Continuous Degeneracy Research Articles

Casting Light on Degeneracies: A Comprehensive Study of Lightcurve Variations in Microlensing Events OGLE-2017-BLG-0103 and OGLE-2017-BLG-0192

This study investigates orbital parallax in gravitational microlensing events, focusing on OGLE-2017-BLG-0103 and OGLE-2017-BLG-0192. For events with timescales ≤60 days, a Jerk-Parallax degeneracy arises due to high Jerk velocity ( vj˜ ), causing a fourfold continuous parallax degeneracy. OGLE-2017-BLG-0103, after incorporating orbital parallax, reveals four discrete degenerate parallax solutions, while OGLE-2017-BLG-0192 exhibits four discrete solutions without degeneracy. The asymmetric lightcurve of OGLE-2017-BLG-0103 suggests a more probable model where Xallarap is added to the parallax model, introducing tension. The galactic model analysis predicts a very low-mass stellar lens for OGLE-2017-BLG-0192. For OGLE-2017-BLG-0103, degenerate solutions suggest a low-mass star or a darker lens in the disk, while the Xallarap+Parallax model also predicts a stellar lens in the bulge, with the source being a solar-type star orbited by a dwarf star. This study presents five degenerate solutions for OGLE-2017-BLG-0103, emphasizing the potential for confirmation through high-resolution Adaptive Optics observations with Extremely Large Telescopes in the future. The complexities of degenerate scenarios in these microlensing events underscore the need to analyze special single-lens events in the Roman Telescope Era.

Signed eigenvalue/vector distribution of complex order-three random tensor

Abstract We compute the signed distribution of the eigenvalues/vectors of the complex order-three random tensor by computing a partition function of a four-fermi theory, where signs are from a Hessian determinant associated to each eigenvector. The issue of the presence of a continuous degeneracy of the eigenvectors is properly treated by a gauge-fixing. The final expression is compactly represented by a generating function, which has an expansion whose powers are the dimensions of the tensor index spaces. A crosscheck is performed by Monte Carlo simulations. By taking the large-N limit we obtain a critical point where the behavior of the signed distribution qualitatively changes, and also the end of the signed distribution. The expected agreement of the end of the signed distribution with that of the genuine distribution provides a few applications, such as the largest eigenvalue, the geometric measure of entanglement, and the best rank-one approximation in the large-N limit.

Numerically studying the degeneracy problem in extreme finite-source microlensing events

ABSTRACT Most transit microlensing events due to very low mass lens objects suffer from extreme finite-source effects. While modelling their light curves, there is a known continuous degeneracy between their relevant lensing parameters, i.e. the source angular radius normalized to the angular Einstein radius ρ⋆, the Einstein crossing time tE, the lens impact parameter u0, the blending parameter, and the stellar apparent magnitude. In this work, I numerically study the origin of this degeneracy. I find that these light curves have five observational parameters (i.e. the baseline magnitude, the maximum deviation in the magnification factor, the full width at half-maximum $\rm {FWHM}=2 \mathit{ t}_{\rm {HM}}$, the deviation from a top-hat model, and the time of the maximum time derivative of microlensing light curves $T_{\rm {max}}=t_{\rm E}\sqrt{\rho _{\star }^{2}-u_{0}^{2}}$). For extreme finite-source microlensing events due to uniform source stars, we get tHM ≃ Tmax and the deviation from the top-hat model tends to zero, which both cause the known continuous degeneracy. When either ρ⋆ ≲ 10 or the limb-darkening effect is considerable, tHM and Tmax are two independent observational parameters. I use a numerical approach, i.e. random forests containing 100–120 decision trees, to study how these observational parameters are efficient in yielding the lensing parameters. These machine learning models find the mentioned five lensing parameters for finite-source microlensing events from uniform and limb-darkened source stars with the average R2-scores of 0.87 and 0.84, respectively. R2-score for evaluating the lens impact parameter gets worse on adding limb darkening, and for extracting the limb-darkening coefficient itself this score falls as low as 0.67.

Interface potential and line tension for Bose-Einstein condensate mixtures near a hard wall

Within Gross-Pitaevskii (GP) theory we derive the interface potential V (l) which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance l. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore non-equilibrium properties by using l as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, V (l) for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, V(l) is independent of l. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using V(l) we study the three-phase contact line where the interface meets the wall under a contact angle theta. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension tau. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, tau does not approach a nonzero positive constant for theta going to zero, but instead approaches zero (from below) as would be expected for a critical wetting transition. This hybrid character of tau is a consequence of the absence of a barrier in V(l) at wetting. For a typical V(l) we provide a conjecture for the exact line tension within GP theory.

Pattern Formation and Aggregation in Ensembles of Solitons in Quasi One-Dimensional Electronic Systems

Broken symmetries of quasi one-dimensional electronic systems give rise to microscopic solitons taking roles of carriers of the charge or spin. The double degeneracy gives rise to solitons as kinks of the scalar order parameter A; the continuous degeneracy for the complex order parameter Aexp(iθ) gives rise to phase vortices, amplitudes solitons, and their combinations. These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge doping. The long-range ordering in dimensions above one imposes super-long-range confinement forces upon the solitons, leading to a sequence of phase transitions in their ensembles. The higher-temperature T transition enforces the confinement of solitons into topologically bound complexes: pairs of kinks or the amplitude solitons dressed by exotic half-integer vortices. At a second lower T transition, the solitons aggregate into rods of bi-kinks or into walls of amplitude solitons terminated by rings of half-integer vortices. With lowering T, the walls multiply, passing sequentially across the sample. Here, we summarize results of a numerical modeling for different symmetries, for charged and neutral soliton, in two and three dimensions. The efficient Monte Carlo algorithm, preserving the number of solitons, was employed which substantially facilitates the calculations, allowing to extend them to the three-dimensional case and to include the long-range Coulomb interactions.

A Multiparameter Degeneracy in Microlensing Events with Extreme Finite Source Effects

Abstract For microlenses with sufficiently low mass, the angular radius of the source star can be much larger than the angular Einstein ring radius of the lens. For such extreme finite source effect (EFSE) events, finite source effects dominate throughout the duration of the event. Here, we demonstrate and explore a continuous degeneracy between multiple parameters of such EFSE events. The first component in the degeneracy arises from the fact that the directly observable peak change of the flux depends on both the ratio of the angular source radius to the angular Einstein ring radius and the fraction of the baseline flux that is attributable to the lensed source star. The second component arises because the directly observable duration of the event depends on both the impact parameter of the event and the relative lens-source proper motion. These two pairwise degeneracies become coupled when the detailed morphology of the light curve is considered, especially when including a limb-darkening profile of the source star. We derive these degeneracies mathematically through analytic approximations and investigate them further numerically with no approximations. We explore the likely physical situations in which these mathematical degeneracies may be realized and potentially broken. As more and more low-mass lensing events (with ever decreasing Einstein ring radii) are detected with improving precision and increasing cadence from microlensing surveys, one can expect that more of these EFSE events will be discovered. In particular, the detection of EFSE microlensing events could increase dramatically with the Roman Space Telescope Galactic Bulge Time Domain Survey.

Relativistic Topological Insulator Model

A relativistic topological insulator model in three spatial dimensions which is a non trivial extension of the non-abelian Landau problem is proposed. The model is exactly soluble and energy levels have both a discrete and a continuous degeneracy. The chromomagnetic field is strong and the fermions are confined in a plane and the physical effects that appear reflects the ${\bm Z}_2$ symmetry.

Combined Lorentz Symmetry: Lessons from Superfluid ^3He

We consider the possibility of the scenario in which the P, T and Lorentz symmetry of the relativistic quantum vacuum are all the combined symmetries. These symmetries emerge as a result of the symmetry breaking of the more fundamental P, T and Lorentz symmetries of the original vacuum, which is invariant under separate groups of the coordinate transformations and spin rotations. The condensed matter vacua (ground states) suggest two possible scenarios of the origin of the combined Lorentz symmetry, and both are realized in the superfluid phases of liquid ^3He: the ^3He-A scenario and the ^3He-B scenario. In these scenarios, the gravitational tetrads are considered as the order parameter of the symmetry breaking in the quantum vacuum. The ^3He-B scenarios applied to the Minkowski vacuum lead to the continuous degeneracy of the Minkowski vacuum with respect to the O(3, 1) spin rotations. The symmetry breaking leads to the corresponding topological objects, which appear due to the nontrivial topology of the manifold of the degenerate Minkowski vacua, such as torsion strings. The fourfold degeneracy of the Minkowski vacuum with respect to discrete P and T symmetries suggests that the Weyl fermions are described by four different tetrad fields: the tetrad for the left-handed fermions, the tetrad for the right-handed fermions, and the tetrads for their antiparticles. This may lead to the gravity with several metric fields, so that the parity violation may lead to the breaking of equivalence principle. Finally, we considered the application of the gravitational tetrads for the solution of the cosmological constant problem.

Emergence of nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets

The appearance of nontrivial phases in Kitaev materials exposed to an external magnetic field has recently been a subject of intensive studies. Here, we elucidate the relation between the field-induced ground states of the classical and quantum spin models proposed for such materials, by using the infinite density matrix renormalization group (iDMRG) and the linear spin wave theory (LSWT). We consider the $K \Gamma \Gamma'$ model, where $\Gamma$ and $\Gamma'$ are off-diagonal spin exchanges on top of the dominant Kitaev interaction $K$. Focusing on the magnetic field along the $[111]$ direction, we explain the origin of the nematic paramagnet, which breaks the lattice-rotational symmetry and exists in an extended window of magnetic field, in the quantum model. This phenomenon can be understood as the effect of quantum order-by-disorder in the frustrated ferromagnet with a continuous manifold of degenerate ground states discovered in the corresponding classical model. We compute the dynamical spin structure factors using a matrix operator based time evolution and compare them with the predictions from LSWT. We, thus, provide predictions for future inelastic neutron scattering experiments on Kitaev materials in an external magnetic field along the $[111]$ direction. In particular, the nematic paramagnet exhibits a characteristic pseudo-Goldstone mode which results from the lifting of a continuous degeneracy via quantum fluctuations.

Triangular array of iron oxide nanoparticles: Simulation study of intraparticle and interparticle magnetism

A study of spherical maghemite nanoparticles on a two dimensional triangular array was carried out using a stochastic Landau-Lifshitz-Gilbert (sLLG) approach. The simulation method was first validated with a triangular array of simple dipoles, where results show the expected phase transition to a ferromagnetic state at a finite temperature. The ground state exhibited a continuous degeneracy that was lifted by an order-from-disorder mechanism at infinitesimal temperatures with the appearance of a six-fold planar anisotropy. The nanoparticle array consisted of 7.5 nm diameter maghemite spheres with bulk-like superexchange interactions between Fe-ions in the core, and weaker exchange between surface Fe-ions and a radial anisotropy. The triangular nanoparticle array ordered at the same reduced temperature as the simple dipole array, but exhibited different behaviour at low temperatures due to the surface anisotropy. We find that the vacancies on the octahedral sites in the nanoparticles combine with the surface anisotropy to produce an effective random temperature-dependent anisotropy for each particle. This leads to a reduction in the net magnetization of the nanoparticle array at zero temperature compared to the simple dipole array.

Continuous ground-state degeneracy of classical dipoles on regular lattices

Dipolar interactions are crucial in the modeling of many complex magnetic systems, such as the pyrochlores and artificial spin systems. Remarkably, many classical dipolar coupled spin systems exhibit a continuous ground-state degeneracy, which is unexpected as the Hamiltonian does not possess a continuous symmetry. In this paper, we explain, how such a finite point-symmetry leads to a continuous ground-state degeneracy of specific classical dipolar-coupled systems. This work, therefore, provides new insight into the theory of classical dipolar-coupled spin-systems and opens the way to understand more complex dipolar coupled systems.

Classical Ground State Spin Ordering of the Antiferromagnetic J1–J2 Model**Supported by the National Natural Science Foundation of China under Grant No 11774002.

The classical frustrated antiferromagnetic J1–J2 model is considered in a description of the classical spin wave for a vector spin system. Its ground state (GS) spin ordering is analyzed by minimizing its energy. Our analytical derivations show that all the spins in the GS phase must lie in planes that are parallel to each other. When applying the derived formulations to concrete lattices such as the square and simple cubic lattices, we find that in the large J2 region, a large continuous GS degeneracy concluded by a qualitative analysis is lifted, and collinear striped ordering is selected as the GS phase.

Continuous degeneracy of the fcc kagome lattice with magnetic dipolar interactions

Results are presented on analytic and computational analyses of the spin states associated with a 3D fcc lattice composed of ABC stacked kagome planes of magnetic ions with only long-range dipole-dipole interactions. Extending previous work on the 2D kagome system, where discrete six-fold discrete degeneracy of the ground state was revealed [Holden et al. Phys. Rev. B 91, 224425 (2015)], we show that the 3D lattice exhibits a continuous degeneracy characterized by just two spherical angles involving six sublattice spin vectors. Application of a Heat Bath Monte Carlo algorithm shows that thermal fluctuations reduce this degeneracy at very low temperature in an order-by-disorder process. A magnetic field applied along directions of high symmetry also results in lifting the continuous degeneracy to a subset of states from the original set of ground states. Metropolis Monte Carlo simulation results are also presented on the temperature and system size dependence of the energy, specific heat, and magnetization, providing evidence for a phase transition at T $\simeq$ 0.38 (in units of the dipole strength). The results can be relevant to a class of magnetic compounds having the AuCu$_3$ crystal structure.

Nondegenerate Parametric Resonance in a Tunable Superconducting Cavity

We develop a theory for non-degenerate parametric resonance in a tunable superconducting cavity. We focus on nonlinear effects that are caused by nonlinear Josephson elements connected to the cavity. We analyze parametric amplification in a strong nonlinear regime at the parametric instability threshold, and calculate maximum gain values. Above the threshold, in the parametric oscillator regime the linear cavity response diverges at the oscillator frequency at all pump strengths. We show that this divergence is related to the continuous degeneracy of the free oscillator state with respect to the phase. Applying on-resonance input lifts the degeneracy and removes the divergence. We also investigate the quantum noise squeezing. It is shown that in the strong amplification regime the noise undergoes four-mode squeezing, and that in this regime the output signal to noise ratio can significantly exceed the input value. We also analyze the intermode frequency conversion and identify parameters at which full conversion is achieved.

Supersolid formation in a quantum gas breaking a continuous translational symmetry.

The concept of a supersolid state combines the crystallization of a many-body system with dissipationless flow of the atoms from which it is built. This quantum phase requires the breaking of two continuous symmetries: the phase invariance of a superfluid and the continuous translational invariance to form the crystal. Despite having been proposed for helium almost 50 years ago, experimental verification of supersolidity remains elusive. A variant with only discrete translational symmetry breaking on a preimposed lattice structure-the 'lattice supersolid'-has been realized, based on self-organization of a Bose-Einstein condensate. However, lattice supersolids do not feature the continuous ground-state degeneracy that characterizes the supersolid state as originally proposed. Here we report the realization of a supersolid with continuous translational symmetry breaking along one direction in a quantum gas. The continuous symmetry that is broken emerges from two discrete spatial symmetries by symmetrically coupling a Bose-Einstein condensate to the modes of two optical cavities. We establish the phase coherence of the supersolid and find a high ground-state degeneracy by measuring the crystal position over many realizations through the light fields that leak from the cavities. These light fields are also used to monitor the position fluctuations in real time. Our concept provides a route to creating and studying glassy many-body systems with controllably lifted ground-state degeneracies, such as supersolids in the presence of disorder.

Kitaev materials beyond iridates: Order by quantum disorder and Weyl magnons in rare-earth double perovskites

Motivated by the experiments on the rare-earth double perovskites, we propose a generalized Kitaev-Heisenberg model to describe the generic interaction between the spin-orbit-entangled Kramers' doublets of the rare-earth moments. We carry out a systematic analysis of the mean-field phase diagram of this new model. In the phase diagram, there exist large regions with a continuous U(1) or O(3) degeneracy. Since no symmetry of the model protects such a continuous degeneracy, we predict that the quantum fluctuation lifts the continuous degeneracy and favors various magnetic orders in the phase diagram. From this order by quantum disorder mechanism, we further predict that the magnetic excitations of the resulting ordered phases are characterized by nearly gapless pseudo-Goldstone modes. We find that there exist Weyl magnon excitations for certain magnetic orders. We expect our prediction to inspire further study of Kitaev physics, the order by quantum disorder phenomenon and topological spin wave modes in the rare-earth magnets and the systems alike.

Degeneracies in long-baseline neutrino experiments from nonstandard interactions

We study parameter degeneracies that can occur in long-baseline neutrino appearance experiments due to nonstandard interactions (NSI) in neutrino propagation. For a single off-diagonal NSI parameter, and neutrino and antineutrino measurements at a single L/E, there exists a continuous four-fold degeneracy (related to the mass hierarchy and $\theta_{23}$ octant) that renders the mass hierarchy, octant, and CP phase unknowable. Even with a combination of NO$\nu$A and T2K data, which in principle can resolve the degeneracy, both NSI and the CP phase remain unconstrained because of experimental uncertainties. A wide-band beam experiment like DUNE will resolve this degeneracy if the nonzero off-diagonal NSI parameter is $\epsilon_{e\mu}$. If $\epsilon_{e\tau}$ is nonzero, or the diagonal NSI parameter $\epsilon_{ee}$ is O(1), a wrong determination of the mass hierarchy and of CP violation can occur at DUNE. The octant degeneracy can be further complicated by $\epsilon_{e\tau}$, but is not affected by $\epsilon_{ee}$.

Where Infinite Spin Particles are Localizable

Particles states transforming in one of the infinite spin representations of the Poincar\'e group (as classified by E. Wigner) are consistent with fundamental physical principles, but local fields generating them from the vacuum state cannot exist. While it is known that infinite spin states localized in a spacelike cone are dense in the one-particle space, we show here that the subspace of states localized in any double cone is trivial. This implies that the free field theory associated with infinite spin has no observables localized in bounded regions. In an interacting theory, if the vacuum vector is cyclic for a double cone local algebra, then the theory does not contain infinite spin representations. We also prove that if a Doplicher-Haag-Roberts representation (localized in a double cone) of a local net is covariant under a unitary representation of the Poincar\'e group containing infinite spin, then it has infinite statistics. These results hold under the natural assumption of the Bisognano-Wichmann property, and we give a counter-example (with continuous particle degeneracy) without this property where the conclusions fail. Our results hold true in any spacetime dimension s+1 where infinite spin representations exist, namely s > 1.

Parameter choices and ranges for continuous gravitational wave searches for steadily spinning neutron stars

We consider the issue of selecting parameters and their associated ranges for carrying out searches for continuous gravitational waves from steadily rotating neutron stars. We consider three different cases (i) the "classic" case of a star spinning about a principal axis; (ii) a biaxial star, not spinning about a principal axis; (iii) a triaxial star spinning steady, but not about a principal axis (as described in Jones, MNRAS vol 402, 2503 (2010)). The first of these emits only at one frequency; the other two at a pair of harmonically related frequencies. We show that in all three cases, when written in terms of the original "source parameters", there exist a number of discrete degeneracies, with different parameter values giving rise to the same gravitational wave signal. We show how these can be removed by suitably restricting the source parameter ranges. In the case of the model as written down by Jones, there is also a continuous degeneracy. We show how to remove this through a suitable rewriting in terms of "waveform parameters", chosen so as to make the specialisations to the other stellar models particularly simple. We briefly consider the (non-trivial) relation between the assignment of prior probabilities on one set of parameters verses the other. The results of this paper will be of use when designing strategies for carrying out searches for such multi-harmonic gravitational wave signals, and when performing parameter estimation in the event of a detection.

ChemInform Abstract: The Phenomenological Theory of Magnetization Relaxation (Review Article)

AbstractReview: 38 refs.