اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSecond-Order Perturbation in Adaptive Perturbation Method
93
0
0.0
(
0
)
تأليف
Chen-Te Ma
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The perturbation method is an approximation scheme with a solvable leading-order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part in bosonic systems by using all diagonal elements of the Fock state. We consider the harmonic oscillator with the interacting term, $lambda_1x^4/6+lambda_2x^6/120$, where $lambda_1$ and $lambda_2$ are coupling constants, and $x$ is the position operator. The spectrum shows a quantitative result, less than 1 percent error, compared to a numerical solution when we use the adaptive perturbation method up to the second-order and turn off the $lambda_2$. When we turn on the $lambda_2$, the deviation becomes larger, but the error is still less than 2 percent error. Our qualitative results are demonstrated in different values of coupling constants, not only focused on a weakly coupled region.
قيم البحث
اقرأ أيضاً
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants. We study th
e harmonic oscillator with the interacting potential, $lambda_1x^4/6+lambda_2x^6/120$, where $lambda_1$ and $lambda_2$ are coupling constants, and $x$ is the position operator. In this study, each perturbed term has an exact solution. We demonstrate the accurate study of the spectrum and $langle x^2rangle$ up to the next leading-order correction. In particular, we study a similar problem of Higgs field from the inverted mass term to demonstrate the possible non-trivial application of particle physics.
We give an explicit relation, up to second-order terms, between scalar-field fluctuations defined on spatially-flat slices and the curvature perturbation on uniform-density slices. This expression is a necessary ingredient for calculating observable
quantities at second-order and beyond in multiple-field inflation. We show that traditional cosmological perturbation theory and the `separate universe approach yield equivalent expressions for superhorizon wavenumbers, and in particular that all nonlocal terms can be eliminated from the perturbation-theory expressions.
We present the results of our perturbative calculations of the static quark potential, small Wilson loops, the static quark self energy, and the mean link in Landau gauge. These calculations are done for the one loop Symanzik improved gluon action, and the improved staggered quark action.
Working with perturbations about an FLRW spacetime, we compute the gauge-invariant curvature perturbation to second order solely in terms of scalar field fluctuations. Using the curvature perturbation on uniform density hypersurfaces as our starting
point, we give our results in terms of field fluctuations in the flat gauge, incorporating both large and small scale behaviour. For ease of future numerical implementation we give our result in terms of the scalar field fluctuations and their time derivatives.
The galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future Large Scale Structure surveys. The precision demanded by these Stage IV surveys requires the use of second order cosmolog
ical perturbation theory. Based on the independent calculation published previously, we present the result of the comparison with the results of three other groups at leading order. Overall we find that the differences between the different approaches lie mostly on the definition of certain quantities, where the ambiguity of signs results in the addition of extra terms at second order in perturbation theory.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
