Related papers: Two-particle coalescence conditions revisited
In a generic random system, the coexistence of extended and localized states can be evidenced by the subextensive width of energy distribution of a physical initial state in, for example, the quantum quenches which involving the local…
The recently introduced auxiliary Hamiltonian approach [Balzer K and Eckstein M 2014 Phys. Rev. B 89 035148] maps the problem of solving the two-time Kadanoff-Baym equations onto a noninteracting auxiliary system with additional bath…
In this article we are interested in the microscopic modeling of a two-dimensional two-well problem which arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on…
The exact values of the presently determined components 26of the angular Fock coefficients at the two-particle coalescences were obtained and systematized. The Green Function approach was successfully applied to simplify the most…
For one-dimensional many-body systems interacting via the \textit{Coulomb force} and with \textit{arbitrary} external potential energy, we derive (\textit{i}) the \textit{node coalescence condition} for the wave function. This condition…
For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a…
The formation of a higher-order singularity by the coalescence of two exceptional points is studied in the anti-hermitian limit of the complex-extended 3-level Richardson-Gaudin model.
We have derived the integral form of the cusp and node coalescence conditions satisfied by the wavefunction at the coalescence of two charged particles in $D \geq 2$ dimension space. From it we have obtained the differential form of the…
We derive expressions for the expectation values of the local energy and the local power transferred by an external electrical field to a many-particle system of interacting spinless electrons. In analogy with the definition of the (local)…
We study the coalescence of two bound energy eigenstates embedded in the continuous spectrum of a real Hamiltonian $H[4]$ and the singular point produced by this coalescence. At the singular point, the two unnormalized Jost eigenfunctions…
The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate CFHHM wave functions. The asymptotic solutions of the proper…
A new class of time-energy uncertainty relations is directly derived from the Schr\"odinger equations for time-dependent Hamiltonians. Only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full…
In non-hermitian systems, the particular position at which two eigenstates coalesce under a variation of a parameter in the complex plane is called an exceptional point. A non-perturbative theory is proposed which describes the evolution of…
A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics on the canonical example of…
We consider a Hamiltonian system of particles, interacting through of a smooth pair potential. We look at the system on a space scale of order {\epsilon}^1, times of order {\epsilon}^2, and mean velocities of order {\epsilon}, with…
We recently derived a quantization condition for the energy of three relativistic particles in a cubic box. Here we use this condition to study the energy level closest to the three-particle threshold when the total three-momentum vanishes.…
In a full solution for a scalar quantum field coupled to an accelerating isotropic universe, all constituent non-autonomous modes of elementary excitation cease to oscillate and become unstable at a discrete sequence of times. After…
We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in geosciences or medical applications. We propose a port-Hamiltonian formulation of the system…
When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…
It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While…