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We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
The partition function of a quantum statistical system in flat space can always be written as an integral over a classical Boltzmann factor $\exp[ -\beta V^{\rm eff cl({\bf x}_0)]$, where $V^{\rm eff cl({\bf x}_0)$ is the so-called…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…
Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…
Time-Dependent Density Functional Theory is mathematically formulated through non-linear coupled time-dependent 3-dimensional partial differential equations and it is natural to expect a strong sensitivity of its solutions to variations of…
Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…
We derive backward and forward fractional Schr\"odinger type of equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and…
Analytical formulae for functional differentiation under simultaneous K-conservation constraints, with K the integral of some function of the functional variable, are derived, making the proper account for the simultaneous conservation of…
The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some…
Accurate electronic bandstructures of solids are indispensable for a wide variety of applications and should provide a sound prediction of phonon-induced band gap renormalization at finite temperatures. We employ our previously introduced…
The analytical approximations for the moderating neutrons flux density like Fermi spectra, widely used in reactor physics, involve the probability function for moderating neutron to avoid the resonant absorption obtained using some…
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
Evaluating a lattice path integral in terms of spectral data and matrix elements pertaining to a suitably defined quantum transfer matrix, we derive form-factor series expansions for the dynamical two-point functions of arbitrary local…
The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…
As for the Fourier transforms of positive and integrable functions supported in the unit interval, we make a list of improvements for P\'olya's results on the distribution of their positive zeros and give new sufficient conditions under…
The conventional surface integral formula $J_{\rm surf}[\Phi]$ and an alternative volume integral formula $J_{\rm var}[\Phi]$ are used to compute the asymptotic exchange splitting of the interaction energy of the hydrogen atom and a proton…
We present a fully analytic approach for evaluating boundary integrals in two dimensions for Smoothed Particle Hydrodynamics (SPH). Conventional methods often rely on boundary particles or wall re-normalization approaches derived from…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…