Related papers: The functional integral with unconditional Wiener …
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
We apply a `dimensional reduction' mechanism to the evaluation of the functional integral for the vacuum energy of a real scalar field in the presence of non-trivial backgrounds, in d+1 dimensions. The reduction is implemented by applying a…
We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called…
This paper presents a comprehensive investigation of the problem of a harmonic oscillator with time-depending frequencies in the framework of the Vlasov theory and the Wigner function apparatus for quantum systems in the phase space. A new…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
The general Weyl -- Wigner formalism in finite dimensional phase spaces is investigated. Then this formalism is specified to the case of symmetric ordering of operators in an odd -- dimensional Hilbert space. A respective Wigner function on…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds…
We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that…
By using the localized character of canonical coherent states, we give a straightforward derivation of the Bargmann integral representation of Wigner function (W). A non-integral representation is presented in terms of a quadratic form…
We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the…
We present a perturbation analysis of the semiclassical Wigner equation which is based on the interplay between configuration and phase spaces via Wigner transform. We employ the so-called harmonic approximation of the Schrodinger…
For the creation operator $\adag $ and the annihilation operator $a$ of a harmonic oscillator, we consider Weyl ordering expression of $(\adag a)^n$ and obtain a new symmetric expression of Weyl ordering w.r.t. $\adag a \equiv N$ and…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u" + g_1(x) u' + g_2(x) u + g_3(x) u^n + g_4(x) = 0, n real. Its physical applications…
In this paper we gather and extend classical results for parabolic cylinder functions, namely solutions of the Weber differential equations, using a systematic approach by Borel-Laplace methods. We revisit the definition and construction of…
We consider Gaussian random waves on hyperbolic spaces and establish variance asymptotics and central limit theorems for a large class of their integral functionals, both in the high-frequency and large domain limits. Our strategy of proof…
On four-dimensional closed manifolds we introduce a class of canonical Riemannian metrics, that we call weak harmonic Weyl metrics, defined as critical points in the conformal class of a quadratic functional involving the norm of the…