Angular Momentum Cutoff Research Articles

Gravitational bremsstrahlung in plasmas and clusters

We study the gravitational bremsstrahlung owing to collisions mediated by a 1/r potential. We combine classical and first order Born approximation results in order to construct an approximate gravitational “Gaunt factor” for the total emitted energy. We also obtain the cross section with an angular momentum cutoff and hence the cross section for emission via close hyperbolic encounters in a gravitating cluster. These effects are the dominant source of very high frequency gravitational noise in the Solar System. The total gravitational wave power of the Sun is 76±20 MW. Published by the American Physical Society 2024

Qubitization strategies for bosonic field theories

Quantum simulations of bosonic field theories require a truncation in field space to map the theory onto finite quantum registers. Ideally, the truncated theory preserves the symmetries of the original model and has a critical point in the same universality class. In this paper, we explore two different truncations that preserve the symmetries of the 1+1-dimensional $O(3)$ non-linear $\sigma$-model - one that truncates the Hilbert space for the unit sphere by setting an angular momentum cutoff and a fuzzy sphere truncation inspired by non-commutative geometry. We compare the spectrum of the truncated theories in a finite box with the full theory. We use open boundary conditions, a novel method that improves on the correlation lengths accessible in our calculations. We provide evidence that the angular-momentum truncation fails to reproduce the $\sigma$-model and that the anti-ferromagnetic fuzzy model agrees with the full theory.

Deformed relativistic Hartree-Bogoliubov theory in continuum with a point-coupling functional. II. Examples of odd Nd isotopes

Background: One fascinating frontier in nuclear physics is the study of exotic nuclei. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), which simultaneously includes the nuclear superfluidity, deformation, and continuum effects, can provide proper descriptions for both stable and exotic nuclei. In a previous work [Zhang et al., Phys. Rev. C 102, 024314 (2020)], the DRHBc theory based on the point-coupling density functionals was developed and the DRHBc calculation, previously accessible only for light nuclei, was extended for all even-even nuclei in the nuclear chart. The ground-state properties for the even-even nuclei with 8≤Z≤120 from the DRHBc calculations have been summarized [Zhang et al., At. Data Nucl. Data Tables 144, 101488 (2022)]. Purpose: The aim of this paper is to extend the point-coupling DRHBc theory to odd-A and odd-odd nuclei and examine its applicability by taking odd-A Nd isotopes as examples. Method: In the DRHBc theory, the densities and potentials with axial deformation are expanded in terms of Legendre polynomials, and the relativistic Hartree-Bogoliubov equations are solved in a Dirac Woods-Saxon basis to include the continuum effects. For an odd-A or odd-odd nucleus, the blocking effect of the unpaired nucleon(s) is taken into account with the equal filling approximation. To determine its ground state, an automatic blocking procedure is adopted, in which the orbital with the lowest quasiparticle energy is blocked during the iteration. This procedure is justified by comparing with the results from the orbital-fixed blocking calculations, in which the blocked orbital near the Fermi surface is fixed during the iteration. The ground states for both light and heavy nuclei can be provided by the automatic blocking procedure as the orbital-fixed blocking procedure, but with considerably reduced computational cost. Results: The numerical details for even-even nuclei, including the convergence on the energy cutoff, angular momentum cutoff, and Legendre expansion, are found to be valid for odd-A and odd-odd nuclei as well. The ground-state properties of odd-A Nd isotopes are calculated with the density functional PC-PK1. The calculated physical observables, such as binding energies, two-neutron and one-neutron separation energies, and charge radii, are in good agreement with the available experimental data for the whole Nd isotopic chain. Conclusions: The point-coupling DRHBc theory is extended to odd-A and odd-odd nuclei by including the blocking effect. Taking Nd isotopes including both even-even and odd-A ones as examples, the calculated ground-state properties with PC-PK1 are in good agreement with the available experimental data. This paper paves the way to construct the DRHBc mass table including all even-even, odd-A, and odd-odd nuclei in the nuclear chart.6 MoreReceived 4 May 2022Accepted 12 July 2022DOI:https://doi.org/10.1103/PhysRevC.106.014316©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBinding energy & massesEnergy levels & level densitiesNuclear bindingNuclear charge distributionNuclear many-body theoryNuclear spin & parityNuclear structure & decaysNucleon distributionNuclear Physics

Bottomonium production in heavy-ion collisions using quantum trajectories: Differential observables and momentum anisotropy

We report predictions for the suppression and elliptic flow of the $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ as a function of centrality and transverse momentum in ultra-relativistic heavy-ion collisions. We obtain our predictions by numerically solving a Lindblad equation for the evolution of the heavy-quarkonium reduced density matrix derived using potential nonrelativistic QCD and the formalism of open quantum systems. To numerically solve the Lindblad equation, we make use of a stochastic unraveling called the quantum trajectories algorithm. This unraveling allows us to solve the Lindblad evolution equation efficiently on large lattices with no angular momentum cutoff. The resulting evolution describes the full 3D quantum and non-abelian evolution of the reduced density matrix for bottomonium states. We expand upon our previous work by treating differential observables and elliptic flow; this is made possible by a newly implemented Monte-Carlo sampling of physical trajectories. Our final results are compared to experimental data collected in $\sqrt{s_{NN}} = 5.02$ TeV Pb-Pb collisions by the ALICE, ATLAS, and CMS collaborations.

Analysis of Fusion Cross Sections in the 9Be Projectile Breakup on Different Target Nuclei

We present a theoretical study of total fusion (TF), complete fusion (CF), and incomplete fusion (ICF) cross sections in the breakup of 9Be (described as n −8Be) projectile on 124Sn, 144Sm and 208Pb target nuclei. We use the continuum discretized coupled-channel formalism together with a sum-rule model, by extending an approach outlined in Mukeru et al. (Nucl. Phys. A 996:121700, 2020) to another weakly bound projectile in different targets. The applicability of the model to incident energies below and around the Coulomb barrier is verified, being confirmed for all three reactions an empirical energy-dependent cutoff angular momentum expression. We show that the TF and ICF cross sections are strongly dependent on the projectile binding energy eb, whereas the CF is weakly affected by that. Despite this weak dependence, the CF contribution to the TF cross section becomes more suppressed by decreasing eb. The dependence of the ICF probability on the breakup threshold is also highlighted.

Theoretical analysis of 8Li + 208Pb reaction and the critical angular momentum for complete fusion

In a theoretical approach, the complete and incomplete fusions are investigated by considering the Li8+208Pb reaction, within a three-body model where the projectile is described as n−7Li with binding energy εb. By decreasing εb from its known experimental value, the complete fusion is shown to have no meaningful dependence on such variations, whereas the incomplete fusion strongly depends on that. The complete and incomplete fusion cross sections are calculated by using a combination of both continuum-discretized coupled-channel and sum-rule models. To this end, an incident-energy dependent cut-off angular momentum Lc is first obtained by using the available complete fusion experimental data, within an approach which is extended to model results obtained for other incident-energies. An approximated fitted expression linking Lc to the well-known critical value Lcrit derived by Wilczyński (1973) [28] suggests that the sum-rule model could be generalized to energies around and below the Coulomb barrier.

Quantifying entanglement of rotor chains using basis truncation: Application to dipolar endofullerene peapods.

We propose a variational approach for the calculation of the quantum entanglement entropy of assemblies of rotating dipolar molecules. A basis truncation scheme based on the total angular momentum quantum number is proposed. The method is tested on hydrogen fluoride (HF) molecules confined in C60 fullerene cages themselves trapped in a nanotube to form a carbon peapod. The rotational degrees of freedom of the HF molecules and dipolar interactions between neighboring molecules are considered in our model Hamiltonian. Both screened and unscreened dipoles are simulated and results are obtained for the ground state and one excited state that is expected to be accessible via a far-infrared collective excitation. The effect of basis truncation on energetic and entanglement properties is examined and discussed in terms of size extensivity. It is empirically found that for unscreened dipoles, a total angular momentum cutoff that increases linearly with the number of rotors is required in order to obtain proper system size scaling of the chemical potential and entanglement entropy. Recent experiments [A. Krachmalnicoff et al., Nat. Chem. 8, 953 (2016)] suggest substantial screening of the HF dipole moment, so much smaller basis sets are required to obtain converged results in this realistic case. Static correlation functions are also computed and are shown to decay much quicker in the case of screened dipoles. Our variational results are also used to test the accuracy of perturbative and pairwise ansatz treatments.

Quantum design using a multiple internal reflections method in a study of fusion processes in the capture of alpha-particles by nuclei

A high precision method to determine fusion in the capture of α-particles by nuclei is presented. For α-capture by 40Ca and 44Ca, such an approach gives (1) the parameters of the α–nucleus potential and (2) fusion probabilities. This method found new parametrization and fusion probabilities and decreased the error by 41.72 times for α+Ca40 and 34.06 times for α+Ca44 in a description of experimental data in comparison with existing results. We show that the sharp angular momentum cutoff proposed by Glas and Mosel is a rough approximation, Wong's formula and the Hill–Wheeler approach determine the penetrability of the barrier without a correct consideration of the barrier shape, and the WKB approach gives reduced fusion probabilities. Based on our fusion probability formula, we explain the difference between experimental cross-sections for α+Ca40 and α+Ca44, which is connected with the theory of coexistence of the spherical and deformed shapes in the ground state for nuclei near the neutron magic shell N=20. To provide deeper insight into the physics of nuclei with the new magic number N=26, the cross-section for α+Ca46 is predicted for future experimental tests. The role of nuclear deformations in calculations of the fusion probabilities is analyzed.

Projection potentials and angular momentum convergence of total energies in the full-potential Korringa–Kohn–Rostoker method

Although the full-potential Korringa–Kohn–Rostoker Green function method yields accurate results for many physical properties, the convergence of calculated total energies with respect to the angular momentum cutoff is usually considered to be less satisfactory. This is surprising because accurate single-particle energies are expected if they are calculated by Lloyd’s formula and because accurate densities and hence accurate double-counting energies should result from the total energy variational principle. It is shown how the concept of projection potentials can be used as a tool to analyse the convergence behaviour. The key factor blocking fast convergence is identified and it is illustrated how total energies can be improved with only a modest increase of computing time.

Universality of the holographic angular momentum cutoff

The AdS/CFT dual description of a peripheral heavy ion collision involves an asymptotically AdS rotating black hole. The explicitly known black holes of this kind, with planar event horizon topology [the “KMV0” spacetimes], have been shown to be unstable when string-theoretic effects are taken into account. It has been argued that this implies a “holographic” angular momentum cutoff for peripheral collisions at very high energies. However, the KMV0 black hole corresponds to a specific velocity distribution in the aftermath of a peripheral collision, and this distribution is not realistic at all points of the interaction zone. It could therefore be argued that the angular momentum cutoff is an artefact of this particular choice of bulk geometry. We demonstrate that, on the contrary, a quark–gluon plasma with any physically reasonable internal velocity distribution corresponds to a black hole which is still unstable, in the same way as the KMV0 spacetime. The angular momentum cutoff is therefore a universal prediction of the holographic description of these collisions.

Fragile black holes and an angular momentum cutoff in peripheral heavy ion collisions

In collisions of heavy ions at extremely high energies, it is possible for a significant quantity of angular momentum to be deposited into the Quark–Gluon Plasma which is thought to be produced. We develop a simple geometric model of such a system, and show that it is dual, in the AdS/CFT sense, to a rotating AdS black hole with a topologically planar event horizon. However, when this black hole is embedded in string theory, it proves to be unstable, for all non-zero angular momenta, to a certain non-perturbative effect: the familiar planar black hole, as used in most AdS/CFT analyses of QGP physics, is “fragile”. The upshot is that the AdS/CFT duality apparently predicts that the QGP should always become unstable when it is produced in peripheral collisions. However, we argue that holography indicates that relatively low angular momenta delay the development of the instability, so that in practice it may be observable only for peripheral collisions involving favorable impact parameters, generating extremely large angular momenta. In principle, the result may be holographic prediction of a cutoff for the observable angular momenta of the QGP, or perhaps of an analogous phenomenon in condensed matter physics.

On Blowup for Time-Dependent Generalized Hartree–Fock Equations

We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree–Fock and Hartree–Fock–Bogoliubov-type equations, which describe the evolution of attractive fermionic systems (e.g. white dwarfs). Our main results are twofold: first, we extend the recent blowup result of Hainzl and Schlein (Comm. Math. Phys. 287:705–714, 2009) to Hartree–Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree–Fock–Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree–Fock–Bogoliubov theory.

Unusual thermodynamics on the fuzzy 2-sphere

Higher spin Dirac operators on both the continuum sphere($S^2$) and its fuzzy analog($S^2_F$) come paired with anticommuting chirality operators. A consequence of this is seen in the fermion-like spectrum of these operators which is especially true even for the case of integer-spin Dirac operators. Motivated by this feature of the spectrum of a spin 1 Dirac operator on $S_F^2$, we assume the spin 1 particles obey Fermi-Dirac statistics. This choice is inspite of the lack of a well defined spin-statistics relation on a compact surface such as $S^2$. The specific heats are computed in the cases of the spin $\frac{1}{2}$ and spin 1 Dirac operators. Remarkably the specific heat for a system of spin $\frac{1}{2}$ particles is more than that of the spin 1 case, though the number of degrees of freedom is more in the case of spin 1 particles. The reason for this is inferred through a study of the spectrums of the Dirac operators in both the cases. The zero modes of the spin 1 Dirac operator is studied as a function of the cut-off angular momentum $L$ and is found to follow a simple power law. This number is such that the number of states with positive energy for the spin 1 and spin $\frac{1}{2}$ system become comparable. Remarks are made about the spectrums of higher spin Dirac operators as well through a study of their zero-modes and the variation of their spectrum with degeneracy. The mean energy as a function of temperature is studied in both the spin $\frac{1}{2}$ and spin 1 cases. They are found to deviate from the standard ideal gas law in 2+1 dimensions.

Fast way to compute functional determinants of radially symmetric partial differential operators in general dimensions

Recently the partial-wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive explicitly radial-WKB series in the angular momentum cutoff for $d=2$, 3, 4, and 5 ($d$ is the space-time dimension), which has uniform validity irrespectively of any specific values assumed for other parameters. Utilizing this series, precision evaluation of the renormalized functional determinant is possible with a relatively small number of low partial-wave contributions determined separately. We illustrate the power of this scheme in a numerically exact evaluation of the prefactor (expressed as a functional determinant) in the case of the false vacuum decay of 4D scalar field theory.

Effective actions of the IIB matrix model onS3

${S}^{3}$ is a simple principle bundle which is locally ${S}^{2}\ifmmode\times\else\texttimes\fi{}{S}^{1}$. It has been shown that such a space can be constructed in terms of matrix models. It has also been shown that such a space can be realized by a generalized compactification procedure in the ${S}^{1}$ direction. We investigate the effective action of supersymmetric gauge theory on ${S}^{3}$ with an angular momentum cutoff and that of a matrix model compactification. Both cases can be realized in a deformed IIB matrix model with a Myers term. We find that the highly divergent contributions at the tree and 1-loop level are sensitive to the UV cutoff. However, the 2-loop level contributions are universal since they are only logarithmically divergent. We expect that the higher loop contributions are insensitive to the UV cutoff since 3-dimensional gauge theory is superrenormalizable.

Functional determinants for radial operators

We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of Gel'fand and Yaglom to higher dimensions. We use the zeta function formalism, and the results agree with what one would obtain using the angular momentum cutoff method based on radial WKB. The final expression is numerically equal to an alternative expression derived in a Feynman diagrammatic approach, but is considerably simpler.

Connecting the chiral and heavy quark limits: full mass dependence of fermion determinant in an instanton background

This talk reports work done in collaboration with Jin Hur, Choonkyu Lee and Hyunsoo Min concerning the computation of the precise mass dependence of the fermion determinant for quarks in the presence of an instanton background. The result interpolates smoothly between the previously known chiral and heavy quark limits of extreme small and large mass. The computational method makes use of the fact that the single instanton background has radial symmetry, so that the computation can be reduced to a sum over partial waves of logarithms of radial determinants, each of which can be computed numerically in an efficient manner using a theorem of Gelfand and Yaglom. The bare sum over partial waves is divergent and must be regulated and renormalized. We use the angular momentum cutoff regularization and renormalization scheme. Our results provide an extension of the Gelfand-Yaglom result to higher dimensional separable differential operators. I also comment on the application of this approach to a wide variety of fluctuation determinant computations in quantum field theory.

Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a self-interacting scalar field theory modeling the process of nucleation in four-dimensional space-time. This technique does not rely on the thin-wall approximation. The method is based on the Gelfand-Yaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvili, but we implement the regularization and renormalization in a different manner, and compare directly with analytic computations made in the thin-wall approximation. We also derive a simple new formula for the zero mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behavior of the classical bounce solution.

Tetrahedrally invariant discrete variable representation basis on the sphere

This paper explores the difficulties of constructing multidimensional discrete variable representation (DVR) basis sets and the strategies that can be used to overcome them. A parameter count shows that the conditions on a DVR basis set cannot be satisfied on most spaces of wave functions. One-dimensional, orthogonal polynomials are an exception, but the Ylm’s on the sphere only go 3/4 of the way, in a certain sense, toward supplying enough parameters to satisfy the DVR conditions. It is shown that DVR sets involving rotationally invariant subspaces of wave functions on the sphere (consisting of complete subshells only) exist only for small values of the angular momentum cutoff. However, an exploration of DVR sets invariant under subgroups of the full rotation group leads to the discovery of a 12-point DVR set that is invariant under the tetrahedral group, whose grid points are the vertices of an icosahedron.

Casimir Force on a Dielectric Cylinder

The Casimir surface force density on a compact material cylinder of radius a is calculated, at zero temperature. A Green function approach is followed. The general theory is formulated so as to hold for arbitrary permittivities ϵ(ω) and permeabilities μ(ω), whereas when it comes to explicit calculations the condition ϵ(ω) μ(ω) = 1 is assumed to hold. A simple dispersion relation is chosen, implying a high frequency cutoff ω 0. The theory yet diverges, at high angular momenta. Divergences of this sort usually appear whenever there are curved boundaries present. On physical grounds an angular momentum cutoff m 0 can be introduced, being of order ω 0 a. A semi-quantitative calculation of the force thereby becomes possible. The calculated force is attractive.