Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRevisiting the variational two-particle reduced density matrix for nuclear systems
99
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In most nuclear many-body methods, observables are calculated using many-body wave functions explicitly. The variational two-particle reduced density matrix method is one of the few exceptions to the rule. Ground-state energies of both closed-shell and open-shell nuclear systems can indeed be evaluated by minimizing a constrained linear functional of the two-particle reduced density matrix. However, it has virtually never been used in nuclear theory, because nuclear ground states were found to be well overbound, contrary to those of atoms and molecules. Consequently, we introduced new constraints in the nuclear variational two-particle reduced density matrix method, developed recently for atomic and molecular systems. Our calculations then show that this approach can provide a proper description of nuclear systems where only valence neutrons are included. For the nuclear systems where both neutrons and protons are active, however, the energies obtained with the variational two-particle reduced density matrix method are still overbound. The possible reasons for the noticed discrepancies and solutions to this problem will be discussed.
rate research
Read More
Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density matrix (2-RDM). We develop a closed equation of motion for the 2-RDM employing a novel reconstruction functional for the three-particle reduced density matrix (3-RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing $N$-representability during time evolution is essential for achieving stable solutions. As a prototypical test case which features long-range Coulomb interactions we employ the one-dimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both one-particle observables such as the time-dependent dipole moment and two-particle observables such as the pair density and mean electron-electron interaction energy. Our results are in very good agreement with numerically exact solutions for the $N$-electron wavefunction obtained from the multiconfigurational time-dependent Hartree-Fock method.
We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity based on the reduced density matrix by exploring different types of quantum circuits. Through explicit calculations on a toy model of two coupled harmonic oscillators, where one or both of the oscillators are inverted, we demonstrate that the evolution of complexity is a possible diagnostic of chaos.
In [arxiv:2106.02560] we proposed a reduced density matrix functional theory (RDMFT) for calculating energies of selected eigenstates of interacting many-fermion systems. Here, we develop a solid foundation for this so-called $boldsymbol{w}$-RDMFT and present the details of various derivations. First, we explain how a generalization of the Ritz variational principle to ensemble states with fixed weights $boldsymbol{w}$ in combination with the constrained search would lead to a universal functional of the one-particle reduced density matrix. To turn this into a viable functional theory, however, we also need to implement an exact convex relaxation. This general procedure includes Valones pioneering work on ground state RDMFT as the special case $boldsymbol{w}=(1,0,ldots)$. Then, we work out in a comprehensive manner a methodology for deriving a compact description of the functionals domain. This leads to a hierarchy of generalized exclusion principle constraints which we illustrate in great detail. By anticipating their future pivotal role in functional theories and to keep our work self-contained, several required concepts from convex analysis are introduced and discussed.
We introduce the Nuclear Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG) method for solving the time-independent Schrodinger equation simultaneously for electrons and other quantum species. In contrast to already existing multicomponent approaches, in this work we construct from the outset a multi-reference trial wave function with stochastically optimized non-orthogonal Gaussian orbitals. By iterative refining of the Gaussians positions and widths, we obtain a compact multi-reference expansion for the multicomponent wave function. We extend the DMRG algorithm to multicomponent wave functions to take into account inter- and intra-species correlation effects. The efficient parametrization of the total wave function as a matrix product state allows NEAP-DMRG to accurately approximate full configuration interaction energies of molecular systems with more than three nuclei and twelve particles in total, which is currently a major challenge for other multicomponent approaches. We present NEAP-DMRG results for two few-body systems, i.e., H$_2$ and H$_3^+$, and one larger system, namely BH$_3$
The nuclear matrix elements (NMEs) for two-neutrino double-beta decay ($2 ubetabeta$) are studied in the framework of the relativistic nuclear energy density functional. The properties of nuclei involved in the decay are obtained using relativistic Hartree-Bogoliubov model and relevant nuclear transitions are described using the relativistic proton-neutron quasiparticle random phase approximation (pn-ReQRPA). Three effective interactions have been employed, including density-dependent meson-exchange and point coupling interactions, supplemented with nuclear pairing correlations. The $2 ubetabeta$ matrix elements and half-lives are calculated for several nuclides experimentally known to undergo this kind of decay: $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, and $^{128}$Te. The model dependence of the NMEs and their sensitivity on the isoscalar pairing strength $V_0$ is investigated, and the optimized value of this parameter is determined. The results of the present study represent an important benchmark for the future applications of the relativistic framework in studies of neutrinoless double-beta decay.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
