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We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions…
We study both the static properties of $^{11}$Be and its reaction dynamics during electromagnetic breakup under a unified framework. A many-body approach - the antisymmetrized molecular dynamics (AMD) is used to describe the structure of…
Coherent properties of a two dimensional spatially periodic structure - polaritonic crystal (PolC) formed by trapped two-level atoms in an optical cavity array interacting with a light field, are analyzed. By considering the wave function…
The non-linear response of a beam splitter to the coincident arrival of interacting particles enables numerous applications in quantum engineering and metrology yet poses considerable challenge to achieve focused interactions on the…
We derive an exact, continuous-variable path integral (PI) representation of the canonical partition function for electronically nonadiabatic systems. Utilizing the Stock-Thoss (ST) mapping for an N-level system, matrix elements of the…
Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in…
Electronic structure calculations based on Density Functional Theory have successfully predicted numerous ground state properties of a variety of molecules and materials. However, exchange and correlation functionals currently used in the…
Point-to-point reflection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more general elliptic equations. We develop a non-local,…
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
It is shown that `bipartite' wave functions can present a mathematical formalism of quantum theory for a single particle, in which the associated Schr\"{o}dinger's wave functions correspond to those `bipartite' wave functions of product…
The asymptotic wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A 47, 2004 (1993)] and Mukhamedzhanov and Lieber [Phys. Rev. A 54, 3078 (1996)] has been refined in the region where the pair $ (\beta,\gamma)$ remains close to each…
Non-thermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of non-thermal…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are…
We provide a rigorous justication of nonlinear geometric optics expansions for reflecting \emph{pulses} in space dimensions $n>1$. The pulses arise as solutions to variable coefficient semilinear first-order hyperbolic systems. The…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
We present an analysis of the two-dimensional Schrodinger equation for two electrons interacting via Coulombic force and confined in an anizotropic harmonic potential. The separable case of wy = 2wx is studied particularly carefully. The…
We propose a many-body method for band-structure calculations in strongly correlated electron systems and apply it to NiO. The method may be viewed as a translationally invariant version of the cluster method of Fujimori and Minami. Thereby…
It is shown that, for isolated many-electron Coulomb systems with Coulombic external potentials, the usual reductio ad absurdum proof of the Hohenberg-Kohn theorem is unsatisfactory since the to-be-refuted assumption made about the…
Range-separated density-functional theory is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into…