Macroscopically Degenerate Exactly Solvable Point in the Spin- 1 / 2 Kagome Quantum Antiferromagnet
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Changlani, Hitesh J.↗
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Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides
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Carnemolla, Enrico Giuseppe↗
SINGLE-DEGENERATE TYPE Ia SUPERNOVAE ARE PREFERENTIALLY OVERLUMINOUS
Recent observational and theoretical progress has favored merging and helium-accreting sub-Chandrasekhar mass white dwarfs (WDs) in the double-degenerate and the double-detonation channels, respectively, as the most promising progenitors of normal Type Ia supernovae (SNe Ia). Thus the fate of rapidly accreting Chandrasekhar mass WDs in the single-degenerate channel remains more mysterious then ever. In this paper, we clarify the nature of ignition in Chandrasekhar-mass single-degenerate SNe Ia by analytically deriving the existence of a characteristic length scale which establishes a transition from central ignitions to buoyancy-driven ignitions. Using this criterion, combined with data from three-dimensional simulations of convection and ignition, we demonstrate that the overwhelming majority of ignition events within Chandrasekhar-mass WDs in the single-degenerate channel are buoyancy-driven, and consequently lack a vigorous deflagration phase. We thus infer that single-degenerate SNe Ia are generally expected to lead to overluminous 1991T-like SNe Ia events. We establish that the rates predicted from both the population of supersoft X-ray sources (SSSs) and binary population synthesis models of the single-degenerate channel are broadly consistent with the observed rates of overluminous SNe Ia, and suggest that the population of SSSs are the dominant stellar progenitors of SNe 1991T-like events. We further demonstrate that the single-degenerate channel contribution to the normal and failed 2002cx-like rates is not likely to exceed 1% of the total SNe Ia rate. We conclude with a range of observational tests of overluminous SNe Ia which will either support or strongly constrain the single-degenerate scenario.
79 ASTRONOMY AND ASTROPHYSICS↗
Development of Multistep and Degenerate Variational Integrators for Applications in Plasma Physics
Geometric integrators yield high-fidelity numerical results by retaining conservation laws in the time advance. A particularly powerful class of geometric integrators is symplectic integrators, which are widely used in orbital mechanics and accelerator physics. An important application presently lacking symplectic integrators is the guiding center motion of magnetized particles represented by non-canonical coordinates. Because guiding center trajectories are foundational to many simulations of magnetically confined plasmas, geometric guiding center algorithms have high potential for impact. The motivation is compounded by the need to simulate long-pulse fusion devices, including ITER, and opportunities in high performance computing, including the use of petascale resources and beyond. This dissertation uses a systematic procedure for constructing geometric integrators - known as variational integration - to deliver new algorithms for guiding center trajectories and other plasma-relevant dynamical systems. These variational integrators are non-trivial because the Lagrangians of interest are degenerate - the Euler-Lagrange equations are first-order differential equations and the Legendre transform is not invertible. The first contribution of this dissertation is that variational integrators for degenerate Lagrangian systems are typically multistep methods. Multistep methods admit parasitic mode instabilities that can ruin the numerical results. These instabilities motivate the second major contribution: degenerate variational integrators. By replicating the degeneracy of the continuous system, degenerate variational integrators avoid parasitic mode instabilities. The new methods are therefore robust geometric integrators for degenerate Lagrangian systems. These developments in variational integration theory culminate in one-step degenerate variational integrators for non-canonical magnetic field line flow and guiding center dynamics. The guiding center integrator assumes coordinates such that one component of the magnetic field is zero; it is shown how to construct such coordinates for nested magnetic surface configurations. Additionally, collisional drag effects are incorporated in the variational guiding center algorithm for the first time, allowing simulation of energetic particle thermalization. Advantages relative to existing canonical-symplectic and non-geometric algorithms are numerically demonstrated. All algorithms have been implemented as part of a modern, parallel, ODE-solving library, suitable for use in high-performance simulations.
Guiding Center↗
Differential expression of extracellular-signal-regulated kinase 5 (ERK5) in normal and degenerated human nucleus pulposus tissues and cells
Highlights: • ERK5 involved in NP cells. • ERK5 involved in NP tissue. • It was important modulator. - Abstract: Extracellular-signal-regulated kinase 5 (ERK5) is a member of the mitogen-activated protein kinase (MAPK) family and regulates a wide variety of cellular processes such as proliferation, differentiation, necrosis, apoptosis and degeneration. However, the expression of ERK5 and its role in degenerated human nucleus pulposus (NP) is hitherto unknown. In this study, we observed the differential expression of ERK5 in normal and degenerated human nucleus pulposus tissues by using immunohistochemical staining and Western blot. Treatment of NP cells with Pro-inflammatory cytokine, TNF-α decreased ERK5 gene expression as well as NP marker gene expression; including the type II collagen and aggrecan. Suppression of ERK5 gene expression in NP cells by ERK5 siRNA resulted in decreased gene expression of type II collagen and aggrecan. Furthermore, inhibition of ERK5 activation by BIX02188 (5 μM) decreased the gene expression of type II collagen and aggrecan in NP cells. Our results document the expression of ERK5 in degenerated nucleus pulposus tissues, and suggest a potential involvement of ERK5 in human degenerated nucleus pulposus.
60 APPLIED LIFE SCIENCES↗
Anomalous skin effects in a weakly magnetized degenerate electron plasma
Fully relativistic analysis of anomalous skin effects for parallel propagating waves in a weakly magnetized degenerate electron plasma is presented and a graphical comparison is made with the results obtained using relativistic Maxwellian distribution function [G. Abbas, M. F. Bashir, and G. Murtaza, Phys. Plasmas 18, 102115 (2011)]. It is found that the penetration depth for R- and L-waves for degenerate case is qualitatively small in comparison with the Maxwellian plasma case. The quantitative reduction due to weak magnetic field in the skin depth in R-wave for degenerate plasma is large as compared to the non-degenerate one. By ignoring the ambient magnetic field, previous results for degenerate field free case are salvaged [A. F. Alexandrov, A. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Springer-Verlag, Berlin/Heidelberg, 1984), p. 90].
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Arbitrary amplitude electrostatic wave propagation in a magnetized dense plasma containing helium ions and degenerate electrons
The obliquely propagating arbitrary amplitude electrostatic wave is studied in a dense magnetized plasma having singly and doubly charged helium ions with nonrelativistic and ultrarelativistic degenerate electrons pressures. The Fermi temperature for ultrarelativistic degenerate electrons described by N. M. Vernet [(Cambridge University Press, Cambridge, 2007), p. 57] is used to define ion acoustic speed in ultra-dense plasmas. The pseudo-potential approach is used to solve the fully nonlinear set of dynamic equations for obliquely propagating electrostatic waves in a dense magnetized plasma containing helium ions. The upper and lower Mach number ranges for the existence of electrostatic solitons are found which depends on the obliqueness of the wave propagation with respect to applied magnetic field and charge number of the helium ions. It is found that only compressive (hump) soliton structures are formed in all the cases and only subsonic solitons are formed for a singly charged helium ions plasma case with nonrelativistic degenerate electrons. Both subsonic and supersonic soliton hump structures are formed for doubly charged helium ions with nonrelativistic degenerate electrons and ultrarelativistic degenerate electrons plasma case containing singly as well as doubly charged helium ions. The effect of propagation direction on the soliton amplitude and width of the electrostatic waves is also presented. The numerical plots are also shown for illustration using dense plasma parameters of a compact star (white dwarf) from literature.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The involvement of regulated in development and DNA damage response 1 (REDD1) in the pathogenesis of intervertebral disc degeneration
Regulated in development and DNA damage response 1 (REDD1) is an evolutionarily conserved, ubiquitous protein that responds to various cell stresses. Studies have proved REDD1 is involved in many diseases, such as osteoarthritis and cancer. The present study aimed to investigate the potential role of REDD1 in the pathogenesis of intervertebral disc degeneration (IDD). Analysis of clinical tissue samples showed REDD1 expression was up-regulated during IDD and was correlated with the grade of disc degeneration. Overexpression of REDD1 in normal human nucleus pulposus (NP) cells resulted in extracellular matrix (ECM) degeneration. Further, we investigated the function of REDD1 using a serum deprivation-induced IDD vitro model and found that REDD1 was up-regulated in a temporal manner. However, hypoxia abolished this increase through down-regulation of NF-κB. Knockdown of REDD1 or NF-κB by si-RNA significantly rescued ECM from degeneration both in normoxia and hypoxia. In addition, NF-κB/REDD1 mediated the protection of hypoxia from serum deprivation-induced apoptosis and autophagy in NP cells. These results suggest that REDD1 might play a pivotal role in IDD pathogenesis, thereby potentially providing a new therapeutic target for IDD treatment.
60 APPLIED LIFE SCIENCES↗
Degenerate mixing of plasma waves on cold, magnetized single-species plasmas
In the cold-fluid dispersion relation {omega}={omega}{sub p}/[1+(k{sub perpendicular}/k{sub z}){sup 2}]{sup 1/2} for Trivelpiece-Gould waves on an infinitely long magnetized plasma cylinder, the transverse and axial wavenumbers appear only in the combination k{sub perpendicular}/k{sub z}. As a result, for any frequency {omega}<{omega}{sub p}, there are infinitely many degenerate waves, all having the same value of k{sub perpendicular}/k{sub z}. On a cold finite-length plasma column, these degenerate waves reflect into one another at the ends; thus, each standing-wave normal mode of the bounded plasma is a mixture of many degenerate waves, not a single standing wave as is often assumed. A striking feature of the many-wave modes is that the short-wavelength waves often add constructively along resonance cones given by dz/dr={+-}({omega}{sub p}{sup 2}/{omega}{sup 2}-1){sup 1/2}. Also, the presence of short wavelengths in the admixture for a predominantly long-wavelength mode enhances the viscous damping beyond what the single-wave approximation would predict. Here, numerical solutions are obtained for modes of a cylindrical plasma column with rounded ends. Exploiting the fact that the modes of a spheroidal plasma are known analytically (the Dubin modes), a perturbation analysis is used to investigate the mixing of low-order, nearly degenerate Dubin modes caused by small deformations of a plasma spheroid.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Coupled modes in magnetized dense plasma with relativistic-degenerate electrons
Low frequency electrostatic and electromagnetic waves are investigated in ultra-dense quantum magnetoplasma with relativistic-degenerate electron and non-degenerate ion fluids. The dispersion relation is derived for mobile as well as immobile ions by employing hydrodynamic equations for such plasma under the influence of electromagnetic forces and pressure gradient of relativistic-degenerate Fermi gas of electrons. The result shows the coexistence of shear Alfven and ion modes with relativistically modified dispersive properties. The relevance of results to the dense degenerate plasmas of astrophysical origin (for instance, white dwarf stars) is pointed out with brief discussion on ultra-relativistic and non-relativistic limits.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Effect of trapping in a degenerate plasma in the presence of a quantizing magnetic field
Effect of trapping as a microscopic phenomenon in a degenerate plasma is investigated in the presence of a quantizing magnetic field. The plasma comprises degenerate electrons and non-degenerate ions. The presence of the quantizing magnetic field is discussed briefly and the effect of trapping is investigated by using the Fermi-Dirac distribution function. The linear dispersion relation for ion acoustic wave is derived in the presence of the quantizing magnetic field and its influence on the propagation characteristics of the linear ion acoustic wave is discussed. Subsequently, fully nonlinear equations for ion acoustic waves are used to obtain the Sagdeev potential and the investigation of solitary structures. The formation of solitary structures is studied both for fully and partially degenerate plasmas in the presence of a quantizing magnetic field. Both compressive and rarefactive solitons are obtained for different conditions of temperature and magnetic field.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Three dimensional electrostatic solitary waves in a dense magnetoplasma with relativistically degenerate electrons
In this paper, small but finite amplitude electrostatic solitary waves in a relativistic degenerate magnetoplasma, consisting of relativistically degenerate electrons and non-degenerate cold ions, are investigated. The Zakharov-Kuznetsov equation is derived employing the reductive perturbation technique and its solitary wave solution is analyzed. It is shown that only compressive electrostatic solitary structures can propagate in such a degenerate plasma system. The effects of plasma number density, ion cyclotron frequency, and direction cosines on the profiles of ion acoustic solitary waves are investigated and discussed at length. The relevance of the present investigation vis-a-vis pulsating white dwarfs is also pointed out.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonlinear electrostatic excitations in magnetized dense plasmas with nonrelativistic and ultra-relativistic degenerate electrons
Linear and nonlinear electrostatic waves in magnetized dense electron-ion plasmas are studied with nonrelativistic and ultra-relativistic degenerate and singly, doubly charged helium (He{sup +}, He{sup ++}) and hydrogen (H{sup +}) ions, respectively. The dispersion relation of electrostatic waves in magnetized dense plasmas is obtained under both the energy limits of degenerate electrons. Using reductive perturbation method, the Zakharov-Kuznetsov equation for nonlinear propagation of electrostatic solitons in magnetized dense plasmas is derived for both nonrelativistic and ultra-relativistic degenerate electrons. It is found that variations in plasma density, magnetic field intensity, different mass, and charge number of ions play significant role in the formation of electrostatic solitons in magnetized dense plasmas. The numerical plots are also presented for illustration using the parameters of dense astrophysical plasma situations such as white dwarfs and neutron stars exist in the literature. The present investigation is important for understanding the electrostatic waves propagation in the outer periphery of compact stars which mostly consists of hydrogen and helium ions with degenerate electrons in dense magnetized plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Analytical model of electron transport in polycrystalline, degenerately doped ZnO films
An analytical description of the charge carrier transport, valid for non-degenerated and degenerated semiconductors, was developed, critically reviewed, and fitted to the temperature-dependent Hall mobility data of magnetron sputtered, degenerately doped ZnO:Al films. Our extended model for grain boundary scattering in semiconductors of arbitrary degeneracy is based on previous models from literature and suitable to describe the Hall mobility of the carriers as a function of the free carrier concentration and the temperature at the same time. It is mathematically simple enough for a fast fit procedure, which is not possible with most of the previous models. Applying a combined transport model consisting of ionized impurity scattering, phonon scattering, and grain boundary scattering in degenerate semiconductors, we were able to determine the trap density at the grain boundaries Nₜ ≈ 3×10¹³ to 5×10¹³cm⁻² and the deformation potential E{sub ac} in the range of 5 eV to 9 eV depending on the details of the transport model.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads
In previous works, we have introduced an alternative perturbation scheme to find approximate solutions of the spectral problem for the rotation-vibration molecular Hamiltonian. An important feature of our approach is that the zero order Hamiltonian is the direct product of a purely vibrational Hamiltonian with the identity on the rotational degrees of freedom. The convergence of our method for the methane vibrational ground state was very satisfactory and our predictions were quantitative. In the present article, we provide further details on the implementation of the method in the degenerate and quasi-degenerate cases. The quasi-degenerate version of the method is tested on excited polyads of methane, and the results are assessed with respect to a variational treatment. The optimal choice of the size of quasi-degenerate spaces is determined by a trade-off between speed of convergence of the perturbation series and the computational effort to obtain the effective super-Hamiltonian.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
TIME-SERIES SPECTROSCOPY OF TWO CANDIDATE DOUBLE DEGENERATES IN THE OPEN CLUSTER NGC 6633
SNe Ia are heavily used tools in precision cosmology, yet we still are not certain what the progenitor systems are. General plausibility arguments suggest there is potential for identifying double degenerate SN Ia progenitors in intermediate-age open star clusters. We present time-resolved high-resolution spectroscopy of two white dwarfs (WDs) in the field of the open cluster NGC 6633 that had previously been identified as candidate double degenerates in the cluster. However, three hours of continuous observations of each candidate failed to detect any significant radial velocity variations at the ≳10 km s{sup −1} level, making it highly unlikely that either WD is a double degenerate that will merge within a Hubble Time. The WD LAWDS NGC 6633 4 has a radial velocity inconsistent with cluster membership at the 2.5σ level, while the radial velocity of LAWDS NGC 6633 7 is consistent with cluster membership. We conservatively conclude that LAWDS 7 is a viable massive double degenerate candidate, though unlikely to be a Type Ia progenitor. Astrometric data from GAIA will likely be needed to determine if either WD is truly a cluster member.
79 ASTRONOMY AND ASTROPHYSICS↗
Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering ''degenerate'' Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm
The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗