Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2203.04843

Measures of complexity and entanglement in fermionic many-body systems

Aurel Bulgac·Matthew Kafker·Ibrahim Abdurrahman
View original source ↗Read source document ↗Export metadata ↓

Abstract

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in case of CI calculations reaches about 20 billion terms. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. The canonical wave functions/natural orbitals and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex non-equilibrium time-dependent process, induced nuclear fission described within a real-time Density Functional Theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short range correlations between fermions.

Explore related subjects

nucl-thcond-mat.supr-con

Keep this discovery

BibTeXRIS

Aurel Bulgac, Matthew Kafker, Ibrahim Abdurrahman. 2022-03-09. Measures of complexity and entanglement in fermionic many-body systems. https://doi.org/10.1103/physrevc.107.044318

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fission Modes and Fragment Shell Structures in $^{258}$Md$^*$ from Six-Dimensional Langevin Calculations

The fission of $^{258}$Md$^*$ is calculated in the excitation energy range of $E^*=6$--36 MeV using a six-dimensional Langevin equation. The calculated events are classified into two symmetric and two asymmetric fission modes based on the fragment mass and the quadrupole deformations of the two fragments at scission. The symmetric modes are separated by their total kinetic energies into the short (high TKE) and superlong (low TKE) modes, whereas the asymmetric modes differ in mass asymmetry. With increasing excitation energy, the yield of the short mode decreases, whereas the combined yield of the two asymmetric modes increases, as observed in the in-beam prompt-fission study of $^{258}$Md$^*$. From an analysis of the fragment shapes and associated single-particle levels, the short mode and the dominant asymmetric mode with the smaller mass asymmetry are found to involve a compact fragment characterized by deformed shell gaps at $Z=52$ and $N=84$, while the complementary fragments have different quadrupole deformations in the two modes.

nucl-th↗
arXiv2026

Classification of fission modes in $^{236}$U using a six-dimensional Langevin approach

Thermal neutron-induced fission of $^{235}$U is studied using a six-dimensional Langevin approach based on the Cassini shape parametrization. Scission events are classified into Asymmetric 1 (AS1), Asymmetric 2 (AS2), and Superlong (SL) fission modes by applying the $k$-means algorithm to the fragment mass and the quadrupole deformations of both fragments. For each mode, proton and neutron single-particle levels are calculated for representative fragments to examine their shell structures. The AS1 heavy fragment exhibits proton gaps at $Z=50$ and 52 and neutron gaps at $N=82$ and 84, whereas well-developed gaps appear at $Z=56$ and $N=88$ in the AS2 heavy fragment. The mass splits of AS1 and AS2 are close to those of the conventional Standard I and Standard II modes, respectively. However, the average total kinetic energy is lower for AS1 than for AS2, opposite to the conventional ordering of Standard I and Standard II. This reversal reflects the more elongated shape of the AS1 light fragment. The SL mode is conventionally interpreted in terms of macroscopic liquid-drop effects, whereas the pronounced proton shell gap at $Z=46$ suggests that proton shell effects also contribute to the elongated symmetric configuration. The classification based on fragment mass and the quadrupole deformations of both fragments provides a basis for distinguishing fission modes and examining the corresponding fragment shell structures at scission.

nucl-th↗
arXiv2026

Gogny interaction from beginnings to current challenges

The main goal of the present review article is to gather for the first time various facets of the phenomenological effective Gogny interaction which was originally proposed in the 70's. This involves both nuclear phenomena of interest that led to its creation and evolution as well as highly technical aspects that led the objectives to be achieved. With this in mind, we propose a discussion structured around four points. After a general introduction, the history and philosophy of the Gogny interaction is exposed. In particular, one highlights an intuitive way of guiding the determination of the parameters of the phenomenological interaction with the results obtained from a realistic interaction using Hartree-Fock calculations and second order corrections and a G-matrix. One also shows that physical phenomena such as pairing or fission were essential to improve the parameterization. The evolution of the original analytical form over the years is also discussed. The second point concern the emulator that was used for the generation of parameterizations. Its modifications, consistent with the evolution of the analytical form, are given. Other fitting procedures, more recent, are also evoked. The third key point is dedicated to the role of the nuclear matter in the fitting process and the acceptance of a parameterization. The objective of the last key point is to highlight some results obtained with the Gogny interaction in nuclear structure, fission and reactions that have allowed to interpret experimental data.

nucl-th↗