相关论文: Analytic structure of solutions to multiconfigurat…
We study the performance of self-consistent mean-field and beyond-mean-field approximations in shell-model valence spaces. In particular, Hartree-Fock-Bogolyubov, particle-number variation after projection and projected generator coordinate…
Reliable predictions of the static and dynamic properties of a nucleus require a fully microscopic description of both ground and excited states of this complicated many-body quantum system. Predictive calculations are key to understanding…
Consider the focussing cubic nonlinear Schr\"odinger equation in $R^3$: $$ i\psi_t+\Delta\psi = -|\psi|^2 \psi. $$ It admits special solutions of the form $e^{it\alpha}\phi$, where $\phi$ is a Schwartz function and a positive ($\phi>0$)…
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound…
The multiconfiguration Dirac-Fock method allows to calculate the state of relativistic electrons in atoms or molecules. This method has been known for a long time to provide certain wrong predictions in the nonrelativistic limit. We study…
This paper is a continuation of our previous work [21], where we have established that, for the second-order degenerate hyperbolic equation (\p_t^2-t^m\Delta_x)u=f(t,x,u), locally bounded, piecewise smooth solutions u(t,x) exist when the…
This work completes the construction of purely algebraic version of the theory of non-linear quantum chemistry methods. It is shown that at the heart of these methods there lie certain algebras close in their definition to the well-known…
We give a brief overview of recent work examining the presence of $\alpha$-clusters in light nuclei within the Skyrme-force Hartree-Fock model. Of special significance are investigations into $\alpha$-chain structures in carbon isotopes and…
Consider the focusing cubic semilinear Schroedinger equation in R^3 i \partial_t \psi + \Delta \psi + | \psi |^2 \psi = 0. It admits an eight-dimensional manifold of special solutions called ground state solitons. We exhibit a…
We organize the quantum hyperbolic invariants (QHI) of $3$-manifolds into sequences of rational functions indexed by the odd integers $N\geq 3$ and defined on moduli spaces of geometric structures refining the character varieties. In the…
A multi-configuration mixing approach built on essentially complex, symmetry-projected Hartree-Fock-Bogoliubov (HFB) mean fields is introduced. The mean fields are obtained by variation after projection. The configuration space consists out…
We present a unified treatment of nuclear density cores recovering the classic results for neutral atoms with heavy nuclei having a mass number $A\approx 10^2--10^6$ and extrapolating these results to massive nuclear density cores with…
We present an overview of the Hartree-Fock-Bogoliubov (HFB) theory of nucleonic superfluidity for finite nuclei. After introducing basic concepts related to pairing correlations, we show how the correlated pairs are incorporated into the…
We study a stationary scattering problem related to the nonlinear Helmholtz equation $-\Delta u - k^2 u = f(x,u) \ \ \text{in $\mathbb{R}^N$,}$ where $N \ge 3$ and $k>0$. For a given incident free wave $\varphi \in L^\infty(\mathbb{R}^N)$,…
This paper is devoted to the study of the following autonomous Kirchhoff-type equation $$-M\left(\int_{\mathbb{R}^N}|\nabla{u}|^2\right)\Delta{u}= f(u),~~~~u\in H^1(\mathbb{R}^N),$$ where $M$ is a continuous non-degenerate function and…
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the…
In this article, we consider quantum crystals with defects in the reduced Hartree-Fock framework. The nuclei are supposed to be classical particles arranged around a reference periodic configuration. The perturbation is assumed to be small…
Inspired by a recent work of Wang-Zhao, in this note we prove that for a fixed $n$-dimensional closed Riemannian manifold $(M^n, g)$, if an $\mathrm{RCD}(K, n)$ space $(X, \mathsf{d}, \mathfrak{m})$ is Gromov-Hausdorff close to $M^n$, then…
Expanding a double tetrahedron formation of equal spheres arranged in fcc structure correlation between the positions of the nucleons and quantum numbers has been detected. The number of protons in the structure is not simply consistent…
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…