}+2p {}^{3}$P$_{0}$ is studied using a second-order perturbative treatment of the line shifts valid for low laser intensities, and two variants of a non-perturbative close-coupled treatment, one based upon dressed states of the matter plus laser system, and the other on a modified radiative coupling which vanishes asymptotically, thus simulating experimental conditions. These non-perturbative treatments are valid for arbitrary laser intensities and yield the complete photoassociation resonance profile. Both variants give nearly identical results for the line shifts and widths of the resonances and show that their dependence upon laser intensity is very close to linear and quadratic respectively for the two lowest levels. The resonance profiles are superimposed upon a significant background loss, a feature for this metastable helium system not present in studies of photoassociation in other systems, which is due to the very shallow nature of the excited state $0_u^+$ potential. The results for the line shifts from the close-coupled and perturbative calculations agree very closely at low laser intensities.

Theoretical analysis of higher-order phonon sidebands in semiconductor luminescence spectra

A semiconductor luminescence formula is derived that includes phonon replica of arbitrary order based on a non-perturbative treatment of the electron–phonon interaction. The formula is used to analyze the extraordinarily strong sidebands observed with ZnO nanorods in recent experiments. Sidebands due to free and impurity-bound excitons are compared, and the generic differences between bulk and quantum-well emission are discussed.

Frustration effects in rapidly rotating square and triangular optical lattices

We discuss the ground state of the two-dimensional Bose-Hubbard (BH) Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing \mathrm{U}\left(1\right) quantum rotor approach and the topologically constrained path integral that includes a summation over \mathrm{U}\left(1\right) topological charge. We derive an effective quantum action for the BH model, which enables a non-perturbative treatment of the zero-temperature phase transition. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f=0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice, which improves upon previous theoretical treatments. The ground state of the rotating Bose-Einstein condensates on a triangular lattice appears to be most stable against the effects of rotation. Performed calculations revealed strong dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.

Coarse-grained density functional theory of order-disorder phase transitions in metallic alloys

The technological performances of metallic compounds are largely influenced by atomic ordering. At finite temperatures metallic alloys are not perfectly ordered nor ideally disordered. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue, existing nonperturbative high-temperature treatments are based on effective classical atomic Hamiltonians. We propose a solution for the above paradox and offer a fully quantum mechanical, though approximate, theory that on equal footing deals with both electrons and ions. Thus, the amount of order and the electronic properties of metallic alloys are self-consistently determined as a function of the temperature. Our formulation is based on a coarse-grained version of the density functional theory and a Monte Carlo technique, which are jointly implemented allowing for the efficient evaluation of finite temperature statistical averages. Calculations of the relevant thermodynamic quantities and of the electronic structures for CuZn and ${\text{Ni}}_{3}\text{V}$ support that our theory provides an appropriate description of order-disorder phase transitions.

Spectral line-shape calculations for multielectron ions in hot plasmas submitted to a strong oscillating electric field

Spectral line shapes in hot plasmas submitted to a strong oscillating electric field have been theoretically studied by applying the standard hypotheses of plasma line broadening together with a nonperturbative Floquet treatment of the external oscillating field. The formulation has been applied to the lines of nonhydrogenic emitters like He-like and Ne-like ions. It is found that the simultaneous action of a strong oscillating field and plasma particle fields can lead to dramatic changes in the spectral emission.

Laser-pulse photoassociation in a thermal gas of atoms

A nonperturbative treatment is presented for laser-pulse-driven formation of heteronuclear diatomic molecules in a thermal gas of atoms. Based on the assumption of full controllability, the maximum possible photoassociation yield is obtained. A one-dimensional model is used for calculating the photoassociation probability as a function of the laser parameters as well as for different temperatures. The dependence of the photoassociation yield on the laser frequency and amplitude reveals complex patterns of one- and multiphoton transitions. The photoassociation yield induced by subpicosecond pulses of a priori fixed shape is very low compared to the maximum possible yield.

Cold atoms photoassociation with intense laser pulses

We study the vibrational dynamics produced when two cold atoms are photoassociated in a diatomic molecule by an intense laser pulse (with the duration of hundreds ps), inducing a resonance condition at small interatomic distances. The example analysed is the population transfer from the a3Σu+(6s+6s) continuum to the 1g(6s+6p3/2) excited electronic potential of the Cs2 molecule, at a temperature T≈0.11mK. We use a non-perturbative treatment by following the wavepackets dynamics on the ground and excited surfaces. We show that cold molecules can be efficiently produced in both ground and excited electronic potentials.

Crystallization of magnetic dipolar monolayers: a density functional approach

We employ density functional theory to study in detail the crystallization ofsuper-paramagnetic particles in two dimensions under the influence of an external magneticfield that lies perpendicular to the confining plane. The field induces non-fluctuatingmagnetic dipoles on the particles, resulting in an interparticle interaction that scales as theinverse cube of the distance separating them. In line with previous findings for long-rangeinteractions in three spatial dimensions, we find that explicit inclusion of liquid-statestructural information on the triplet correlations is crucial to yield theoreticalpredictions that agree quantitatively with experiment. A non-perturbative treatment issuperior to the oft-employed functional Taylor expansions, truncated at second orthird order. We go beyond the usual Gaussian parametrization of the densitysite-orbitals by performing free minimizations with respect to both the shapeand the normalization of the profiles, allowing for finite defect concentrations.

Nonequilibrium energy gaps in carbon nanotubes: Role of phonon symmetries

We report on a theoretical study of inelastic basckscattering processes and quantum transport in metallic carbon nanotubes. The consequences of a Peierls-like mechanism due to e-ph interaction with optic phonons in the transport properties is explored. The occurence of non-equilibrium energy gaps driven by an applied bias voltage is derived from a non-perturbative treatment of electronphonon coupling with longitudinal optic as well as K A1 modes. The case of armchair tubes is explicitly considered, and further generalizations to tubes of arbitrary helicity are outlined.

CASIMIR ENERGY OF 5D ELECTRO-MAGNETISM AND SPHERE LATTICE REGULARIZATION

Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called sphere lattice regularization, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do not take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its Λ(4D UV-cutoff), ω(5D bulk curvature, warpedness parameter) and T(extra space IR parameter) dependence.

Many-mode Floquet theoretical approach for coherent control of multiphoton dynamics driven by intense frequency-comb laser fields

We extend the many-mode Floquet theorem (MMFT) for the investigation of multiphoton resonance dynamics driven by intense frequency-comb laser fields. The frequency comb structure generated by a train of short laser pulses can be exactly represented by a combination of the main frequency and the repetition frequency. MMFT allows non-perturbative and exact treatment of the interaction of a quantum system with the frequency-comb laser fields. We observe simultaneous multiphoton resonance processes between a two-level system and frequency-comb laser. The multiphoton processes can be coherently controlled by tuning the laser parameters such as the carrier-envelope phase (CEP) shift. In particular, high-order harmonic generation shows immense enhancement by tuning the CEP shift, due to simultaneous multiphoton resonances.