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At least 19 records

Quasiperiodically forced damped pendula and Schroedinger equations with quasiperiodic potentials - Implications of their equivalence

Certain first-order nonlinear ordinary differential equations exemplified by strongly damped, quasiperiodically driven pendula and Josephson junctions are isomorphic to Schroedinger equations with quasiperiodic potentials. The implications of this equivalence are discussed. In particular, it is shown that the transition to Anderson localization in the Schroedinger problem corresponds to the occurrence of a novel type of strange attractor in the pendulum problem. This transition should be experimentally observable in the frequency spectrum of the pendulum of Josephson junction.

Bondeson, A.↗

Universality and quantum criticality in quasiperiodic spin chains

Abstract Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quasiperiodic potassium adlayer on decagonal Al–Ni–Co quasicrystal

Quasiperiodicity in free-electron-like metals is a subject of significant interest within the scientific community. In this work, utilizing scanning tunneling microscopy (STM), low energy electron diffraction (LEED), and density functional theory (DFT), we demonstrate the formation of a quasiperiodic potassium monolayer on the tenfold surface of decagonal Al–Ni–Co quasicrystal. A dispersed growth comprising of isolated K adatoms is observed at sub-monolayer coverage, which coalesce with increasing coverage and forms pentagonal and decagonal quasiperiodic motifs. LEED demonstrates distinct rings of spots displaying decagonal symmetry. Furthermore, our DFT calculation using the W-approximant surface that closely resembles d-Al–Ni–Co shows that sizable adsorbate-substrate interaction makes the potassium adatoms bind to the quasiperiodically dispersed favorable adsorption sites resulting in the formation of quasiperiodic potassium monolayer. Notably, the experimental motifs obtained from STM measurements align remarkably well with the DFT predictions, underscoring the intricate relationship between the electronic structure of the substrate that drives the quasiperiodic growth of the potassium adlayer.

alkali metal↗

Local integrals of motion and the quasiperiodic many-body localization transition

We study the many-body localization (MBL) transition for interacting fermions subject to quasiperiodic potentials by constructing the local integrals of motion (LIOMs) in the MBL phase as time-averaged local operators. Here, we study numerically how these time-averaged operators evolve across the MBL transition. We find that the norm of such time-averaged operators drops discontinuously to zero across the transition; as we discuss, this implies that LIOMs abruptly become unstable at some critical localization length of order unity. We analyze the LIOMs using hydrodynamic projections and isolating the part of the operator that is associated with interactions. Equipped with these data we perform a finite-size scaling analysis of the quasiperiodic MBL transition. Our results suggest that the quasiperiodic MBL transition occurs at considerably stronger quasiperiodic modulations and has a larger correlation-length critical exponent than previous studies had found.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Topological edge modes without symmetry in quasiperiodically driven spin chains

Here we construct an example of a 1d quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. In a sharp departure from topological phases in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this emergent dynamical symmetry-protected topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long timescales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a type of boundary critical with no known static or Floquet analogue, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

36 MATERIALS SCIENCE↗

Effect of quasiperiodic and random noise on many-body dynamical decoupling protocols

Symmetries (and their spontaneous rupturing) can be used to protect and engender novel quantum phases and lead to interesting collective phenomena. In the work of K. Agarwal and I. Martin, the authors described a general dynamical decoupling (polyfractal) protocol that can be used to engineer multiple discrete symmetries in many-body systems. This work expands on the former by studying the effect of quasiperiodic and random noise on such a dynamical scheme. We find generally that relaxation of engineered symmetry generators proceeds by (i) an initial relaxation on microscopic timescales to a prethermal plateau whose height is independent of noise, (ii) a linear relaxation regime with a noise-dependent rate, followed by (iii) a slow logarithmic relaxation regime that is only present for quasiperiodic noise. We glean the essential features of these regimes via scaling collapses and show that they can be generally explained by the spectral properties of the various noise waveforms considered. In particular, the quasiperiodic noise is characterized by highly time-dependent spectrum with a noise floor that mimics white noise, and peaks that grow sharper with time. We argue that both the noise floor and peaks contribute to the initial linear-in-time relaxation while the logarithmic regime is initiated when the peaks become sufficiently well resolved and cease to contribute to further relaxation. Here, we provide numerical evidence to justify these findings.

74 ATOMIC AND MOLECULAR PHYSICS↗

Quantum Criticality in the 2D Quasiperiodic Potts Model

Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic q-state Potts model in 2+1D. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of q, and is controlled by an infinite-quasiperiodicity fixed point. In conclusion, the correlation length exponent is found to be ν = 1, saturating a modified version of the Harris-Luck criterion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quench dynamics of two-component dipolar fermions subject to a quasiperiodic potential

Motivated by recent experiments in fermionic polar gases, we study the nonequilibrium dynamics of two-component dipolar fermions subject to a quasiperiodic potential. We investigate the localization of charge and spin degrees of freedom time evolving with a long-range spin-SU(2) symmetric fermionic Hamiltonian by calculating experimentally accessible dynamical observables. To study the nonequilibrium dynamics, we start the time evolution with two initial states at half-filling: (i) product state with doublons |↑↓0↑↓0↑↓0↑↓0↑↓$\rangle$ and (ii) product state with singlons |↑↓↑↓↑↓↑↓↑↓$\rangle$. We carried out the real-time evolution via the fermionic Hamiltonian using exact diagonalization (ED) and the time-dependent variational principle (TDVP) for finite matrix product states (MPS), within experimentally relevant timescales. For the product state with doublons, we observe a delocalized to localized phase transition varying disorder strengths by monitoring the decay of charge imbalance with time. For the long-range interacting Hamiltonian of our focus, and in the presence of strong enough disorder, starting the time evolution with singlons we find a strong reduction in the spin delocalization, contrary to results of previous studies using the disordered short-range (on-site) Hubbard model with SU(2) symmetry. In addition to the quench dynamics, we also demonstrate the localization of charge and spin in the full energy spectrum of the long-range spin-SU(2) symmetric Hamiltonian by monitoring spin and charge autocorrelation functions. Finally, our predictions for localization of both charge and spin should be observable in ultracold experiments with fermionic dipolar atoms subject to a quasiperiodic potential.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Temporally quasiperiodic data, propagating in the laboratory frame, can be rendered periodic by Galilean transformation

For a broad class of distributions of temperature, concentration, or another quantity propagating rectilinearly, we show that temporally quasiperiodic behavior in the laboratory frame can be rendered periodic by Galilean transformation. The approach is illustrated analytically and numerically using as an example a closed-form model distribution generated from a one-dimensional partial differential equation, and a detailed process is developed to determine frame speed from more general quasiperiodic, one-dimensional, temporally- and spatially-discretized data. Furthermore, the approach is extended to two- and three-dimensional rectilinear propagation, and its application to nonrectilinear propagation, along with implications for interpreting noise-corrupted data, are also discussed.

97 MATHEMATICS AND COMPUTING↗

Quasiperiodic behavior in beam-driven strong Langmuir turbulence

The evolution of unmagnetized beam-driven strong Langmuir turbulence is studied in two dimensions by numerically integrating the Zakharov equations for systems pumped by monochromatic and broadband negative-damping drivers with nonzero central wavenumber. Long-time statistically steady states are reached for which the dependence of the evolution on the driver wavenumber, growth rate, and bandwidth is examined in detail. For monochromatic drivers, a quasiperiodic cycle is found to develop if the driver wavenumber is sufficiently large. The characteristic frequency of the quasiperiodic cycle and the average system energy are both approximately proportional to the growth rate. Broadening of the driver in wavenumber tends to degrade the system-wide coherence of the cycle, but its main features appear to survive on the scale of the coherence length of the driver.

Robinson, P. A.↗

Comment on "The Predicted Size of Cycle 23 Based on the Inferred three-cycle Quasiperiodicity of the Planetary Index Ap"

Recently, Ahluwalia reviewed the solar and geomagnetic data for the last 6 decades and remarked that these data "indicate the existence of a three-solar-activity-cycle quasiperiodicity in them." Furthermore, on the basis of this inferred quasiperiodicity, he asserted that cycle 23 represents the initial cycle in a new three-cycle string, implying that it "will be more modest (a la cycle 17) with an annual mean sunspot number count of 119.3 +/- 30 at the maximum", a prediction that is considerably below the consensus prediction of 160 +/- 30 by Joselin et al. and of similar predictions by others based on a variety of predictive techniques. Several major sticking points of Ahluwalia's presentation, however, must be readdressed, and these issues form the basis of this comment. First, Ahluwalia appears to have based his analysis on a data set of Ap index values that is erroneous. For example, he depicts for the interval of 1932-1997 the variation of the Ap index in terms of annual averages, contrasting them against annual averages of sunspot number (SSN), and he lists for cycles 17-23 the minimum and maximum value of each, as well as the years in which they occur and a quantity which he calls "Amplitude" (defined as the numeric difference between the maximum and minimum values). In particular, he identifies the minimum Ap index (i.e., the minimum value of the Ap index in the vicinity of sunspot cycle minimum, which usually occurs in the year following sunspot minimum and which will be called hereafter, simply, Ap min) and the year in which it occur for cycles 17 - 23 respectively.

Wilson, Robert M.↗

Multipoint Observations of Quasiperiodic Emission Intensification and Effects on Energetic Electron Precipitation

The two Van Allen Probes simultaneously recorded a coherently modulated quasiperiodic (QP) emission that persisted for 3 h. The magnetic field pulsation at the locations of the two satellites showed a substantial difference, and their frequencies were close to but did not exactly match the repetition frequency of QP emissions for most of the time, suggesting that those coherent QP emissions probably originated from a common source, which then propagated over a broad area in the magnetosphere. The QP emissions were amplified by local anisotropic electron distributions, and their large-scale amplitudes were modulated by the plasma density. A novel observation of this event is that chorus waves at frequencies above QP emissions exhibit a strong correlation with QP emissions. Those chorus waves intensified when the QP emissions reach their peak frequency. This indicates that embryonic QP emissions may be critical for its own intensification as well as chorus waves under certain circumstances. A Low-Earth-Orbit POES satellite observed enhanced energetic electron precipitation in conjunction with the Van Allen Probes, providing direct evidence that QP emissions precipitate energetic electrons into the atmosphere. Finally, this scenario is quantitatively confirmed by our quasilinear diffusion simulation results.

79 ASTRONOMY AND ASTROPHYSICS↗

Magnetic devil's staircaselike behavior in quasiperiodic qubit lattices

The devil's staircase (DS) phenomenon is a fractal response of magnetization to external fields, traditionally observed in periodic ferromagnetic systems, where the commensurability between spin arrangements, lattice parameters, and external magnetic fields governs abrupt changes in magnetization. Its occurrence in aperiodic, fractal-type systems has remained largely unexplored, despite their natural compatibility with such phenomena. Using a quantum annealing device, we uncover a wealth of abrupt magnetic transitions between spin manifolds driven by increasing external magnetic fields within a simple yet effective Ising-model framework. In contrast to periodic systems, where DS arises from long-range competing interactions, our findings reveal that short-range, purely antiferromagnetic couplings in aperiodic geometries produce equally rich ground-state magnetization patterns. Here, we demonstrate that while magnetic textures are determined by the lattice size, their formation remains remarkably robust and independent of scale, with commensurability emerging locally. Our results challenge the prevailing view that DS behavior is limited to periodic systems and establish quasiperiodic geometries as a natural host for this phenomenon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tight Bound on the Neutron Star Radius with Quasiperiodic Oscillations in Short Gamma-Ray Bursts

Abstract Quasiperiodic oscillations (QPOs) have been recently discovered in the short gamma-ray bursts (GRBs) 910711 and 931101B. Their frequencies are consistent with those of the quasiradial and quadrupolar oscillations of binary neutron star (BNS) merger remnants, as obtained in numerical relativity simulations. These simulations reveal quasi-universal relations between the remnant oscillation frequencies and the tidal coupling constant of the binaries. Under the assumption that the observed QPOs are due to these postmerger oscillations, we use the frequency–tide relations in a Bayesian framework to infer the source redshift, as well as the chirp mass and the binary tidal deformability of the BNS progenitors for GRBs 910711 and 931101B. We further use this inference to estimate bounds on the mass–radius relation for neutron stars. By combining the estimates from the two GRBs, we find a 68% credible range R 1.4 = 12.4 8 − 0.40 + 0.41 km for the radius of a neutron star with mass M = 1.4 M ⊙ , which is one of the tightest bounds to date.

Guedes, Victor↗

Energetic Nonthermal Electrons within the Above-the-looptop Regions in Solar Flares: Acceleration, Feedback, and Quasiperiodic Pulsations

Solar flares are among the most dramatic events in the solar system, releasing substantial magnetic energy and accelerating a large number of electrons to high energies. Notably, in certain events, the above-the-looptop region may contain a significant population of nonthermal electrons, both in number and energy. For the first time, we adopt a novel numerical method that combines magnetohydrodynamics with energetic particles incorporating feedback from nonthermal electrons to investigate electron acceleration and transport in solar flares. We find that a large fraction of energetic electrons are accelerated via the current sheet and termination shock regions. Most energetic electrons are concentrated in the above-the-looptop region, carrying a sizable amount of the released energy. We observe that greater feedback of nonthermal electrons leads to steeper energy spectra. The energy density of the nonthermal electrons oscillates due to the periodic impact of magnetic islands into the above-the-looptop region, which may help explain the observed quasiperiodic pulsations. Our simulations provide new insights into the origin of nonthermal electrons and associated emissions in the above-the-looptop region.

79 ASTRONOMY AND ASTROPHYSICS↗

Quasiperiodic oscillations in bright galactic-bulge X-ray sources

Quasiperiodic oscillations with frequencies in the range 5-50 Hz have recently been discovered in X-rays from two bright galactic-bulge sources and Sco X-1. These sources are weakly magnetic neutron stars accreting from disks which the plasma is clumped. The interaction of the magnetosphere with clumps in the inner disk causes oscillations in the X-ray flux with many of the properties observed.

Lamb, F. K.↗

Interpretation and modeling of quasiperiodic diffraction patterns observed in equatorial VHF scintillation due to plasma bubbles

Quasiperiodic diffraction patterns have been observed in VHF scintillation recorded at Ascension Island in 1981. The patterns occur most often at the beginning or end of a scintillation patch and are shown to be consistent with those expected from irregularities having east-west scale sizes of a few hundred meters that are associated with the walls (edges) of equatorial plasma bubbles. By adjusting the geophysical parameters in a computer simulation of the amplitude fluctuations expected simultaneously at VHF, L-Band and C-Band, we model a specific event in detail. The model contains information on the size and strength of the structures that cause the regular fading patterns. In addition, multi-frequency diffraction patterns are computed for a 'phase screen' model based on high resolution measurements of a structured plasma bubble wall made using the AE-E satellite. The results are qualitatively very similar to the observations. Finally, implications of the model results for the extraction of information about the vertical structure of the irregularities are discussed.

Franke, S. J.↗

6 Hz quasiperiodic oscillations from low-mass X-ray binaries - The sound of an accretion disk?

Quasiperiodic oscillations (QPOs) at frequencies of 5-8 Hz are a common feature of low-mass X-ray binaries (LMXBs) during their normal branch (NB) spectral states. We propose that this frequency band is essentially a band of rotation frequencies in a thick accretion disk. The high luminosities in the NB state give rise to the thick disk and slow down the dynamical timescales. Density and optical-thickness perturbations in a subsonic region of the disk have the frequency spectrum of sound in a rotating medium. X-rays scattered through the subsonic region are modulated by long wavelength optical-thickness oscillations whose frequencies, determined by the rotation rate and vorticity, are observed as the NB QPOs.

Alpar, M. A.↗