Perturbation Theory For Dynamics Research Articles

A link between static and dynamical perturbation theory

Dynamics, the physical change in time and a pillar of natural sciences, can be regarded as an emergent phenomenon when the system of interest is part of a larger, static one. This ‘relational approach to time’, in which the system’s environment provides a temporal reference, does not only provide insight into foundational issues of physics, but holds the potential for a deeper theoretical understanding as it intimately links statics and dynamics. Reinforcing the significance of this connection, we demonstrate, based on recent progress (Gemsheim and Rost 2023 Phys. Rev. Lett. 131 140202), the role of emergent time as a vital link between time-independent and time-dependent perturbation theory in quantum mechanics. We calculate first order contributions, which are often the most significant, and discuss the issue of degenerate spectra. Based on our results, we envision future applications for the calculation of dynamical phenomena based on a single pure energy eigenstate.

QCD tests with an infrared finite gluon propagator and coupling constant

Recent progress in the solution of Schwinger-Dyson equations, as well as lattice simulation of pure glue QCD, indicate that the gluon propagator and coupling constant are infrared finite. Such non-perturbative information can be introduced in the QCD perturbative expansion in the scheme named Dynamical Perturbation Theory. We exemplify this procedure with the calculation of some two-body non-leptonic annihilation B meson decays, which show agreement with the experimental data in the case of a gluon propagator characterized by a dynamical gluon mass of 500MeV, compatible with the value found in several processes computed with this method. We give a preliminary account of the application of this procedure at the loop level in the case of the Bjorken sum rule.

EFFECTIVE DYNAMICS FOR SOLITONS IN THE NONLINEAR KLEIN–GORDON–MAXWELL SYSTEM AND THE LORENTZ FORCE LAW

We consider the nonlinear Klein–Gordon–Maxwell system derived from the Lagrangian [Formula: see text] on four-dimensional Minkowski space-time, where ϕ is a complex scalar field and Fμν = ∂μ𝔸ν - ∂ν𝔸μ is the electromagnetic field. For appropriate nonlinear potentials [Formula: see text], the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons introduced and studied by Lee and collaborators for pure complex scalar fields. In this article, we develop a rigorous dynamical perturbation theory for these solitons in the small e limit, where e is the electromagnetic coupling constant. The main theorems assert the long time stability of the solitons with respect to perturbation by an external electromagnetic field produced by the background current 𝕁B, and compute their effective dynamics to O(e). The effective dynamical equation is the equation of motion for a relativistic particle acted on by the Lorentz force law familiar from classical electrodynamics. The theorems are valid in a scaling regime in which the external electromagnetic fields are O(1), but vary slowly over space-time scales of [Formula: see text], and δ = e1 - k for [Formula: see text] as e → 0. We work entirely in the energy norm, and the approximation is controlled in this norm for times of [Formula: see text].

Inverse damage prediction in structures using nonlinear dynamic perturbation theory

A non-linear perturbation theory which furnishes an exact relationship between the perturbation of structural parameters and the perturbation of modal parameters is presented. A system of governing equations is derived, where the information about incomplete modal data can be directly adopted. The Direct Iteration and the Gauss–Newton Least Squares techniques for an inverse prediction of structural damage are discussed, where both the location and the extent of structural damage can be correctly determined using only a limited amount of incomplete modal measurements data. Structural damage is assumed to be associated with a proportional reduction of the original element stiffness matrix or with a proportional reduction of the contribution of a Gauss point to the element stiffness matrix, which characterises a structure at an element level or at a Gauss point level. Finally, a damaged cantilever beam is considered using different model problems to demonstrate the effectiveness of the proposed techniques.

High-precision time-resolved cyclotron resonance measurements at microwave frequencies

This work is a theoretical and experimental study of the time-resolved microwave spectroscopy, close to the limit ΔωΔτ∼1, especially applied for the case of cyclotron resonance. A dynamic perturbation theory of a resonator is presented. While the amplitude of a transmitted signal in a standard measuring setup can be determined quickly and accurately, the phase relation requires much longer time for the same accuracy. The use of a resonant system enhances the sensitivity for determination of amplitude and phase, but reduces the time resolution, both by a factor Q. The nonlinear regime for conductivity in cyclotron resonance conditions is compensated by the use of constant energy density in the resonator, independent of frequency. Examples for classical semiconductors are presented. Compared with terahertz time-resolved spectroscopy, this method offers precise information in a different time scale and essentially in a different experimental regime of conductivity: pulsed, E∼1kV∕cm in the first case; cw, E∼1V∕cm in ours.

Calculation of the chiral Lagrangian coefficients from the underlying theory of QCD: A simple approach

We calculate the coefficients in the chiral Lagrangian approximately from QCD based on a previous study of deriving the chiral Lagrangian from the first principles of QCD in which the chiral Lagrangian coefficients are defined in terms of certain Green's functions in QCD. We first show that, in the large N(c)-limit, the anomaly part contributions to the coefficients are exactly cancelled by certain terms in the normal part contributions, and the final results of the coefficients only concern the remaining normal part contributions depending on QCD interactions. We then do the calculation in a simple approach with the approximations of taking the large-N(c) limit, the leading order in dynamical perturbation theory, and the improved ladder approximation, thereby the relevant Green's functions are expressed in terms of the quark self energy. By solving the Schwinger-Dyson equation for the quark self energy, we obtain the approximate QCD predicted coefficients and the quark condensate which are consistent with the experimental values.

Critical behavior of O(n)-symmetric systems with reversible mode-coupling terms: Stability against detailed-balance violation

We investigate nonequilibrium critical properties of O(n)-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy (SSS) is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures ${\mathrm{T}}_{\mathrm{S}}$ and ${\mathrm{T}}_{\mathrm{M}}$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first fixed point corresponds to \ensuremath{\Theta}=${\mathrm{T}}_{\mathrm{S}}$/${\mathrm{T}}_{\mathrm{M}}$=\ensuremath{\infty} and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at \ensuremath{\Theta}=0 and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent z=d/2 equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.

Dynamical perturbation theory and the auxiliary field method

By introducing auxiliary fields, which by their quantum numbers vanish in perturbation theory, we relate the dynamical perturbation theory of Pagels and Stokar and a successful gauged nonlocal constituent quark model to $U(N)$ gauge theory and to QCD. This sheds light on the duality between quark models and resonance models. We then derive the effective action in the loop expansion without dropping cubic and quartic gluon couplings.

Electroweak radiative corrections in dynamical models with Majorana neutrinos

The electroweak radiative correction parameter T= δρ ∗ α is estimated in dynamical models such as technicolour and fourth family condensate models in the presence of Majorana neutrino masses. The parameter T is calculated in lowest order dynamical perturbation theory from a generalisation of the Pagel-Stokar formulae. Parameter ranges exist that give negative values of T which may help to alleviate problems with technicolour models with orthogonal technicolour groups, SO( N) TC.

Dynamical perturbation theory for the evaluation of the relaxation function

Use of the infinite continued-fraction representation has played an important role in the evaluation of the relaxation function of many-body systems. By using the method of recurrence relations, we propose here a dynamical perturbation theory for the evaluation of the infinite continued fraction. The analytic expression of the relaxation function is given in terms of the known relaxation function for the unperturbed system. Two illustrative examples are also given.

Dynamic perturbation theory of energy transfer in nonrigid molecular systems: Vibrational predissociation of I2he van der waals molecule

AbstractThe appearance of the maximum linewidth by the vibrational predissociation of I2He van der Waals (vdW) molecule as a function of the initial vibrational quantum number of I2 is predicted by the dynamic perturbation theory. The kinetic energy perturbation is introduced in addition to perturbation potential. The linewidth agrees quite well with experiment.

Pseudoscalar meson amplitudes in the composite operator formalism

The amplitudes among pseudoscalar mesons including possible real or virtual weak and EM bosons are derived by expanding the effective action of the composite operator formalism. In particular the results of “dynamical perturbation theory” are reproduced in the corresponding approximations.

Self-consistent perturbation theory for dynamics of valence fluctuations

A perturbation-theoretic scheme is developed for dynamics of valence fluctuations in rare-earth systems with unstable 4f shells. The theory is formulated in close analogy to the standard Green-function method for many-body systems but without use of the linked-cluster theorem. This formulation regards hybridization between 4f and conduction-band states as perturbation and naturally incorporates the strong on-site 4f-electron correlation. Some favorable features are: (i) the approximation scheme automatically satisfies conservation laws required for response functions; (ii) realistic 4f-shell structures with crystalline-electric-field effects can be taken into account; (iii) the theory does not have divergence difficulties over the whole temperature range. In the lowest-order self-consistent approximation, explicit formulae for dynamical susceptibilities and 4f-electron density of states are presented. At high temperatures, the theory reproduces previous results obtained by the Mori method.

Dynamic perturbation theory of vibrational energy transfer in a nonrigid molecular system

A theory for van der Waals molecules (AB---C) is presented, which is based on the concept that a van der Waals molecule can be considered as a nonrigid molecule because it is loosely bound in comparison with proper chemical bonds. A perturbation method is performed for the three-body internal Hamiltonian which has been obtained for the case in which the angular momentum of the whole molecular system is equal to zero (J=0). A new idea, the dynamic perturbation mechanism of vibrational energy transfer, is presented which originates in the coupling of the kinetic energy of the chemical and van der Waals bonds. This is applied to the vibrational predissociation process of the van der Waals molecule and linewidths and lifetimes are calculated by estimating the dynamic coupling. The decay rates calculated by this new mechanism are quite large and are comparable to those values estimated by the usual treatment of the perturbation potential.

Self-consistent perturbation theory for dynamics of valence fluctuations

Self-consistent perturbation theory for dynamics of valence fluctuations

Self-consistent perturbation theory for dynamics of valence fluctuations

Etude des proprietes dynamiques des systemes a valence fluctuante au zero absolu. Des resultats numeriques extensifs sont rapportes pour les densites d'etats 4f et la susceptibilite magnetique. Ces resultats correspondent a la fois aux problemes de la valence intermediaire et de valence entiere de systemes a impurete cerium

Self-consistent perturbation theory for dynamics of valence fluctuations

Etude de la dynamique des fluctuations de valence dans les systemes de terres rares ayant des niveaux 4f instables a l'aide d'un modele theorique de perturbations: theorie tres proche de la methode standard de la fonction de Green, mais sans utiliser le theoreme des amas lies. L'hybridation entre niveaux 4f et de la bande de conduction est vue en tant que perturbation; prise en compte de la correlation forte entre electrons 4f. Presentation de formules des succeptibilites dynamiques et des densites electroniques 4f dans l'approximation autocoherente d'ordre le plus faible. Confirmation des resultats obtenus par la methode de Mori a hautes temperatures