Search results for "Integral form"
showing 10 items of 71 documents
Path integral quantization for massive vector bosons
2010
A parity-conserving and Lorentz-invariant effective field theory of self-interacting massive vector fields is considered. For the interaction terms with dimensionless coupling constants the canonical quantization is performed. It is shown that the self-consistency condition of this system with the second-class constraints in combination with the perturbative renormalizability leads to an SU(2) Yang-Mills theory with an additional mass term.
On new efficient algorithms for PIMC and PIMD
2002
Abstract The properties of various algorithms, estimators, and high-temperature density matrix (HTDM) decompositions relevant for path integral simulations are discussed. It is shown that Fourier accelerated path integral molecular dynamics (PIMD) completely eliminates slowing down with increasing Trotter number P . A new primitive estimator of the kinetic energy for use in PIMD simulations is found to behave less pathologically than the original virial estimator. In particular, its variance does not increase significantly with P . Two non-primitive HTDM decompositions are compared as well: one decomposition used in the Takahashi Imada algorithm and another one based on an effective propaga…
Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral
2014
A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…
Bicoherent-State Path Integral Quantization of a non-Hermitian Hamiltonian
2020
We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from hermitian quantum physics. We do all this by working out a concrete example, namely, computation of the propagator of a certain quasi-hermitian variant of Swanson's model, which is not invariant under conventional $PT$-transformation. The resulting propagator coincides with that of the propagator of the standard harmonic oscillator, which is isospectral with the model under consideration by virtue of a similarity transformation relating the corresponding…
Path integral solution by fractional calculus
2008
In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed.
A Wiener Path Integral Technique for Non-Stationary Response Determination of Nonlinear Oscillators with Fractional Derivative Elements
2014
In this paper a novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators with fractional derivative elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes. In this manner, the analytical Wi…
Investigation of eutectic transformation of Zn−Al alloy by DTA
1995
The paper discusses the investigation of crystallization of metals and alloys by differential thermal analysis (DTA). It was assumed that this method allows determination of the mechanism and kinetics of volumetric crystallization underiso conditions (e.g. anisothermal) on the basis of the parameters of the equation expressing an integral form of the DTA curve. From DTA, a course of eutectic transformation was determined for a technical Zn−Al alloy containing 4wt% Al. Investigations were carried out under continuous cooling at various rates and the kinetics parameters were determined with the KEKAM equation:-ln(1-x)=kln
First-passage problem for nonlinear systems under Lévy white noise through path integral method
2016
In this paper, the first-passage problem for nonlinear systems driven by $$\alpha $$ -stable Levy white noises is considered. The path integral solution (PIS) is adopted for determining the reliability function and first-passage time probability density function of nonlinear oscillators. Specifically, based on the properties of $$\alpha $$ -stable random variables and processes, PIS is extended to deal with Levy white noises with any value of the stability index $$\alpha $$ . Application to linear and nonlinear systems considering different values of $$\alpha $$ is reported. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the results.
Integral holomorphic functions
2004
We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Frechet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity. In this paper we define and study a class of holomorphic functions over infinite- dimensional Banach spaces admitting integral representation. Our purpose, and the motivation for our definition, are two-fold: we wish to obtain an integral repre- sentation formula …
Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution
2008
An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac's deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.