Related papers: On the "Causality Paradox" of Time-Dependent Densi…
An explicit expression for the quadratic density-response function of a many-electron system is obtained in the framework of the time-dependent density-functional theory, in terms of the linear and quadratic density-response functions of…
Irreversibility and acausality of a sub-system are established in exactly soluble harmonic models with reversible and causal dynamics. It is shown that initial conditions, imposed on some dynamical degrees of freedom may break time reversal…
The particle-hole interaction problem is longstanding within time-dependent density functional theory (TDDFT) and leads to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that…
We comment on a recent paper by Yuen-Zhou et al. [ Phys. Chem. Chem. Phys. 2009, 11, 4509 ] which extends some of the results of Time-Dependent Current Density Functional Theory applied to open quantum systems. Besides pointing out some…
Due to the strongly nonlocal nature of $f_{xc}({\bf r},{\bf r}',\omega)$ the {\em scalar} exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT), the formula for Q the friction coefficient of an…
The classical logical antinomy known as Richard-Berry paradox is combined with plausible assumptions about the size i.e. the descriptional complexity of Turing machines formalizing certain sentences, to show that formalization of language…
Linear-response time-dependent density-functional theory (TDDFT) can describe excitonic features in the optical spectra of insulators and semiconductors, using exchange-correlation (xc) kernels behaving as $-1/k^{2}$ to leading order. We…
This thesis reports progress in the analysis of causality and multi-agent logical paradoxes in quantum and post-quantum theories. These research areas are highly relevant for the foundations of physics as well as the development of quantum…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
A theoretical model of cosmic expansion has been formulated on an assumption of inter-conversion of matter and dark energy, in the framework of Brans-Dicke theory. An empirical scale factor has been used, which generates a signature flip of…
We show how to incorporate the possibility of kinetic control in the conceptual Density Functional Theory formalism. This allow us to prove that the hard/soft acid/base principle will likely fail when the reactions are not…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to…
We identify the key property that the exchange-correlation (XC) kernel of time-dependent density functional theory must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as…
The principle of invariance of the velocity of light is only valid for the wrong measurements of inertial observers who ignore their own movement and consider themselves at rest. The Langevin (or clock) paradox arises when it is assumed…
We propose a framework for determining whether the causal dependence of an outcome $Y$ on a covariate $X$ changes at a given time point, given confounders $\boldsymbol{Z}$. For instance, in financial markets, the effect of a market…
We present an overview of the decision-theoretic framework of statistical causality, which is well-suited for formulating and solving problems of determining the effects of applied causes. The approach is described in detail, and is related…
Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory…