Related papers: Variational approximation for two-time correlation…
Electron-positron interactions have been utilized in various fields of science. Here we develop time-dependent multi-component density functional theory to study the coupled electron-positron dynamics from first principles. We prove that…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
This paper considers the problem of estimating the time auto-correlation function for a quantity that is defined in configuration space, given a knowledge of the mean-square displacement as function of time in configuration space. The…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…
We study the problem of estimating time-varying coefficients in ordinary differential equations. Current theory only applies to the case when the associated state variables are observed without measurement errors as presented in…
We extend the time-dependent variational principle to the setting of dissipative dynamics. This provides a locally optimal (in time) approximation to the dynamics of any Lindblad equation within a given variational manifold of mixed states.…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
The coupling constant dependence is derived in time-dependent {\em current} density functional theory. The scaling relation can be used to check approximate functionals and in conjunction with the adiabatic connection formula to obtain the…
In the nonrelativistic many-electron approximation of the theory of photoionization of the atom in the formalism of secondary quantization and the theory of irreducible tensor operators, analytical structures for the quadrupole transition…
We investigate the variable-exponent Abel integral equations and corresponding fractional Cauchy problems. The main contributions of the work are enumerated as follows: (i) We develop an approximate inversion technique for variable-exponent…
A theoretical description of time correlation functions for electron properties in the presence of a positive ion of charge number Z is given. The simplest case of an electron gas distorted by a single ion is considered. A semi-classical…
The phase shift of the O(4) symmetric $\phi^4$ theory in the symmetric phase is calculated numerically using the relation between phase shift and energy levels of two-particle states recently derived by L\"{u}scher. The results agree with…
We discuss a formulation of Galileon actions in terms of matrix determinants in four dimensions. This approach allows one to straightforwardly determine derivative couplings between Galileons and scalar or vector degrees of freedom that…
We investigate the influences of variables on a Boolean function $f$ based on the quantum Bernstein-Vazirani algorithm. A previous paper (Floess et al. in Math. Struct. in Comp. Science 23: 386, 2013) has proved that if a $n$-variable…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
The Balian-V\'en\'eroni (BV) variational principle, which optimizes the evolution of the state according to the relevant observable in a given variational space, is used at the mean-field level to determine the particle number fluctuations…
In this work, approximations for real two variables function $f$ which has continuous partial $(n-1)$-derivatives $(n \ge 1)$ and has the $n$--th partial derivative of bounded bivariation or absolutely continuous are established. Explicit…
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and…
Recent advances are being discussed on the calculation, within the conformal field theory approach, of the correlation functions for local operators in the theory of 2D gravity coupled to the minimal models of matter.