Collective Degrees Of Freedom Research Articles

Measuring entanglement entropy and its topological signature for phononic systems

Entanglement entropy is a fundamental concept with rising importance in various fields ranging from quantum information science, black holes to materials science. In complex materials and systems, entanglement entropy provides insight into the collective degrees of freedom that underlie the systems’ complex behaviours. As well-known predictions, the entanglement entropy exhibits area laws for systems with gapped excitations, whereas it follows the Gioev-Klich-Widom scaling law in gapless fermion systems. However, many of these fundamental predictions have not yet been confirmed in experiments due to the difficulties in measuring entanglement entropy in physical systems. Here, we report the experimental verification of the above predictions by probing the nonlocal correlations in phononic systems. We obtain the entanglement entropy and entanglement spectrum for phononic systems with the fermion filling analog. With these measurements, we verify the Gioev-Klich-Widom scaling law. We further observe the salient signatures of topological phases in entanglement entropy and entanglement spectrum.

Non-empirical description of nuclear collective motion with optimized basis for multi-reference density functional theory

The generator coordinate method (GCM) has been a well-known method to describe nuclear collective motions. In this method, one a priori specifies collective degrees of freedom as inputs of the method based on empirical and/or phenomenological assumptions. We here present an extension of the GCM, in which both the basis Slater determinants and weight factors are optimized in a non-empirical manner. The result for 16O nucleus with the Skyrme functional suggests that a collective coordinate should be determined in a more complex way than what has been assumed so far.

Cluster properties of heavy nuclei predicted with the Barcelona-Catania-Paris-Madrid energy density functional

We study the cluster emission properties of 224\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{224}$$\\end{document}Ra and 238\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{238}$$\\end{document}Pu employing the Barcelona-Catania-Paris-Madrid (BCPM) energy density functional (EDF). Starting from two-dimensional potential energy surfaces, coexisting fission paths are identified. A fission valley located at large octupole deformations, corresponding to a highly-asymmetric mass distribution, is found in both nuclei. As the corresponding fragments are dominated by the presence of 208\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{208}$$\\end{document}Pb, we can relate this fission path to the emergence of cluster emission. Using the octupole moment as collective degree of freedom, we compute the cluster decay half-lives and study the impact of collective inertias, pairing strength and collective zero-point energy. The agreement with experimental data resembles the results obtained for spontaneous fission half-lives, indicating the capability of BCPM to consistently describe a large variety of fission phenomena, including cluster emission.

Fission studies in inverse kinematics with the R3B setup

Nuclear fission is a complex dynamical process, whose description involves the coupling between intrinsic and collective degrees of freedom, as well as different quantum-mechanical phenomena. For this reason, to this day it still lacks a satisfactory and complete microscopic description. In addition to the importance of describing fission itself, studies of the r-process in astrophysics depend on fission observables to constrain the theoretical models that explain the isotopic abundances in the Universe. To improve on the existing data, fission reactions of heavy nuclei in inverse kinematics are produced in quasi-free (p,2p) scattering reactions, which induce fission through particle-hole excitations that can range from few to tens of MeV. In order to study the evolution of the fission yields with temperature, the excitation energy of the fissioning system must be reconstructed, which is possible by measuring the four-momenta of the two outgoing protons. Performing this kind of experiment requires a complex experimental setup, providing full isotopic identification of both fission fragments and an accurate measurement of the momenta of the two outgoing protons. This was realized recently at the GSI/FAIR facility and some of the results obtained for the charge distributions are presented in this work.

Langevin equation for the collective motions of a binary astrophysical system.

According to Thirring's condition, the thermodynamic equilibrium is not possible between two systems with negative heat capacities. Since the existence of negative heat capacity is a rule rather an exception in astrophysics, we would like to analyze the possibility of the thermodynamic equilibrium for a paradigmatic astrophysical situation: the binary system. The possible explanation arises after decomposing the dynamical variables into internal and collective degrees of freedom, which enables us to reinterpret binary systems as two systems A and B that interact between them through a third low dimensional system C. Our central result is the derivation of a Langevin equation to describe the dynamics of the collective degrees of freedom. Our preliminary analysis evidences that the proposed framework is able not only to describe the system stability, but also unstable processes, such as escape or collapse of the binary system. These processes crucially depend on the angular momentum, the quadrupole-orbit coupling among internal and collective degrees of freedom, as well as internal temperatures of each system.

Fusion systematics for weakly bound nuclei using neutron flow and collective degrees of freedom

A systematic analysis of the fusion cross sections around the Coulomb barrier energies with stable weakly bound ($^{6}$Li,$^{7}$Li,$^{9}$Be) and strongly bound $^{12}$C projectiles on various targets was performed by using neutron flow model and coupled channels approach. The analysis show that both the models are successful in explaining the near barrier fusion data. Further, it is also observed that the collective degrees of freedom as well as the neutron flow influence the near barrier fusion process involving weakly bound projectiles.

Compact hidden charm pentaquark states and QCD isomers

We make an exhaustive investigation on the pentaquark states $qqqc\overline{c}$ ($q=u$, $d$ and $s$) and discuss the effect of color structures in a multiquark color flux-tube model. We exhibit a novel picture of the structure and properties of the states ${P}_{c}$ and ${P}_{cs}$ observed by the LHCb Collaboration. We can describe the states as the compact pentaquark states in the model. The spin-parity of the group of ${P}_{c}(4312{)}^{+}$ and ${P}_{c}(4337{)}^{+}$ is ${\frac{1}{2}}^{\ensuremath{-}}$ while that of the group of ${P}_{c}(4380{)}^{+}$, ${P}_{c}(4440{)}^{+}$ and ${P}_{c}(4457{)}^{+}$ is ${\frac{3}{2}}^{\ensuremath{-}}$. Their structures are pentagon, diquark, pentagon, diquark, and octet, respectively. The members in each group can be analogically called QCD isomers because of their the same spin-parity and quark content but different color structures. The singlet ${P}_{cs}(4459{)}^{0}$ has pentagon structure and spin-parity of ${\frac{1}{2}}^{\ensuremath{-}}$. In addition, we also predict the ${P}_{cs}$, ${P}_{css}$ and ${P}_{csss}$ families in the model. The five-body confinement potential based on the color flux-tube picture, which is a collective degree of freedom and induces QCD isomer phenomenon, plays an important role in the formation of the compact states.

Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long times under reversible dynamics, determining the space of emergent collective degrees of freedom (the ballistic waves), showing that projection occurs onto them, and establishing their dynamics (the hydrodynamic equations). We make progress in these directions, focussing for simplicity on one-dimensional systems. Under a model-independent definition of the complete space of extensive conserved charges, we show that hydrodynamic projection occurs in Euler-scale two-point correlation functions. A fundamental ingredient is a property of relaxation: we establish ergodicity of correlation functions along almost every direction in space and time. We further show that to every extensive conserved charge with a local density is associated a local current and a continuity equation; and that Euler-scale two-point correlation functions of local conserved densities satisfy a hydrodynamic equation. The results are established rigorously within a general framework based on Hilbert spaces of observables. These spaces occur naturally in the C^* algebra description of statistical mechanics by the Gelfand–Naimark–Segal construction. Using Araki’s exponential clustering and the Lieb–Robinson bound, we show that the results hold, for instance, in every nonzero-temperature Gibbs state of short-range quantum spin chains. Many techniques we introduce are generalisable to higher dimensions. This provides a precise and universal theory for the emergence of ballistic waves at the Euler scale and how they propagate within homogeneous, stationary states.

Time-Lagged Independent Component Analysis of Random Walks and Protein Dynamics.

Time-lagged independent component analysis (tICA) is a widely used dimension reduction method for the analysis of molecular dynamics (MD) trajectories and has proven particularly useful for the construction of protein dynamics Markov models. It identifies those “slow” collective degrees of freedom onto which the projections of a given trajectory show maximal autocorrelation for a given lag time. Here we ask how much information on the actual protein dynamics and, in particular, the free energy landscape that governs these dynamics the tICA-projections of MD-trajectories contain, as opposed to noise due to the inherently stochastic nature of each trajectory. To answer this question, we have analyzed the tICA-projections of high dimensional random walks using a combination of analytical and numerical methods. We find that the projections resemble cosine functions and strongly depend on the lag time, exhibiting strikingly complex behavior. In particular, and contrary to previous studies of principal component projections, the projections change noncontinuously with increasing lag time. The tICA-projections of selected 1 μs protein trajectories and those of random walks are strikingly similar, particularly for larger proteins, suggesting that these trajectories contain only little information on the energy landscape that governs the actual protein dynamics. Further the tICA-projections of random walks show clusters very similar to those observed for the protein trajectories, suggesting that clusters in the tICA-projections of protein trajectories do not necessarily reflect local minima in the free energy landscape. We also conclude that, in addition to the previous finding that certain ensemble properties of nonconverged protein trajectories resemble those of random walks; this is also true for their time correlations.

Impact of complex many-body correlations on electron capture in thermally excited nuclei around Ni78

We link complex many-body correlations, which play a decisive role in the structural properties of atomic nuclei, to the electron capture occurring during star evolution. The recently developed finite-temperature response theory, taking into account the coupling between single-nucleon and collective degrees of freedom, is applied to spin-isospin transitions, which dominate the electron capture rates. Calculations are performed for $^{78}\mathrm{Ni}$ and for the surrounding even-even nuclei associated with a high-sensitivity region of the nuclear chart in the context of core-collapse supernova simulations. The obtained electron capture rates are compared to those of a simpler thermal quasiparticle random phase approximation (TQRPA), which is standardly used in such computations. The comparison indicates that correlations beyond TQRPA lead to significantly higher electron capture rates under the typical thermodynamical conditions.

A dynamical study of fusion hindrance with the Nakajima–Zwanzig projection method

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima–Zwanzig projection operator method is employed to eliminate fast variables and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin for the so-called “injection point $s$” introduced by Swiatecki et al. in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

Convergence of electric quadrupole rotational invariants from the nuclear shell model

Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of convergence will be addressed. Shell-model calculations performed in the $sd$- and $pf$-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined. It is found that on average, the inclusion of four intermediate states results in the leading-order invariant, $\left<Q^2\right>$, converging to within 10% of its true value and the triaxiality term, $\left<\cos{\left(3\delta\right)}\right>$, converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly. The convergence of quadrupole rotationally invariant sum rules was quantified in the $sd$- and $pf$-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Larger spaces, such as the rare-earth region, potentially offer faster convergence.

Analysis of two-nucleon transfer reactions in the Ne20+Cd116 system at 306 MeV

Background: Heavy-ion induced two-nucleon transfer reactions are powerful tools to reveal peculiar aspects of the atomic nucleus, such as pairing correlations, single-particle and collective degrees of freedom, and more. Also, these processes are in competition with the direct meson exchange in the double charge exchange reactions, which have recently attracted great interest due to their possible connection to neutrinoless double-beta decay. In this framework, the exploration of two-nucleon transfer reactions in the 20Ne+116Cd collision at energies above the Coulomb barrier is particularly relevant since the 116Cd nucleus is a candidate for the double-beta decay. Methods: We measured the excitation energy spectra and absolute cross sections for the two reactions using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. We performed direct coupled reaction channels and sequential distorted wave Born approximation calculations using the double folding S\~ao Paulo potential to model the initial and final state interactions. The spectroscopic amplitudes for two- and singleparticle transitions were derived by different nuclear structure approaches: microscopic large-scale shell model, interacting boson model-2 and quasiparticle random phase approximation. Results: The calculations are able to reproduce the experimental cross sections for both two-neutron and twoproton transfer reactions. The role of couplings with the inelastic channels are found to be important in the two-proton transfer case. A competition between the direct and the sequential process is found in the reaction mechanism. For the two-proton transfer case, the inclusion of the 1g7/2 and 2d5/2 orbitals in the model space is crucial.

SD-pair shell model: Vibrational and rotational limits in the interacting boson–fermion model for like-nucleon system

Typical features of the Bose–Fermi symmetries associated with [Formula: see text] and [Formula: see text] limits in the interacting boson model are described in the SD-pair shell model (SDPSM) framework for like-nucleon system. It is found that the limiting spectra associated with [Formula: see text] (vibrational) and [Formula: see text] (rotational) in the interacting boson–fermion model can be well reproduced in the SDPSM framework. It is shown that coupling of collective degree of freedom with the single-particle degree of freedom in the pairing interaction almost has no effect on the spectrum of odd-A system comparing to the adjacent even–even system, while the coupling of the collective degree of freedom with the single-particle degree of freedom in the quadrupole–quadrupole interaction results in the level splitting of several excited levels.

Electron Induced Massive Dynamics of Magnetic Domain Walls.

We study the dynamics of domain walls (DWs) in a metallic, ferromagnetic nanowire, focusing on inertial effects on the DW due to interaction with a conduction electron bath. We develop a Keldysh collective coordinate technique to describe the effect of conduction electrons on rigid magnetic structures. The effective Lagrangian and Langevin equations of motion for a DW are derived microscopically, including the full response kernel which is nonlocal in time. The DW dynamics is described by two collective degrees of freedom: position and tilt-angle. The coupled Langevin equations therefore involve two correlated noise sources, leading to a generalized fluctuation-dissipation theorem (FDT). The DW response kernel due to electrons contains two parts: one related to dissipation via FDT, and another reactive part. We prove that the latter term leads to a mass for both degrees of freedom, even though the intrinsic bare mass is zero. The electron-induced mass is present even in a clean system without pinning or specifically engineered potentials. The resulting equations of motion contain rich dynamical solutions and point toward a way to control domain wall motion in metals via the electronic system properties. We discuss two observable consequences of the mass, hysteresis in the DW dynamics and resonant response to ac current.

Underlying Structure of Collective Bands and Self-Organization in Quantum Systems.

The underlying structure of low-lying collective bands of atomic nuclei is discussed from a novel perspective on the interplay between single-particle and collective degrees of freedom, by utilizing state-of-the-art configuration interaction calculations on heavy nuclei. Besides the multipole components of the nucleon-nucleon interaction that drive collective modes forming those bands, the monopole component is shown to control the resistance against such modes. The calculated structure of ^{154}Sm corresponds to the coexistence between prolate and triaxial shapes, while that of ^{166}Er exhibits a deformed shape with a strong triaxial instability. Both findings differ from traditional views based on β/γ vibrations. The formation of collective bands is shown to be facilitated from a self-organization mechanism.

Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei with octupole correlations

[Background] Predictions of spectroscopic properties of low-lying states are critical for nuclear structure studies. Theoretical methods can be particularly involved for odd-mass nuclei because of the interplay between the unpaired nucleon and collective degrees of freedom. Only a few models have been developed for systems in which octupole collective degrees of freedom play a role. [Purpose] We aim to predict spectroscopic properties of odd-mass nuclei characterized by octupole shape deformation, employing a model that describes single-particle and collective degrees of freedom within the same microscopic framework. [Method] A microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed, which includes collective excitations of even-mass core nuclei and single-particle states of the odd nucleon, calculated using a quadrupole-octupole collective Hamiltonian combined with a constrained reflection-asymmetric relativistic Hartree-Bogoliubov model. [Results] Model predictions for low-energy excitation spectra and transition rates of odd-mass radium isotopes $^{223, 225, 227}$Ra are shown to be in good agreement with available data. [Conclusions] A microscopic CQC model based on covariant density functional theory has been developed for odd-mass nuclei characterized by both quadrupole and octupole shape deformations. Theoretical results reproduce data in odd-mass Ra isotopes and provide useful predictions for future studies of octupole correlations in nuclei and related phenomena.

Interplay of neutron transfer and collective degrees of freedom in the fusion dynamics of 16O +76Ge and 18O +74Ge reactions

This work examined the fusion dynamics of [Formula: see text] and [Formula: see text] reactions within the framework of the static Woods–Saxon potential model, the energy dependent Woods–Saxon potential (EDWSP) model and coupled channel formulation. The effects of inelastic surface excitations, static deformation of colliding pairs and /or neutron transfer channels on fusion process are investigated through the coupled channel method. The calculations based upon static Woods–Saxon potential in conjunction with one-dimensional Wong formula strongly under predict the fusion data of [Formula: see text] and [Formula: see text] reactions at sub-barrier energies. However, such discrepancies are removed if one uses couplings to nuclear structure degrees of freedom of reacting nuclei. The coupled channel calculations obtained by considering the vibrational nature of the colliding nuclei fairly reproduce the fusion data of [Formula: see text] reactions. For this reaction, the neutron transfer channels, which are expected to influence strongly the fusion yields at below barrier energies, in reality contribute very weakly to fusion process. While in case of [Formula: see text] reaction, the consideration of vibrational couplings as well as the rotational couplings for target provides a reasonable explanation to the fusion cross-section data at near and above barrier energies. In distinction, the energy dependence in the nucleus–nucleus potential causes barrier modulation effects and subsequently modifies the barrier profile of the interaction barrier in such a way that the effective fusion barrier between the colliding pair reduces. This ultimately brings larger fusion cross-sections over the outcomes of one-dimensional barrier penetration model and the EDWSP model based calculations appreciably explained the fusion dynamics of chosen reaction at energy spanning around the Coulomb barrier. Both models (EDWSP and coupled channel model) lead to barrier lowering effects and modeled quantum tunneling in different way, henceforth, adequately explore the fusion dynamics of the studied reactions in near and above barrier energy regions.

Structure of Fe 70: Single-particle and collective degrees of freedom

Structure of Fe 70: Single-particle and collective degrees of freedom

Characterization of the shape-staggering effect in mercury nuclei

In rare cases, the removal of a single proton (Z) or neutron (N) from an atomic nucleus leads to a dramatic shape change. These instances are crucial for understanding the components of the nuclear interactions that drive deformation. The mercury isotopes (Z = 80) are a striking example1,2: their close neighbours, the lead isotopes (Z = 82), are spherical and steadily shrink with decreasing N. The even-mass (A = N + Z) mercury isotopes follow this trend. The odd-mass mercury isotopes 181,183,185Hg, however, exhibit noticeably larger charge radii. Due to the experimental difficulties of probing extremely neutron-deficient systems, and the computational complexity of modelling such heavy nuclides, the microscopic origin of this unique shape staggering has remained unclear. Here, by applying resonance ionization spectroscopy, mass spectrometry and nuclear spectroscopy as far as 177Hg, we determine 181Hg as the shape-staggering endpoint. By combining our experimental measurements with Monte Carlo shell model calculations, we conclude that this phenomenon results from the interplay between monopole and quadrupole interactions driving a quantum phase transition, for which we identify the participating orbitals. Although shape staggering in the mercury isotopes is a unique and localized feature in the nuclear chart, it nicely illustrates the concurrence of single-particle and collective degrees of freedom at play in atomic nuclei.