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At least 109 records · Page 6

Miniature Sapphire Acoustic Resonator - MSAR

A room temperature sapphire acoustics resonator incorporated into an oscillator represents a possible opportunity to improve on quartz ultrastable oscillator (USO) performance, which has been a staple for NASA missions since the inception of spaceflight. Where quartz technology is very mature and shows a performance improvement of perhaps 1 dB/decade, these sapphire acoustic resonators when integrated with matured quartz electronics could achieve a frequency stability improvement of 10 dB or more. As quartz oscillators are an essential element of nearly all types of frequency standards and reference systems, the success of MSAR would advance the development of frequency standards and systems for both groundbased and flight-based projects. Current quartz oscillator technology is limited by quartz mechanical Q. With a possible improvement of more than x 10 Q with sapphire acoustic modes, the stability limit of current quartz oscillators may be improved tenfold, to 10(exp -14) at 1 second. The electromagnetic modes of sapphire that were previously developed at JPL require cryogenic temperatures to achieve the high Q levels needed to achieve this stability level. However sapphire fs acoustic modes, which have not been used before in a high-stability oscillator, indicate the required Q values (as high as Q = 10(exp 8)) may be achieved at room temperature in the kHz range. Even though sapphire is not piezoelectric, such a high Q should allow electrostatic excitation of the acoustic modes with a combination of DC and AC voltages across a small sapphire disk (approximately equal to l mm thick). The first evaluations under this task will test predictions of an estimated input impedance of 10 kilohms at Q = 10(exp 8), and explore the Q values that can be realized in a smaller resonator, which has not been previously tested for acoustic modes. This initial Q measurement and excitation demonstration can be viewed similar to a transducer converting electrical energy to mechanical energy and back. Such an electrostatic tweeter type excitation of a mechanical resonator will be tested at 5 MHz. Finite element calculation will be applied to resonator design for the desired resonator frequency and optimum configuration. The experiment consists of the sapphire resonator sandwiched between parallel electrodes. A DC+AC voltage can be applied to generate a force to act on a sapphire resonator. With the frequency of the AC voltage tuned to the sapphire resonator frequency, a resonant condition occurs and the sapphire Q can be measured with a high-frequency impedance analyzer. To achieve high Q values, many experimental factors such as vacuum seal, gas damping effects, charge buildup on the sapphire surface, heat dissipation, sapphire anchoring, and the sapphire mounting configuration will need attention. The effects of these parameters will be calculated and folded into the resonator design. It is envisioned that the initial test configuration would allow for movable electrodes to check gap spacing dependency and verify the input impedance prediction. Quartz oscillators are key components in nearly all ground- and space-based communication, tracking, and radio science applications. They play a key role as local oscillators for atomic frequency standards and serve as flywheel oscillators or to improve phase noise in high performance frequency and timing distribution systems. With ultra-stable performance from one to three seconds, an Earth-orbit or moon-based MSAR can enhance available performance options for spacecraft due to elimination of atmospheric path degradation.

Wang, Rabi T.↗

High-bandwidth density silicon photonic resonators for energy-efficient optical interconnects

The growth of artificial intelligence applications demands ever larger and more complex deep learning models, dominating today's—and tomorrow's—data center and high-performance computing systems. While traditional electronics are failing to keep pace with application demands, silicon photonic (SiPh) interconnects have emerged as a necessary technology to support these systems. SiPh-driven wavelength-division multiplexing (WDM) offers a particularly promising path toward supporting incredibly high-aggregate link bandwidth in a compact and efficient form factor. One of the basic building blocks of these integrated WDM interconnects is the SiPh resonator. Their inherent wavelength selectivity and compact footprint allow for efficient data transmission multiplexed across dozens of carrier wavelengths. Used as add-drop (AD) filters, SiPh resonators are critical to constructing integrated tunable wavelength-selective optical circuit switches as well as for demultiplexing the different carrier wavelengths toward independent wavelength-insensitive photodiodes in a dense wavelength-division multiplexing receiver. Resonators in the all-pass (AP) configuration are widespread as well, allowing for wavelength-selective modulation to drive aggregate link bandwidths far beyond the individual channel data rate. Unlike SiPh Mach–Zehnder modulators (MZM), resonant modulators can be driven using low, complementary metal-oxide-semiconductor drive voltages, allowing for tight co-integration between photonic integrated circuits, fabricated with larger process node technologies, and electronic integrated circuits, designed to exploit the advantages of the latest node. To push toward practical peta-scale interconnects, a comprehensive review of SiPh resonators is required, addressing bottlenecks and design constraints at both the architecture and device levels. We first describe the predominant integrated link architectures and identify their limits. We then discuss the device-level design considerations that can be made for both AD and AP configuration resonators to overcome the system level limits with novel resonator device designs. Analytical models and numerical simulation of resonators are validated by experimental measurement of devices fabricated in a commercial 300-mm foundry, showing a clear path toward volume manufacturing. The demonstrated resonant modulators and filters support the feasibility of increasing the aggregate bandwidth of resonator-driven SiPh interconnects into the peta-scale regime.

42 ENGINEERING↗

Orbit-orbit resonances in the solar system - Varieties and similarities

Descriptions of various orbit-orbit resonance mechanisms in the solar system are brought together in such a manner that the physical processes underlying the traditional mathematical presentations are apparent. A simple qualitative model based on the resonance between Saturn's satellites Titan and Hyperion is presented, the same resonance is analyzed quantitatively, and the small-eccentricity mechanism is examined. The following resonances are investigated in detail: Enceladus-Dione, Mimas-Tethys, Neptune-Pluto, and Rhea-Titan (secular resonance). Coupled librations of several asteroids near mean motions commensurable with Jupiter's are modeled, the Laplace relation involving Io, Europa, and Ganymede is studied, and the 1:1 resonance between the Trojan asteroids and Jupiter is discussed. Some higher-order commensurabilities involving asteroids are considered, including the 3:1 resonance between Alinda and Jupiter, the 13:5 resonance of Toro with Venus, the 8:5 resonance of Toro with earth, and the 11:28 resonance of Ivar with earth.

Greenberg, R.↗

Electric-optic resonant phase modulator

An electro-optic resonant cavity is used to achieve phase modulation with lower driving voltages. Laser damage thresholds are inherently higher than with previously used integrated optics due to the utilization of bulk optics. Phase modulation is achieved at higher speeds with lower driving voltages than previously obtained with non-resonant electro-optic phase modulators. The instant scheme uses a data locking dither approach as opposed to the conventional sinusoidal locking schemes. In accordance with a disclosed embodiment, a resonant cavity modulator has been designed to operate at a data rate in excess of 100 Mbps. By carefully choosing the cavity finesse and its dimension, it is possible to control the pulse switching time to within 4 ns and to limit the required switching voltage to within 10 V. Experimentally, the resonant cavity can be maintained on resonance with respect to the input laser signal by monitoring the fluctuation of output intensity as the cavity is switched. This cavity locking scheme can be applied by using only the random data sequence, and without the need of additional dithering of the cavity. Compared to waveguide modulators, the resonant cavity has a comparable modulating voltage requirement. Because of its bulk geometry, resonant cavity modulator has the potential of accommodating higher throughput power. Furthermore, mode matching into a bulk device is easier and typically can be achieved with higher efficiency. On the other hand, unlike waveguide modulators which are essentially traveling wave devices, the resonant cavity modulator requires that the cavity be maintained in resonance with respect to the incoming laser signal. An additional control loop is incorporated into the modulator to maintain the cavity on resonance.

Chen, Chien-Chung↗

High Resolution and Large Dynamic Range Resonant Pressure Sensor Based on Q-Factor Measurement

A pressure sensor has a high degree of accuracy over a wide range of pressures. Using a pressure sensor relying upon resonant oscillations to determine pressure, a driving circuit drives such a pressure sensor at resonance and tracks resonant frequency and amplitude shifts with changes in pressure. Pressure changes affect the Q-factor of the resonating portion of the pressure sensor. Such Q-factor changes are detected by the driving/sensing circuit which in turn tracks the changes in resonant frequency to maintain the pressure sensor at resonance. Changes in the Q-factor are reflected in changes of amplitude of the resonating pressure sensor. In response, upon sensing the changes in the amplitude, the driving circuit changes the force or strength of the electrostatic driving signal to maintain the resonator at constant amplitude. The amplitude of the driving signals become a direct measure of the changes in pressure as the operating characteristics of the resonator give rise to a linear response curve for the amplitude of the driving signal. Pressure change resolution is on the order of 10(exp -6) torr over a range spanning from 7,600 torr to 10(exp -6) torr. No temperature compensation for the pressure sensor of the present invention is foreseen. Power requirements for the pressure sensor are generally minimal due to the low-loss mechanical design of the resonating pressure sensor and the simple control electronics.

Gutierrez, Roman C.↗

D-Wave Resonances in Positronium Hydride

The problem of calculating the position and width of the lowest-lying (L = 0, 1) resonances in the Ps + H scattering system has recently been re-examined by the authors [1]. In the model used, resonances axe assumed generated by bound Rydberg states in the closed re-arranged channel [e(+) + H(-)]. This infinite series of Coulomb bound states are shifted somewhat by the coupling with the open scattering channel [Ps + H]. Estimates using this approach, first carried out by one of the authors [2] using a simple form of scattering wavefunction, indicated an anticipated small shift of resonance away from the Rydberg energy in the S-wave (L = 0). More recent results by Ho and Yan [3] using the complex-rotation method showed unexpected significant shifting in the P (L = 1) and D (L = 2)-wave resonance energies from their respective unperturbed values. Our re-calculation of the resonances [I I for L = 0 and I indicates that, in each case, reasonably consistent resonance energies are obtained by coupling the two lowest lying states (IS and 2S for L = 0 and 2P and 3P for L = 1). For each L it is the higher state (2S and 3P, respectively) that produces the resonance. The lower state (1S and 2P, respectively) is effective only in increasing the non-resonant phase shift. In this work we extend the model to L = 2 (D-waves). Our results show that, unlike the S and P-waves, the 313-state alone produces a resonant energy that is very close to the result of Yan and Ho [3]. Inclusion of the 4D-state produces a second resonance in the scattering system shifted up slightly from its unperturbed Rydberg energy.

Drachman, Richard J.↗

An Experimental Study of Nonlinear Standing Waves in Resonators with Numerical Comparison

Lawrenson et. al. [Journal of the Acoustic Society of America, Nov. 1998] described the generation of shock-free high-amplitude pressure waves in closed cavities using large equipment and resonators to produce the reported effects. An attempt is made to generate shock-free high-amplitude pressure waves using relatively small resonators. Ambient air is used as the working fluid. A small cylindrical resonator is tested resulting in the lack of a shocked waveform while a larger model of the same shape produces shock waves. A small conical resonator produces shock-free pressure waves at resonance, but the amplitude of these waves is small. A larger cone resonator model produces shock-free pressure waves of higher amplitude. A large horn-cone resonator also produces shock-free high amplitude pressure waves, A numerical model is used to compare the experimental results to theoretical results. The effects of structural resonances on the production of shock-free high-amplitude pressure waves are discussed, especially concerning difficulties encountered when these resonances were in the frequency ranges of interest. Identifying features of a structural resonance are presented.

Finkbeiner, Joshua R.↗

Few-Mode Whispering-Gallery-Mode Resonators

Whispering-gallery-mode (WGM) optical resonators of a type now under development are designed to support few well-defined waveguide modes. In the simplest case, a resonator of this type would support one equatorial family of WGMs; in a more complex case, such a resonator would be made to support two, three, or some other specified finite number of modes. Such a resonator can be made of almost any transparent material commonly used in optics. The nature of the supported modes does not depend on which material is used, and the geometrical dispersion of this resonator is much smaller than that of a typical prior WGM resonator. Moreover, in principle, many such resonators could be fabricated as integral parts of a single chip. Basically, a resonator of this type consists of a rod, made of a suitable transparent material, from which protrudes a thin circumferential belt of the same material. The belt is integral with the rest of the rod (see figure) and acts as a circumferential waveguide. If the depth (d) and width (w) of the belt are made appropriately small, then the belt acts as though it were the core of a single-mode optical fiber: the belt and its adjacent supporting rod material support a single, circumferentially propagating mode or family of modes. It has been shown theoretically that the fiber-optic-like behavior of the belton- rod resonator structure can be summarized, in part, by the difference, Dn, between (1) an effective index of refraction of an imaginary fiber core and (2) the index of refraction (n) of the transparent rod/belt material. It has also been shown theoretically that for a given required value of Dn, the required depth of the belt can be estimated as d R Dn, where R is the radius of the rod. It must be emphasized that this estimated depth is independent of n and, hence, is independent of the choice of rod material. As in the cases of prior WGM resonators, input/output optical coupling involves utilization of evanescent fields. In the present case, there are two evanescent fields: one at the belt/air interface and one in the boundary region between the belt and the rest of the rod.

Savchenkov, Anatoliy↗

Carbon Nanofiber-Based, High-Frequency, High-Q, Miniaturized Mechanical Resonators

High Q resonators are a critical component of stable, low-noise communication systems, radar, and precise timing applications such as atomic clocks. In electronic resonators based on Si integrated circuits, resistive losses increase as a result of the continued reduction in device dimensions, which decreases their Q values. On the other hand, due to the mechanical construct of bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators, such loss mechanisms are absent, enabling higher Q-values for both BAW and SAW resonators compared to their electronic counterparts. The other advantages of mechanical resonators are their inherently higher radiation tolerance, a factor that makes them attractive for NASA s extreme environment planetary missions, for example to the Jovian environments where the radiation doses are at hostile levels. Despite these advantages, both BAW and SAW resonators suffer from low resonant frequencies and they are also physically large, which precludes their integration into miniaturized electronic systems. Because there is a need to move the resonant frequency of oscillators to the order of gigahertz, new technologies and materials are being investigated that will make performance at those frequencies attainable. By moving to nanoscale structures, in this case vertically oriented, cantilevered carbon nanotubes (CNTs), that have larger aspect ratios (length/thickness) and extremely high elastic moduli, it is possible to overcome the two disadvantages of both bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators. Nano-electro-mechanical systems (NEMS) that utilize high aspect ratio nanomaterials exhibiting high elastic moduli (e.g., carbon-based nanomaterials) benefit from high Qs, operate at high frequency, and have small force constants that translate to high responsivity that results in improved sensitivity, lower power consumption, and im - proved tunablity. NEMS resonators have recently been demonstrated using topdown, lithographically fabricated ap - proaches to form cantilever or bridgetype structures. Top-down approaches, however, rely on complicated and expensive e-beam lithography, and often require a release mechanism. Reso - nance effects in structures synthesized using bottom-up approaches have also recently been reported based on carbon nanotubes, but such approaches have relied on a planar two-dimensional (2D) geometry. In this innovation, vertically aligned tubes synthesized using a bottom- up approach have been considered, where the vertical orientation of the tubes has the potential to increase integration density even further. The simulation of a vertically oriented, cantilevered carbon nanotube was performed using COMSOL Multi - physics, a finite element simulation package. All simulations were performed in a 2D geometry that provided consistent results and minimized computational complexity. The simulations assumed a vertically oriented, cantilevered nanotube of uniform density (1.5 g/cu cm). An elastic modulus was assumed to be 600 GPa, relative permittivity of the nanotube was assumed to be 5.0, and Poisson s ratio was assumed to be 0.2. It should be noted that the relative permittivity and Poisson s ratio for the nanotubes of interest are not known accurately. However, as in previous simulations, the relative permittivity and Poisson s ratios were treated as weak variables in the simulation, and no significant changes were recognized when these variables were varied.

Kaul, Anupama B.↗

A Study of Standing Pressure Waves Within Open and Closed Acoustic Resonators

The first section of the results presented herein was conducted on an axisymmetric resonator configured with open ventilation ports on either end of the resonator, but otherwise closed and free from obstruction. The remaining section presents the results of a similar resonator shape that was closed, but contained an axisymmetric blockage centrally located through the axis of the resonator. Ambient air was used as the working fluid. In each of the studies, the resonator was oscillated at the resonant frequency of the fluid contained within the cavity while the dynamic pressure, static pressure, and temperature of the fluid were recorded at both ends of the resonator. The baseline results showed a marked reduction in the amplitude of the dynamic pressure waveforms over previous studies due to the use of air instead of refrigerant as the working fluid. A sharp reduction in the amplitude of the acoustic pressure waves was expected and recorded when the configuration of the resonators was modified from closed to open. A change in the resonant frequency was recorded when blockages of differing geometries were used in the closed resonator, while acoustic pressure amplitudes varied little from baseline measurements.

Daniels, C.↗

Carbon Nanotubes as Resonators for RF Spectrum Analyzers

Electromechanical resonators of a proposed type would comprise single carbon nanotubes suspended between electrodes (see Figure 1). Depending on the nanotube length, diameter, and tension, these devices will resonate at frequencies in a range from megahertz through gigahertz. Like the carbon-nanotube resonators described in the preceding article, these devices will exhibit high quality factors (Q values), will be compatible with integration with electronic circuits, and, unlike similar devices made from silicone and silicone carbide, will have tunable resonant frequencies as high as several GHz. An efficient electromechanical transduction method for the carbon nanotube resonators is provided by the previously observed variation of carbon nanotube length with charge injection. It was found that injection of electrons or holes, respectively, lengthens or shortens carbon nanotubes, by amounts of the order of a percent at bias levels of a few volts. The charge-dependent length change also enables a simple and direct means of tuning the resonant frequency by varying the DC bias and hence the tension along the tube, much like tuning a guitar string. In its basic form, the invention is a tunable high-Q resonator based on a suspended carbon nanotube bridge with attached electrodes (see Figure 1). An applied DC bias controls the tension and thus the frequency of resonance. If one were to superimpose a radio-frequency (RF) bias on the DC bias, then the resulting rapid variation in tension or length would set the tube into vibration. If, on the other hand, the carbon nanotube were to be set into vibration by interaction between an incident RF electric field and electric charges in the nanotube, then the vibration would give rise to an RF signal output that is proportional to the RF amplitude at the resonance frequency. Because the transduction mechanism is extremely sensitive and the active volume is only a few nanometers in diameter, this device is not well suited for use as a microwave power device. Instead, this carbon nanotube mechanical resonator would be useful primarily as part of a highly precise, sensitive, frequency-selective detector. An array of such devices featuring nanotubes of different lengths (and thus different frequencies) could be made to operate as a highspeed spectrum analyzer (see Figure 2)

Hunt, Brian↗

MEMS-tunable optical ring resonator

A microelectromechanical systems (MEMS)-tunable optical ring resonator is described herein. The ring resonator includes a resonator ring and a tuner ring, along with one or more springs. The springs may be internal or external, i.e., either within or outside the areal footprint of the resonator ring and the tuner ring. The one or more springs are configured to displace the tuner ring from the resonator ring by a desired gap based upon a desired resonant wavelength of the resonator ring. Tuning is implemented by applying a voltage to the ring resonator, with motion of the tuner ring causing a corresponding change in the effective index of the resonator ring. As the ring resonator is essentially a capacitive device, it draws very little power once tuning is achieved.

Wood, Michael↗

Anomalous Loss Reduction Below Two‐Level System Saturation in Aluminum Superconducting Resonators

Superconducting resonators are widely used in many applications such as qubit readout for quantum computing, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms, especially the dissipation due to two-level systems (TLS) which become the dominant source of loss in the few-photon and low temperature regime. In this study, capacitively-coupled aluminum half-wavelength coplanar waveguide resonators are investigated. Surprisingly, the loss of the resonators is observed to decrease with a lowering temperature at low excitation powers and temperatures below the TLS saturation. This behavior is attributed to the reduction of the TLS resonant response bandwidth with decreasing temperature and power to below the detuning between the TLS and the resonant photon frequency in a discrete ensemble of TLS. When response bandwidths of TLS are smaller than their detunings from the resonance, the resonant response and thus the loss is reduced. At higher excitation powers, the loss follows a logarithmic power dependence, consistent with predictions from the generalized tunneling model (GTM). A model combining the discrete TLS ensemble with the GTM is proposed and matches the temperature and power dependence of the measured internal loss of the resonator with reasonable parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multiple Tunable Hyperbolic Resonances in Broadband Infrared Carbon-Nanotube Metamaterials

Aligned densely packed carbon-nanotube metamaterials prepared using vacuum filtration are an emerging infrared nanophotonic material. We report multiple hyperbolic plasmon resonances, together spanning the mid-infrared, in individual resonators made from aligned and densely packed carbon nanotubes. In a near-field scanning optical microscopy (NSOM) imaging study of nanotube metamaterial resonators, we observe distinct deeply subwavelength field profiles at the fundamental and higher-order resonant frequencies. The wafer-scale area of the nanotube metamaterials allows us to combine this near-field imaging with a systematic far-field spectroscopic study of the scaling properties of many resonator arrays. Thorough theoretical modeling agrees with these measurements and identifies the resonances as higher-order Fabry-Perot (FP) resonances of hyperbolic waveguide modes. Nanotube resonator arrays show broadband extinction from 1.5–10 µm and reversibly switchable extinction in the 3–5 µm atmospheric transparency window through the coexistence of multiple modes in individual ribbons. Broadband carbon-nanotube metamaterials supporting multiple resonant modes are a promising candidate for ultracompact absorbers, tunable thermal emitters, and broadband sensors in the mid-infrared.

36 MATERIALS SCIENCE↗

Novel machine-learning method for spin classification of neutron resonances

The performance of nuclear reactors and other nuclear systems depends on a precise understanding of the neutron interaction cross sections for materials used in these systems. These cross sections exhibit resonant structure whose shape is determined in part by the angular-momentum quantum numbers of the resonances. The correct assignment of the quantum numbers of neutron resonances is, therefore, paramount. In this project, we apply machine learning to automate the quantum number assignments using only the resonances' energies and widths and not relying on detailed transmission or capture measurements. The classifier used for quantum number assignment is trained using stochastically generated resonance sequences whose distributions mimic those of real data. Here we explore the use of several physics-motivated features for training our classifier. These features amount to out-of-distribution tests of a given resonance's widths and resonance-pair spacings. We pay special attention to situations where either capture widths cannot be trusted for classification purposes or where there is insufficient information to classify resonances by the total spin J. We demonstrate the efficacy of our classification approach using simulated and actual 52 Cr resonance data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Secular Resonances in Nonrestricted Hierarchical Triple Systems

In this paper, the averaged Hamiltonian of a nonrestricted hierarchical triple system truncated at the third order is investigated. First, each secular resonant term is studied. For the well-studied secular quadrupole theory, it is analytically reformulated in a different manner in our work. The resonance width is numerically determined and displayed on the √(1−e{sub 1}{sup 2})−√(1−e{sub 2}{sup 2}) plane (also denoted as the e-tilde {sub 1}− e-tilde {sub 2} plane). In terms of the octupole terms, we show that for a near-planar configuration of the system, considerable variations of both the eccentricities of the inner and outer orbits can be generated by a single resonant term. The resonance width for every secular resonant angle from the octupole terms is also numerically determined and displayed on the e-tilde {sub 1}− e-tilde {sub 2} plane. The results show that an orbit flip with a near-perpendicular initial mutual inclination is possible for each secular resonance. By displaying the resonance widths of different resonant terms on the same e-tilde {sub 1}− e-tilde {sub 2} plane, we intuitively show the overlap of different secular resonances. Then, the full averaged Hamiltonian with both quadrupole and octupole terms is investigated using the Poincaré surface of section, with a special focus on the orbit flip. For the cases we exploited, we find that the near-planar flip of the inner orbit can be either regular or chaotic while the outer orbit flip is generally chaotic.

79 ASTRONOMY AND ASTROPHYSICS↗

Tidal Circularization of Binaries by Resonance Locking. I. The Importance of the Pre-main Sequence

Although tidal dissipation in binary stars has been studied for over a century, theoretical predictions have yet to match the observed properties of binary populations. This work quantitatively examines the recent proposal of tidal circularization by resonance locking, where tidal dissipation arises from resonances between the star’s natural oscillation frequencies and harmonics of the orbital frequency, and where resonances are “locked” for an extended period of time due to concurrent stellar evolution. We focus on tidal resonances with axi-symmetric gravity modes, and examine binaries with primary masses from one to two solar masses. We find that orbital evolution via resonance locking occurs primarily during the star’s pre-main-sequence phase, with the main-sequence phase contributing negligibly. Resonance locking, ignoring nonlinearity, can circularize binaries with peri-center distances out to ∼10 stellar radii, corresponding to circular periods of ∼4–6 days. However, we find resonantly excited gravity modes will become nonlinear in stellar cores, which prevents them from reaching their full, linear amplitudes. We estimate that such a “saturated resonance lock” reduces the circularization period by about a third, but resonance locking remains much more effective than the cumulative actions of equilibrium tides. In a companion paper, we examine recent binary data to compare against theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Avalanches and many-body resonances in many-body localized systems

Here we numerically study both the avalanche instability and many-body resonances in strongly disordered spin chains exhibiting many-body localization (MBL). Finite-size systems behave like MBL within the MBL regimes, which we divide into the asymptotic MBL phase and the finite-size MBL regime; the latter regime is, however, thermal in the limit of large systems and long times. In both Floquet and Hamiltonian models, we identify some landmarks within the MBL regimes. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition occurs much deeper in the MBL regimes than has been suggested by most previous studies. Our other landmarks involve systemwide many-body resonances: We find that the effective matrix elements producing eigenstates with systemwide many-body resonances are enormously broadly distributed. This broad distribution means that the onset of such resonances in typical samples occurs quite deep in the MBL regimes, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regimes of finite-size systems into three subregimes: (i) at strongest randomness, typical samples do not have any eigenstates that are involved in systemwide many-body resonances; (ii) there is a substantial intermediate subregime where typical samples do have such resonances but the pair of eigenstates with the minimum spectral gap does not, so the size of the minimum gap agrees with expectations from Poisson statistics; and (iii) in the weaker randomness subregime, the minimum gap is larger than predicted by Poisson level statistics because it is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain nonresonant and the system thus still appears MBL in most respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i) and the other subregimes are entirely in the thermal phase, even though they look localized in most respects, so are in the finite-size MBL regime.

36 MATERIALS SCIENCE↗