Conventional Perturbation Theory Research Articles

Chaos perturbation in terms of cycles

The conventional perturbation theory encounters formidable challenges when applied to the quantitative analysis or computation of chaotic systems, due to possibly numerous bifurcations as system parameters vary. In this manuscript, however, based on the cycle expansions formulation we found that the preservation of symbolic dynamics is the key to maintain the analyticity and thus to implement a perturbation computation. Even in the presence of bifurcations, a subset of unstable periodic orbits (UPOs) can be selected to resume the computation, giving rise to new perspectives of treating chaos.

Two-Step Relaxation of Non-Equilibrium Electrons in Graphene: The Key to Understanding Pump–Probe Experiments

In the majority of experiments targeting nonlinear optical phenomena, the application of high-intensity pulses drives electrons in graphene into a strongly non-equilibrium state. Under these conditions, conventional perturbation theory falls short in explaining graphene’s intricate optical response because of significant deviations in electron distribution over energy states from the equilibrium Fermi-Dirac one. In this work, we present a two-step relaxation model capable of predicting the transient dynamics of graphene’s carriers out of equilibrium, from the generation of spectrally narrow populations of non-thermalized electrons and holes to the establishment of a hot-electron gas and its subsequent cooling toward equilibrium with the crystal lattice. By comparing our model calculations to experimental results, we demonstrate its reliability and relevance to pump–probe experiments, providing insights into the pivotal role of hot electrons in comprehending ultrafast dynamics in graphene.

Vacuum-field-induced state mixing

By engineering the electromagnetic vacuum field, the induced Casimir-Polder shift (also known as Lamb shift) and spontaneous emission rates of individual atomic levels can be controlled. When the strength of these effects becomes comparable to the energy difference between two previously uncoupled atomic states, an environment-induced interaction between these states appears after tracing over the environment. This interaction has been previously studied for degenerate levels and simple geometries involving infinite, perfectly conducting half-spaces or free space. Here, we generalize these studies by developing a convenient description that permits the analysis of these non-diagonal perturbations to the atomic Hamiltonian in terms of an accurate non-Hermitian Hamiltonian. Applying this theory to a hydrogen atom close to a dielectric nanoparticle, we show strong vacuum-field-induced state mixing that leads to drastic modifications in both the energies and decay rates compared to conventional diagonal perturbation theory. In particular, contrary to the expected Purcell enhancement, we find a surprising decrease of decay rates within a considerable range of atom-nanoparticle separations. Furthermore, we quantify the large degree of mixing of the unperturbed eigenstates due to the non-diagonal perturbation. Our work opens new quantum state manipulation possibilities in emitters with closely spaced energy levels.

Codebase release 2.2 for HEJ

We present version 2.2 of the High Energy Jets (HEJ) Monte Carlo event generator for hadronic scattering processes at high energies. The new version adds support for two further processes of central phenomenological interest, namely the production of a W boson pair with equal charge together with two or more jets and the production of a Higgs boson with at least one jet. Furthermore, a new prediction for charged lepton pair production with high jet multiplicities is provided in the high-energy limit. The accuracy of HEJ 2.2 can be increased further through an enhanced interface to standard predictions based on conventional perturbation theory. We describe all improvements and provide extensive usage examples. HEJ 2.2 can be obtained from https://hej.hepforge.org.

Dust acoustic waves potentially originate in a self-gravitating magnetized dusty plasma

The dynamics of dust acoustic waves (DAWs) in a collision-magnetized dusty plasma are still unclear. To achieve this, we investigate the dynamics of a plasma system consisting of Boltzmann-distributed electrons and ions, and fluid-negative dust particles. The generalized hydrodynamic model of coupled particles is reduced using conventional reductive perturbation theory to a single evolution equation known as the complex Ginzburg-Landau (CGL) equation. Our results show that the energy of rogue waves (RW) is increased by high-energy electrons and decreased by high-energy ions for small polarization parameter. We also observed that the energy of rogue waves increased with decreasing the polarization parameter and the gravitational force coefficient, while increasing dust grain concentration enhances the wave energy. The application of this study to dusty magnetoplasma in space and laboratory plasmas is pointed out.

Arbitrary (k, l) States-Solutions of the Dirac and Schrödinger Equations Interacting with Improved Spatially-Dependent Mass Coulomb Potential with an improved Coulomb-like tensor interaction Model for H-atoms from 3D-RNCS and 3D-NRNCS symmetries

The deformed Dirac equation has been investigated, in the context of 3D-relativistic noncommutative space (3D-RNCS) symmetries, using the improved spatially dependent mass Coulomb potential with an improved Coulomb-like tensor interaction (ISDM(CP-CLTI)) model under the conditions of spin symmetry and pseudospin symmetry. The ISDM(CP-CLTI) model is the combining the spatially dependent mass Coulomb potential with the Coulomb-like tensor interaction (CP-CLTI) and the two central terms that are generated to the topological defects of spacespace. Within the confines of the parametric Bopp shift method and conventional perturbation theory, the new relativistic and non-relativistic energy eigenvalues for the hydrogen atoms ( H-atoms), such as He+,Li+2, and Be3+ under the ISDM(CP-CLTI) model have been derived. The novel values Encsp(n,C,m0,m1,H,Θ,τ,χ,j,l,s,m) and Encps(n,C,m0,m1,H,Θ,τ,χ,j,l,l̃,s̃,m̃) that we discovered examined to be dependent on the noncommutativity parameters (NP) (Θ,σ,χ), mixed potential depths C/q,m0,m1,H), and quantum atomic discrete quantum numbers (j,k,l,s,m,l̃,s̃,m̃). We have obtained several interesting special examples within the framework of relativistic extended quantum mechanics, which we believe will be of interest to the expert researcher. We were able to retrieve the typical results of relativistic and non-relativistic examples in the literature when we applied the three simultaneous constraints (Θ,σ,χ)→(0,0,0). Compared to previous models that are known from the literature, our new model had novel physical characteristics.

Perturbation theory remixed: Improved nonlinearity modeling beyond standard perturbation theory

We present a novel $n$EPT ($n$th-order Eulerian Perturbation Theory) scheme to model the nonlinear density field by the summation up to $n$th-order density fields in perturbation theory. The obtained analytical power spectrum shows excellent agreement with the results from all 20 Dark-Quest suites of $N$-body simulations spreading over a broad range of cosmologies. The agreement is much better than the conventional two-loop Standard Perturbation Theory and would reach out to $k_{\rm max}\simeq 0.4~h/{\rm Mpc}$ at $z=3$ for the best-fitting Planck cosmology, without any free parameters. The method can accelerate the forward modeling of the non-linear cosmological density field, an indispensable probe of cosmic mysteries such as inflation, dark energy, and dark matter.

Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime

We introduce a second-order stochastic effective theory for light scalar fields in de Sitter spacetime, extending the validity of the stochastic approach beyond the massless limit and demonstrating how it can be used to compute long-distance correlation functions nonperturbatively. The parameters of the second-order stochastic theory are determined from quantum field theory through a perturbative calculation, which is valid if the self-interaction parameter $\ensuremath{\lambda}$ satisfies $\ensuremath{\lambda}\ensuremath{\ll}{m}^{2}/{H}^{2}$, where $m$ is the scalar and $H$ is the Hubble rate. Therefore, it allows stronger self-interactions than conventional perturbation theory, which is limited to $\ensuremath{\lambda}\ensuremath{\ll}{m}^{4}/{H}^{4}$ by infrared divergences. We demonstrate the applicability of the second-order stochastic theory by comparing its results with perturbative quantum field theory and overdamped stochastic calculations, and discuss the prospects of improving its accuracy with a full one-loop calculation of its parameters.

Is the Nicolai map unique?

The Nicolai map is a field transformation that relates supersymmetric theories at finite couplings g with the free theory at g = 0. It is obtained via an ordered exponential of the coupling flow operator integrated from 0 to g. Allowing multiple couplings, we find that the map in general depends on the chosen integration contour in coupling space. This induces a large functional freedom in the construction of the Nicolai map, which cancels in all correlator computations. Under a certain condition on the coupling flow operator the ambiguity disappears, and the power-series expansion for the map collapses to a linear function in the coupling. A special role is played by topological (theta) couplings, which do not affect perturbative correlation functions but also alter the Nicolai map. We demonstate that for certain ‘magical’ theta values the uniqueness condition holds, providing an exact map polynomial in the fields and independent of the integration contour. This feature is related to critical points of the Nicolai map and the existence of ‘instantons’. As a toy model, we work with mathcal{N} = 1 supersymmetric quantum mechanics. For a cubic superpotential and a theta term, we explicitly compute the one-, two- and three-point correlation function to one-loop order employing a graphical representation of the (inverse) Nicolai map in terms of tree diagrams, confirming the cancellation of theta dependence. Comparison of Nicolai and conventional Feynman perturbation theory nontrivially yields complete agreement, but only after adding all (1PI and 1PR) contributions.

Absence of Superdiffusion in Certain Random Spin Models.

The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU(2) symmetry as well as integrability, but the associated methods cannot be readily applied when integrability is broken. We examine spin transport in a spin-1/2 chain in which the exchange couplings fluctuate in space and time around a nonzero mean J, a model introduced by De Nardis etal. [Phys. Rev. Lett. 127, 057201 (2021).PRLTAO0031-900710.1103/PhysRevLett.127.057201]. We show that operator dynamics in the strong noise limit at infinite temperature can be analyzed using conventional perturbation theory as an expansion in J. We find that regular diffusion persists at long times, albeit with an enhanced diffusion constant. The finite time spin dynamics is analyzed and compared with matrix product operator simulations.

Multireference Algebraic Diagrammatic Construction Theory for Excited States: Extended Second-Order Implementation and Benchmark.

We present an implementation and benchmark of new approximations in multireference algebraic diagrammatic construction theory for simulations of neutral electronic excitations and UV/vis spectra of strongly correlated molecular systems (MR-ADC). Following our work on the first-order MR-ADC approximation [J. Chem. Phys. 2018, 149, 204113], we report the strict and extended second-order MR-ADC methods (MR-ADC(2) and MR-ADC(2)-X) that combine the description of static and dynamic electron correlation in the ground and excited electronic states without relying on state-averaged reference wave functions. We present an extensive benchmark of the new MR-ADC methods for excited states in several small molecules, including the carbon dimer, ethylene, and butadiene. Our results demonstrate that, for weakly correlated electronic states, the MR-ADC(2) and MR-ADC(2)-X methods outperform the third-order single-reference ADC approximation and are competitive with the results from equation-of-motion coupled cluster theory. For states with multireference character, the performance of the MR-ADC methods is similar to that of an N-electron valence perturbation theory. In contrast to conventional multireference perturbation theories, the MR-ADC methods have many attractive features, such as a straightforward and efficient calculation of excited-state properties and a direct access to excitations outside of the frontier (active) orbitals.

QCD beyond diagrams

Quantum chromodynamics (QCD), the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation and chiral symmetry breaking. This paper is a colloquium level overview of the framework for understanding how these effects come about.

Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory

Models with dust reference fields in relational formalism have proved useful in understanding the construction of gauge-invariant perturbation theory to arbitrary orders in the canonical framework. These reference fields modify the dynamical equations for perturbation equations. However, important questions remain open on the relation with conventional perturbation theories of inflaton coupled to gravity and of multi-fluid systems, and on understanding modifications in terms of physical degrees of freedom. These gaps are filled in this manuscript for Brown-Kucha\v{r} and Gaussian dust models, both of which involve three scalar physical degrees of freedom. We establish a relationship of these models with conventional inflationary and multi-fluid system of inflation and ordinary dust by introducing a set of gauge invariant variables on the reduced phase space of the dust reference models. We find the modifications due to dust clocks to Bardeen equation in the longitudinal gauge and Mukhanov-Sasaki equation in the spatially-flat gauge, in terms of physical degrees of freedom. This results in a closed system of equations for all the degrees of freedom needed to explore the evolution of the scalar perturbations. Our analysis shows for the first time that even for two-fluid systems, there is a natural choice of the set of gauge invariant variables for each chosen gauge which not only offers a direct physical interpretation but also results in simplifications to the dynamical equations.

Nonperturbative phonon scatterings and the two-channel thermal transport in Tl3VSe4

We study the role of nonperturbative phonon scattering in strongly anharmonic materials having ultralow lattice thermal conductivity with unusual temperature dependence. We take ${\mathrm{Tl}}_{3}{\mathrm{VSe}}_{4}$ as an example and investigate its lattice dynamics using perturbation theory (PT) up to the fourth order and molecular dynamics (MD) with a machine-learning potential. We find distinct differences of phonon linewidth between PT and MD in the whole Brillouin zone. The comparison between the theoretical phonon linewidths and experiments suggests that PT severely underestimates the phonon scatterings, even when the fourth-order anharmonicity is included. Moreover, we extend our calculations to higher temperatures and evaluate the two-channel thermal conductivity based on the unified theory developed by Simoncelli et al. [Nat. Phys. 15, 809 (2019)]. We find a crucial coherence contribution to the total thermal conductivity at high temperatures. Our results pave the path for future studies of phonon properties and lattice thermal conductivities of strongly anharmonic crystals beyond the conventional PT realm.

Baryon axial vector current in large- Nc chiral perturbation theory: Complete analysis for Nc=3

The baryon axial vector current is computed in heavy baryon chiral perturbation theory in the large-$N_c$ limit, where $N_c$ is the number of color charges. One-loop nonanalytic corrections of order $m_q \ln m_q$ are comprised in the analysis, with contributions of both intermediate octet and decuplet baryon states, to all orders in the $1/N_c$ expansion of the axial vector current relevant for $N_c=3$. Theoretical expressions are obtained in the limit of vanishing decuplet-octet mass difference only, which allows one to carry out a full comparison with conventional heavy baryon chiral perturbation theory results for three flavors of light quarks and at the physical value $N_c=3$. Both approaches perfectly agree to all orders considered. Furthermore, a numerical analysis via a least-squares fit is performed in order to extract the values of the free parameters of the theory, using the experimental data available. The predictions of formalism are remarkable.

Density-density correlation function of strongly inhomogeneous Luttinger liquids

In this work, we show in pedagogical detail that the most singular contributions to the slow part of the asymptotic density-density correlation function of Luttinger liquids with fermions interacting mutually with only short-range forward scattering and also with localised scalar static impurities (where backward scattering takes place) has a compact analytical expression in terms of simple functions that have second order poles and involve only the scale-independent bare transmission and reflection coefficients. This proof uses conventional fermionic perturbation theory resummed to all orders, together with the idea that for such systems, the (connected) moments of the density operator all vanish beyond the second order—the odd ones vanish identically and the higher order even moments are less singular than the second order moment which is the only one included. This important result is the crucial input to the recently introduced ‘Non-Chiral Bosonization Technique’ (NCBT) to study such systems. The results of NCBT cannot be easily compared with the results obtained using conventional bosonization as the former only extracts the most singular parts of the correlation functions albeit for arbitrary impurity strengths and mutual interactions. The latter, ambitiously attempts to study all the parts of the asymptotic correlation functions and is thereby unable to find simple analytical expressions and is forced to operate in the vicinity of the homogeneous system or the half line (the opposite extreme). For a fully homogeneous system or its antithesis viz. the half-line, all the higher order connected moments of the density vanish identically which means the results of chiral bosonization and NCBT ought to be the same and indeed they are.

On the axial-vector form factor of the nucleon and chiral symmetry

We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at hbox {N}^3LO for the baryon masses and at hbox {N}^2LO for the form factor. Partial finite-volume effects are considered. We point out that the use of on-shell masses in the loops results in non-analytic behavior of the baryon masses and the form factor as function of the pion mass, which becomes prominent for larger lattice volumes than presently used.

Reaching Full Correlation through Nonorthogonal Configuration Interaction: A Second-Order Perturbative Approach.

Nonorthogonal multireference methods can predict statically correlated adiabatic energies while providing chemical insight through the combination of diabatic reference states. However, reaching quantitative accuracy using nonorthogonal multireference expansions remains a significant challenge. In this work, we present the first rigorous perturbative correction to nonorthogonal configuration interaction, allowing the remaining dynamic correlation to be reliably computed. Our second-order "NOCI-PT2" theory exploits a zeroth-order generalized Fock Hamiltonian and builds the first-order interacting space using single and double excitations from each reference determinant. This approach therefore defines the rigorous nonorthogonal extension to conventional multireference perturbation theories. We find that NOCI-PT2 can quantitatively predict multireference potential energy surfaces and provides state-specific ground and excited states for adiabatic avoided crossings. Furthermore, we introduce an explicit imaginary-shift formalism requiring shift values that are an order of magnitude smaller than those used in conventional multireference perturbation theories.

Estimation of safety parameters of equilibrium cycle of Indian Pressurized Water Reactor (IPWR)

The Indian Pressurized Water Reactor (IPWR) is being designed with enriched uranium fuel and light water as coolant in a hexagonal lattice arrangement. The physics design of the core included optimization of 235U content in the fuel to achieve a target discharge burnup of about 50 GWD/T in a multi-cycle batch re-fuelling mode. The burnup reactivity control during the cycle is achieved by soluble boron. IPWR has been designed as per current safety standards where all the reactivity coefficients are negative in all the operating conditions. The kinetic parameters together with the reactivity coefficients are also used in safety analysis. The reactivity coefficients have been estimated from detailed 3D core simulations and the kinetic parameters have been estimated using the conventional perturbation theory expressions which involve weighting by the adjoint flux. Present work reports the estimation of the range of reactivity coefficients over an equilibrium operating cycle to be used to calculate the effective feedbacks and safety margins.

Analytical double-unitary-transformation approach for strongly and periodically driven three-level systems

Floquet theory combined with the generalized Van Vleck nearly degenerate perturbation theory has been widely employed for studying various two-level systems that are driven by external fields via time-dependent longitudinal (i.e., diagonal) couplings. However, three-level systems strongly driven by time-dependent transverse (i.e., off-diagonal) couplings have rarely been investigated, due to the breakdown of the traditional rotating wave approximation. Meanwhile, the conventional perturbation theory is not directly applicable, since a small parameter for the perturbed part is no longer apparent. Here we develop a double-unitary-transformation approach to deal with periodically modulated and strongly driven systems, where the time-dependent Hamiltonian has large off-diagonal elements. The first unitary transformation converts strong off-diagonal elements to diagonal ones, and the second enables us to harness the generalized Van Vleck perturbation theory to deal with the transformed Floquet matrix and also allows us to reduce the infinite-dimensional Floquet Hamiltonian to a finite effective one. For a strongly modulated three-level system, with the combination of the Floquet theory and the transformed generalized Van Vleck perturbation theory, we obtain analytical results of the system, which agree well with exact numerical solutions. This method offers a useful tool to analytically study multilevel systems with strong transverse couplings.