Related papers: Recursive Calculation of Effective Potential and V…
We present a self-consistent calculation of the finite temperature effective potential for $\lambda \phi^4$ theory, using the composite operator effective potential in which an infinite series of the leading diagrams is summed up. Our…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
Intractable distributions present a common difficulty in inference within the probabilistic knowledge representation framework and variational methods have recently been popular in providing an approximate solution. In this article, we…
The method of the calculation of effective potential (in linear curvature approximation and at any loop) in massless gauge theory in curved space- time by the direct solution of RG equation is given.The closed expression for two-loop…
Using schematic model potentials, we calculate exactly the virial coefficients of a classical gas up to sixth order and use them to assess the convergence properties of the virial expansion of basic thermodynamic quantities such as…
We study Monte Carlo calculations of the effective potential for a scalar field theory using three techniques. One of these is a new method proposed and tested for the first time. In each case we extract the renormalised quantities of the…
We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on…
The analytic properties of the ground state resonance energy E(g) of the cubic potential are investigated as a function of the complex coupling parameter g. We explicitly show that it is possible to analytically continue E(g) by means of a…
In this paper we calculate the leading divergences of the effective potential for an arbitrary scalar theory on a curved spacetime background. Based on the recurrence relation between the leading poles following from the locality condition,…
We derive formulas which connect cumulants of particle numbers observed with efficiency losses with the original ones based on the binomial model. These formulas can describe the case with multiple efficiencies in a compact form. Compared…
Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…
We derive recursively the perturbation series for the ground-state energy of the D-dimensional anharmonic oscillator and resum it using variational perturbation theory (VPT). From the exponentially fast converging approximants, we extract…
In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
We compute the effective potential for $\phi^4$ theory with a squeezed coherent state type of construct for the ground state. The method essentially consists in optimising the basis at zero and finite temperatures. The gap equation becomes…
A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…
A number theoretic algorithm is given for writing gauge theory amplitudes in a compact manner. It is possible to write down all details of the complete $L$ loop amplitude with two integers, or a complex integer. However, a more symmetric…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
A fully algebraic approach to reconstructing one-dimensional reflectionless potentials is described. A simple and easily applicable general formula is derived, using the methods of the theory of determinants. In particular, useful…