scholarly journals Oscillating scalar dissipating in a medium

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Wen-Yuan Ai ◽  
Marco Drewes ◽  
Dražen Glavan ◽  
Jan Hajer
Keyword(s):  
Perturbation Theory ◽  
Quantitative Description ◽  
Early Time ◽  
Scalar Fields ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Local Equation ◽  
Starting Point ◽  
Non Linear ◽  
Non Local

Abstract We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action derived in the Schwinger-Keldysh formalism appropriate for non-equilibrium quantum field theory. We solve this non-local equation by means of multiple-scale perturbation theory appropriate for time-dependent systems, obtaining approximate analytic solutions valid for very long times. The non-linear effects lead to power-law damping of oscillations, that at late times transition to exponentially damped ones characteristic for linear systems. These solutions describe the evolution very well, as we demonstrate numerically in a number of examples. We then approximate the non-local equation of motion by a Markovianised one, resolving the ambiguities appearing in the process, and solve it utilizing the same methods to find the very same leading approximate solution. This comparison justifies the use of Markovian equations at leading order. The standard time-dependent perturbation theory in comparison is not capable of describing the non-linear condensate evolution beyond the early time regime of negligible damping. The macroscopic evolution of the condensate is interpreted in terms of microphysical particle processes. Our results have implications for the quantitative description of the decay of cosmological scalar fields in the early Universe, and may also be applied to other physical systems.

Causality Violation and Non-local Generalization of the Lorentz-Dirac Equation

1977 ◽  
Vol 32 (3-4) ◽  
pp. 319-326
Author(s):  
P. Alber ◽  
W. Heudorfer ◽  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Equation Of Motion ◽  
Local Theory ◽  
Constant Force ◽  
Dirac Theory ◽  
Local Equation ◽  
Causality Violation ◽  
Finite Duration ◽  
Non Local

AbstractIt is demonstrated by a concrete example (constant force of finite duration) that the recently proposed, non-local equation of motion for the radiating electron does exhibit the effect of causality violation. This phenomenon, which occurs in the non-local theory in form of self-oscillations, is however less severe than in the Lorentz-Dirac theory, if only physically reasonable forces are admitted.

Stellar Convection

1991 ◽  
Vol 9 (1) ◽  
pp. 26-31 ◽  
Author(s):  
Da Run Xiong
Keyword(s):  
Time Dependent ◽  
Hydrodynamic Equations ◽  
Dynamic Coupling ◽  
Stellar Convection ◽  
Non Linear ◽  
Non Local ◽  
The Difference ◽  
Thermodynamic Coupling

AbstractTime-dependent convection theory and non-local convection theory are described. The difference between the convection theories results from the different treatment of the non-linear terms of the hydrodynamic equations. We have obtained a better understanding of the thermodynamic coupling between convection and oscillations in comparison to the dynamic coupling.

Tunneling Phenomenon

2021 ◽  
pp. 45-76
Author(s):  
C. Julian Chen
Keyword(s):  
Perturbation Theory ◽  
Three Dimensional ◽  
Hamiltonian Formalism ◽  
Experimental Methods ◽  
Time Dependent ◽  
Starting Point ◽  
Metal Insulator Metal ◽  
Dimensional Version ◽  
Tunneling Phenomenon ◽  
Theory Of Superconductivity

This chapter presents basic experimental methods and the basic theory of tunneling. The classical metal-insulator-metal tunneling junction experiment of Giaever, designed to verify the Bardeen-Cooper-Schrieffer theory of superconductivity, is the motivation for Bardeen to invent his perturbation theory of tunneling. That Bardeen theory then became the starting point of the most useful models of STM. Section 2.2 presents the Bardeen tunneling theory from time-dependent perturbation theory of quantum mechanics, starting from a one-dimensional case, then proceeds to three-dimensional version with wave-function corrections. The Bardeen theory in second-quantization format, the transfer-Hamiltonian formalism, is also presented. As extensions of the original Bardeen theory, the theories and experiments of inelastic tunneling and spin-polarized tunneling are discussed in depth.

Finite Size of the Electron and Runaway Solutions

1977 ◽  
Vol 32 (5) ◽  
pp. 383-389 ◽  
Author(s):  
J. Petzold ◽  
W. Heudorfer ◽  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Free Electron ◽  
Constant Velocity ◽  
Initial Conditions ◽  
Perturbation Expansion ◽  
Finite Size ◽  
Equation Of Motion ◽  
Local Equation ◽  
Causality Violation ◽  
Non Local

Abstract The problem of runaway solutions is studied within the framework of a non-local equation of motion for the classically radiating electron. It is found that the force-free electron oscillates down to a constant velocity under emission of radiation, if certain restrictions on the initial conditions are imposed. Causality violation is not present in this model, but penetrates into the theory as consequence of a false perturbation expansion leading to the notorious Lorentz-Dirac equation of motion.

scholarly journals A survey of RR Lyrae models

1993 ◽  
Vol 139 ◽  
pp. 262-262
Author(s):  
G. Bono ◽  
R.F. Stellingwerf
Keyword(s):  
Convective Transport ◽  
Time Dependent ◽  
Instability Strip ◽  
Rr Lyrae Stars ◽  
Rr Lyrae ◽  
Non Linear ◽  
Non Local ◽  
Lyrae Stars

AbstractAn extensive grid of non-linear pulsating models of RR Lyrae stars have been computed. To simulate the outer regions of these variables a non-local and time-dependent treatment of convective transport has been adopted. In this poster we briefly describe some new features of the instability strip (IS).

scholarly journals Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

2021 ◽  
pp. 175682772110155
Author(s):  
Vincent Kather ◽  
Finn Lückoff ◽  
Christian O. Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Equivalence Ratio ◽  
Transfer Functions ◽  
Transport Model ◽  
Mode Conversion ◽  
Fuel Injector ◽  
One Dimensional ◽  
Flow Fluctuations ◽  
Non Linear ◽  
Non Local ◽  
Acoustic Forcing

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

scholarly journals Spurious poles in the scattering of electric and magnetic charges

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
John Terning ◽  
Christopher B. Verhaaren
Keyword(s):  
Perturbation Theory ◽  
Scattering Amplitudes ◽  
Pair Production ◽  
Magnetic Particles ◽  
Single Photon ◽  
Low Energy ◽  
Magnetic Interactions ◽  
Parity Conservation ◽  
Non Local ◽  
The Way

Abstract Theories with both electric and magnetic charges (“mutually non-local” theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)’s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory. Correct calculations must show how the spurious poles cancel in observable scattering amplitudes. Consistency requires that one type of charge is confined as a result of one of the U(1)’s being broken. Here we show how the constraints of confinement and parity conservation on observable processes manages to cancel the spurious poles in scattering and pair production amplitudes, paving the way for systematic studies of the experimental signatures of “dark” electric-magnetic processes. Along the way we demonstrate some novel effects in electric-magnetic interactions, including that the amplitude for single photon production of magnetic particles by electric particles vanishes.

scholarly journals The power of modelling pulsatile profiles

2021 ◽  
Author(s):  
Michiel J. van Esdonk ◽  
Jasper Stevens
Keyword(s):  
Growth Hormone ◽  
Statistical Power ◽  
Quantitative Description ◽  
Mixed Effects ◽  
Post Dose ◽  
Deconvolution Analysis ◽  
Linear Mixed Effects ◽  
Non Linear ◽  
Over Time ◽  
Modelling Approach

AbstractThe quantitative description of individual observations in non-linear mixed effects models over time is complicated when the studied biomarker has a pulsatile release (e.g. insulin, growth hormone, luteinizing hormone). Unfortunately, standard non-linear mixed effects population pharmacodynamic models such as turnover and precursor response models (with or without a cosinor component) are unable to quantify these complex secretion profiles over time. In this study, the statistical power of standard statistical methodology such as 6 post-dose measurements or the area under the curve from 0 to 12 h post-dose on simulated dense concentration–time profiles of growth hormone was compared to a deconvolution-analysis-informed modelling approach in different simulated scenarios. The statistical power of the deconvolution-analysis-informed approach was determined with a Monte-Carlo Mapped Power analysis. Due to the high level of intra- and inter-individual variability in growth hormone concentrations over time, regardless of the simulated effect size, only the deconvolution-analysis informed approach reached a statistical power of more than 80% with a sample size of less than 200 subjects per cohort. Furthermore, the use of this deconvolution-analysis-informed modelling approach improved the description of the observations on an individual level and enabled the quantification of a drug effect to be used for subsequent clinical trial simulations.

Sign in / Sign up

Export Citation Format

Share Document