Related papers: Variational approximation for two-time correlation…
It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint $4\times 4$ relativistic time operator for…
Four-point correlation functions of hypermultiplet bilinear composites are analysed in N=2 superconformal field theory using the superconformal Ward identities and the analyticity properties of the composite operator superfields. It is…
An exact invariant operator of time-dependent coupled oscillators is derived using the Liouville-von Neumann equation. The unitary relation between this invariant and the invariant of two uncoupled simple harmonic oscillators is…
Controlled invariant set and viability regulation of dynamical control systems have played important roles in many control and coordination applications. In this paper we develop a temporal viability regulation theory for general dynamical…
We explore how to compute, classically at strong coupling, correlation functions of local operators corresponding to classical spinning string states. The picture we obtain is of `fattened' Witten diagrams, the evaluation of which turns out…
We discuss the renormalizability of Phi-derivable approximations in scalar phi^4 theory in four dimensions. The formalism leads to self-consistent equations for the 2-point and the 4-point functions which are plagued by ultraviolet…
Distributional approximations of (bi--) linear functions of sample variance-covariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence…
A pedagogical introduction to the cluster-perturbation theory, the variational cluster approximation and to self-energy-functional theory is given. Some standard applications and the relation to dynamical mean-field theory are discussed.
Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…
This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear…
We introduce a framework for approximate dynamic programming that we apply to discrete time chains on $\mathbb{Z}_+^d$ with countable action sets. Our approach is grounded in the approximation of the (controlled) chain's generator by that…
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…
We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow…
An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $\phi^4$ theory in 1+1 dimensions. We…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a ``control…
We compute general higher-point functions in the sector of large charge operators $\phi^n$, $\bar\phi^n$ at large charge in $O(2)$ $(\bar \phi\phi)^2$ theory. We find that there is a special class of "extremal" correlators having only one…