Binary Spin Research Articles

Geometric Landscape Annealing as an Optimization Principle Underlying the Coherent Ising Machine

Given the fundamental importance of combinatorial optimization across many diverse domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better solutions with lower resource costs. However, a theoretical understanding of their performance remains elusive. We develop such understanding for the case of the coherent Ising machine (CIM), a network of optical parametric oscillators that can be applied to any quadratic unconstrained binary optimization problem. We focus on how the CIM finds low-energy solutions of the Sherrington-Kirkpatrick spin glass. As the laser gain of this system is annealed, the CIM interpolates between gradient descent on coupled soft spins to descent on coupled binary spins. By combining the Kac-Rice formula, the replica method, and supersymmetry breaking, we develop a detailed understanding of the evolving geometry of the high-dimensional energy landscape of the CIM as the laser gain increases, finding several phase transitions in the landscape, from flat to rough to rigid. Additionally, we develop a novel cavity method that provides a geometric interpretation of supersymmetry breaking in terms of the reactivity of a rough landscape to specific external perturbations. Our energy landscape theory successfully matches numerical experiments, provides geometric insights into the principles of CIM operation, and yields optimal annealing schedules. Published by the American Physical Society 2024

Robust T2 estimation with balanced steady state free precession.

To develop a novel signal representation for balanced steady state free precession (bSSFP) displaying its T2 independence on B1 and on magnetization transfer (MT) effects. A signal model for bSSFP is developed that shows only an explicit dependence (up to a scaling factor) on E2 (and, therefore, T2) and a novel parameter c (with implicit dependence on the flip angle and E1). Moreover, it is shown that MT effects, entering the bSSFP signal via a binary spin bath model, can be captured by a redefinition of T1 and, therefore, leading to modification of E1, resulting in the same signal model. Various sets of phase-cycled bSSFP brain scans (different flip angles, different TR, different RF pulse durations, and different number of phase cycles) were recorded at 3 T. The parameters T2 (E2) and c were estimated using a variable projection (VARPRO) method and Monte-Carlo simulations were performed to assess T2 estimation precision. Initial experiments confirmed the expected independence of T2 on various protocol settings, such as TR, the flip angle, B1 field inhomogeneity, and the RF pulse duration. Any variation (within the explored range) appears to directly affect the estimation of the parameter c only-in agreement with theory. BSSFP theory predicts an extraordinary feature that all MT and B1-related variational aspects do not enter T2 estimation, making it a potentially robust methodology for T2 quantification, pending validation against existing standards.

Effect of progressive substitution of spin-3/2 by spin-7/2 on the magnetocaloric properties of a mixed spin binary alloy system: A Monte Carlo study

Using Monte Carlo simulation the concentration dependency of the cooling exponent (n) of a binary alloy AxB1-x mixed spin system (7/2, 3/2) was studied rigorously. For low magnetic field (h) the entropy change (ΔS), excellently follows the relation ΔS∝hn. The exponent n hardly changes with x within the region 0.5 < x < 0.75. But for further increment of x > 0.75, n sharply drops down. The exponent n is strongly affected by the exchange interaction energy (ε). Due to the decrement of the antiferromagnetic interactions n value rapidly decreases. For the increment of x or the number of A(spin-7/2) atom the magnetization M as well as the magnetic entropy change ΔS increases. The phase transition temperature (i.e. Curie temperature) tC linearly decreases for the increase of x.

Searching for structure in the binary black hole spin distribution

Searching for structure in the binary black hole spin distribution

Evidence for a Correlation between Binary Black Hole Mass Ratio and Black Hole Spins

The astrophysical origins of the binary black hole systems seen with gravitational waves are still not well understood. However, features in the distribution of black hole masses, spins, redshifts, and eccentricities provide clues into how these systems form. Much has been learned by investigating these distributions one parameter at a time. However, we can extract additional information by studying the covariance between pairs of parameters. Previous work has shown preliminary support for an anticorrelation between mass ratio q ≡ m 2/m 1 and effective inspiral spin χ eff in the binary black hole population. In this study, we test for the existence of this anticorrelation using updated data from the third gravitational-wave transient catalog and improve our copula-based framework to employ a more robust model for black hole spins. We find evidence for an anticorrelation in (q, χ eff) with 99.7% credibility. This may imply high common-envelope efficiencies, stages of super-Eddington accretion, or a tendency for binary black hole systems to undergo mass-ratio reversal during isolated evolution. Covariance in (q, χ eff) may also be used to investigate the physics of tidal spinup as well as the properties of binary black hole–forming active galactic nuclei.

Too small to fail: characterizing sub-solar mass black hole mergers with gravitational waves

The detection of a sub-solar mass black hole could yield dramatic new insights into the nature of dark matter and early-Universe physics, as such objects lack a traditional astrophysical formation mechanism. Gravitational waves allow for the direct measurement of compact object masses during binary mergers, and we expect the gravitational-wave signal from a low-mass coalescence to remain within the LIGO frequency band for thousands of seconds. However, it is unclear whether one can confidently measure the properties of a sub-solar mass compact object and distinguish between a sub-solar mass black hole or other exotic objects. To this end, we perform Bayesian parameter estimation on simulated gravitational-wave signals from sub-solar mass black hole mergers to explore the measurability of their source properties. We find that the LIGO/Virgo detectors during the O4 observing run would be able to confidently identify sub-solar component masses at the threshold of detectability; these events would also be well-localized on the sky and may reveal some information on their binary spin geometry. Further, next-generation detectors such as Cosmic Explorer and the Einstein Telescope will allow for precision measurement of the properties of sub-solar mass mergers and tighter constraints on their compact-object nature.

Efficient optimization with higher-order ising machines

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order interactions although important classes of optimization problems, such as satisfiability problems, map more seamlessly to Ising networks with higher-order interactions. Here, we demonstrate that higher-order Ising machines can solve satisfiability problems more resource-efficiently in terms of the number of spin variables and their connections when compared to traditional second-order Ising machines. Further, our results show on a benchmark dataset of Boolean k-satisfiability problems that higher-order Ising machines implemented with coupled oscillators rapidly find solutions that are better than second-order Ising machines, thus, improving the current state-of-the-art for Ising machines.

Different assembled nano-MnO2 fiber supercapacitors applied for smart wearable clothing

With rapid development in the smart wearable field, new-style flexible energy storage devices are necessary to satisfy the demands of flexible smart clothing. Thereinto, fiber supercapacitors present promising application prospects. This work puts forward a facile and reliable strategy to fabricate coaxial fiber electrodes via binary wet spinning, and further assembles them into parallel or twisted nano-MnO2 fiber supercapacitors. In the obtained fiber electrode, a carboxymethylcellulose layer onto nano-MnO2 not only allows the requisite ion exchange between the electrochemical active materials and gel electrolyte, but also plays the role of separator to protect the two fiber electrodes effectively from contacting a short circuit, greatly ensuring the electrochemical stability of the nano-MnO2 fiber supercapacitors. The parallel nano-MnO2 fiber supercapacitor reaches a maximum CL of 19.7 μF/cm, EL of 0.0027 μWh/cm and PL of 1.49 μW/cm; the twisted MnO2 fiber supercapacitor achieves maximum CL, EL and PL of 49 μF/cm, 0.0053 μWh/cm and 1.0 μW/cm, respectively. Besides, the outstanding softness and tensile properties of the obtained nano-MnO2 fiber supercapacitors also guarantee stable electrochemical performance under bending, knotting or other large-distortion situations, which is beneficial to develop a new generation of metal oxide fiber supercapacitors for smart wearable clothing.

Secular Spin–Orbit Resonances of Black Hole Binaries in AGN Disks

The spin–orbit misalignment of stellar-mass black hole (sBH) binaries provides important constraints on the formation channels of merging sBHs. Here, we study the role of secular spin–orbit resonance in the evolution of an sBH binary component around a supermassive BH (SMBH) in an AGN disk. We consider the sBH’s spin precession due to the J 2 moment introduced by a circum-sBH disk within the warping/breaking radius of the disk. We find that the sBH’s spin–orbit misalignment (obliquity) can be excited via spin–orbit resonance between the sBH binary’s orbital nodal precession and the sBH spin precession driven by a massive circum-sBH disk. Using an α-disk model with Bondi–Hoyle–Lyttleton accretion, the resonances typically occur for sBH binaries with semimajor axis of 1 au and at a distance of ∼1000 au around a 107 M ⊙ SMBH. The spin–orbit resonances can lead to high sBH obliquities and a broad distribution of sBH binary spin–spin misalignments. However, we note that the Bondi–Hoyle–Lyttleton accretion is much higher than that of Eddington accretion, which typically results in spin precession being too low to trigger spin–orbit resonances. Thus, secular spin–orbit resonances can be quite rare for sBHs in AGN disks.

Erratum: Constraining black-hole binary spin precession and nutation with sequential prior conditioning [Phys. Rev. D 106 , 024019 (2022)

1 MoreReceived 5 April 2023DOI:https://doi.org/10.1103/PhysRevD.107.109901© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitationGravitational wave sourcesGravitational wavesPhysical SystemsAstronomical black holesTechniquesBayesian methodsGravitation, Cosmology & Astrophysics

Do unequal-mass binary black hole systems have larger χeff? Probing correlations with copulas in gravitational-wave astronomy

ABSTRACT The formation history of binary black hole systems is imprinted on the distribution of their masses, spins, and eccentricity. While much has been learned studying these parameters in turn, recent studies have explored the joint distribution of binary black hole parameters in two or more dimensions. Most notably, it has recently been argued that binary black hole mass ratio and effective inspiral spin χeff are anticorrelated. We point out a previously overlooked subtlety in such 2D population studies: in order to conduct a controlled test for correlation, one ought to fix the two marginal distributions – lest the purported correlation be driven by improved fit in just one dimension. We address this subtlety using a tool from applied statistics: the copula density function. We use the previous work correlating mass ratio and χeff as a case study to demonstrate the power of copulas in gravitational-wave astronomy while scrutinizing their astrophysical inferences. Our findings, however, affirm their conclusions that binary black holes with unequal component masses exhibit larger χeff (98.7 per cent credibility). We conclude by discussing potential astrophysical implications of these findings as well as prospects for future studies using copulas.

Making sense of complex systems through resolution, relevance, and mapping entropy.

Complex systems are characterized by a tight, nontrivial interplay of their constituents, which gives rise to a multiscale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those degrees of freedom that mostly determine the behavior of the system and separate them from less prominent players. Here, we tackle this problem making use of three measures of statistical information: Resolution, relevance, and mapping entropy. We address the links existing among them, taking the moves from the established relation between resolution and relevance and further developing novel connections between resolution and mapping entropy; by these means we can identify, in a quantitative manner, the number and selection of degrees of freedom of the system that preserve the largest information content about the generative process that underlies an empirical dataset. The method, which is implemented in a freely available software, is fully general, as it is shown through the application to three very diverse systems, namely, a toy model of independent binary spins, a coarse-grained representation of the financial stock market, and a fully atomistic simulation of a protein.

Close encounters of stars with stellar-mass black hole binaries

ABSTRACT Many astrophysical environments, from star clusters and globular clusters to the discs of active galactic nuclei, are characterized by frequent interactions between stars and the compact objects that they leave behind. Here, using a suite of 3D hydrodynamics simulations, we explore the outcome of close interactions between $1\, \mathrm{M}_{\odot }$ stars and binary black holes (BBHs) in the gravitational wave regime, resulting in a tidal disruption event (TDE) or a pure scattering, focusing on the accretion rates, the back reaction on the BH binary orbital parameters, and the increase in the binary BH effective spin. We find that TDEs can make a significant impact on the binary orbit, which is often different from that of a pure scattering. Binaries experiencing a prograde (retrograde) TDE tend to be widened (hardened) by up to $\simeq 20{{\ \rm per\ cent}}$. Initially circular binaries become more eccentric by $\lesssim 10{{\ \rm per\ cent}}$ by a prograde or retrograde TDE, whereas the eccentricity of initially eccentric binaries increases (decreases) by a retrograde (prograde) TDE by $\lesssim 5{{\ \rm per\ cent}}$. Overall, a single TDE can generally result in changes of the gravitational-wave-driven merger time-scale by order unity. The accretion rates of both black holes are very highly super-Eddington, showing modulations (preferentially for retrograde TDEs) on a time-scale of the orbital period, which can be a characteristic feature of BBH-driven TDEs. Prograde TDEs result in the effective spin parameter χ to vary by ≲0.02, while χ ≳ −0.005 for retrograde TDEs.

The 2PM Hamiltonian for binary Kerr to quartic in spin

From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the classical spin-limit for all graviton helicity sectors. The validity of the resulting Hamiltonian is verified by matching to known lower spin order results, as well as direct computation of the 2PM impulse and spin kicks from the eikonal phase and that from the test black hole scattering based on Mathisson-Papapetrou-Dixon equations.

Constraining black-hole binary spin precession and nutation with sequential prior conditioning

We investigate the detectability of subdominant spin effects in merging black-hole binaries using current gravitational-wave data. Using a phenomenological model that separates the spin dynamics into precession (azimuthal motion) and nutation (polar motion), we present constraints on the resulting amplitudes and frequencies. We also explore current constraints on the spin morphologies, indicating if binaries are trapped near spin-orbit resonances. We dissect such weak effects from the signals using a sequential prior conditioning approach, where parameters are progressively re-sampled from their posterior distribution. This allows us to investigate whether the data contain additional information beyond what is already provided by quantities that are better measured, namely the masses and the effective spin. For the current catalog of events, we find no significant measurements of weak spin effects such as nutation and spin-orbit locking. We synthesize a source with a high nutational amplitude and show that near-future detections will allow us to place powerful constraints, hinting that we may be at the cusp of detecting spin nutations in gravitational-wave data.

Evolution of stellar orbits around merging massive black hole binary

ABSTRACT We study the long-term orbital evolution of stars around a merging massive or supermassive black hole binary (BHB), taking into account the general relativistic effect induced by the black hole (BH) spin. When the BH spin is significant compared to and misaligned with the binary orbital angular momentum, the orbital axis ($\hat{\boldsymbol {l}}$) of the circumbinary star can undergo significant evolution during the binary orbital decay driven by gravitational radiation. Including the spin effect of the primary (more massive) BH, we find that starting from nearly coplanar orbital orientations, the orbital axes $\hat{\boldsymbol {l}}$ of circumbinary stars preferentially evolve towards the spin direction after the merger of the BHB, regardless of the initial BH spin orientation. Such alignment phenomenon, i.e. small final misalignment angle between $\hat{\boldsymbol {l}}$ and the spin axis of the remnant BH $\hat{\boldsymbol {S}}$, can be understood analytically using the principle of adiabatic invariance. For the BHBs with extremely mass ratio (m2/m1 ≲ 0.01), $\hat{\boldsymbol {l}}$ may experience more complicated evolution as adiabatic invariance breaks down, but the trend of alignment still works reasonably well when the initial binary spin–orbit angle is relatively small. Our result suggests that the correlation between the orientations of stellar orbits and the spin axis of the central BH could provide a potential signature of the merger history of the massive BH.

Hints of Spin-Orbit Resonances in the Binary Black Hole Population.

Binary black hole spin measurements from gravitational wave observations can reveal the binary's evolutionary history. In particular, the spin orientations of the component black holes within the orbital plane, ϕ_{1} and ϕ_{2}, can be used to identify binaries caught in the so-called spin-orbit resonances. In a companion paper, we demonstrate that ϕ_{1} and ϕ_{2} are best measured near the merger of the two black holes. In this work, we use these spin measurements to provide the first constraints on the full six-dimensional spin distribution of merging binary black holes. In particular, we find that there is a preference for Δϕ=ϕ_{1}-ϕ_{2}∼±π in the population, which can be a signature of spin-orbit resonances. We also find a preference for ϕ_{1}∼-π/4 with respect to the line of separation near merger, which has not been predicted for any astrophysical formation channel. However, the strength of these preferences depends on our prior choices, and we are unable to constrain the widths of the ϕ_{1} and Δϕ distributions. Therefore, more observations are necessary to confirm the features we find. Finally, we derive constraints on the distribution of recoil kicks in the population and use this to estimate the fraction of merger remnants retained by globular and nuclear star clusters. We make our spin and kick population constraints publicly available.

Measuring binary black hole orbital-plane spin orientations

Binary black hole spins are among the key observables for gravitational wave astronomy. Among the spin parameters, their orientations within the orbital plane, ${\ensuremath{\phi}}_{1}$, ${\ensuremath{\phi}}_{2}$ and $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}={\ensuremath{\phi}}_{1}\ensuremath{-}{\ensuremath{\phi}}_{2}$, are critical for understanding the prevalence of the spin-orbit resonances and merger recoils in binary black holes. Unfortunately, these angles are particularly hard to measure using current detectors, LIGO and Virgo. Because the spin directions are not constant for precessing binaries, the traditional approach is to measure the spin components at some reference stage in the waveform evolution, typically the point at which the frequency of the detected signal reaches 20 Hz. However, we find that this is a poor choice for the orbital-plane spin angle measurements. Instead, we propose measuring the spins at a fixed dimensionless time or frequency near the merger. This leads to significantly improved measurements for ${\ensuremath{\phi}}_{1}$ and ${\ensuremath{\phi}}_{2}$ for several gravitational wave events. Furthermore, using numerical relativity injections, we demonstrate that $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}$ will also be better measured near the merger for louder signals expected in the future. Finally, we show that numerical relativity surrogate models are key for reliably measuring the orbital-plane spin orientations, even at moderate signal-to-noise ratios like $\ensuremath{\sim}30--45$.

Phase-Binarized Spin Hall Nano-Oscillator Arrays: Towards Spin Hall Ising Machines

Ising machines (IMs) are physical systems designed to find solutions to combinatorial optimization (CO) problems mapped onto the IM via the coupling strengths between its binary spins. Using its intrinsic dynamics and different annealing schemes, the IM relaxes over time to its lowest-energy state, which is the solution to the CO problem. IMs have been implemented on different platforms, and interacting nonlinear oscillators are particularly promising candidates. Here we demonstrate a pathway towards an oscillator-based IM using arrays of nanoconstriction spin Hall nano-oscillators (SHNOs). We show how SHNOs can be readily phase binarized and how their resulting microwave power corresponds to well-defined global phase states. To distinguish between degenerate states, we use phase-resolved Brillouin-light-scattering microscopy and directly observe the individual phase of each nanoconstriction. Micromagnetic simulations corroborate our experiments and confirm that our proposed IM platform can solve CO problems, showcased by how the phase states of a $2\ifmmode\times\else\texttimes\fi{}2$ SHNO array are solutions to a modified max-cut problem. Compared with the commercially available D-Wave ${\mathrm{Advantage}}^{\mathrm{TM}}$, our architecture holds significant promise for faster sampling, substantially reduced power consumption, and a dramatically smaller footprint.

Conservation of correlation in measurements underlying the violation of Bell inequalities and a game of joint mapping

What compels quantum measurement to violate the Bell inequalities? Suppose that regardless of measurement, one can assign to a spin-$\frac{1}{2}$ particle (qubit) a definite value of spin, called c-valued spin variable, but, it may take any continuous real number. Suppose further that measurement maps the c-valued spin variable from the continuous range of possible values onto the binary standard quantum spin values $\pm 1$ while preserving the bipartite correlation. Here, we show that such c-valued spin variables can indeed be constructed. In this model, one may therefore argue that it is the requirement of conservation of correlation which compels quantum measurement to violate the Bell inequalities when the prepared state is entangled. We then discuss a statistical game which captures the model of measurement, wherein two parties are asked to independently map a specific ensemble of pairs of real numbers onto pairs of binary numbers $\pm 1$, under the requirement that the correlation is preserved. The conservation of correlation forces the game to respect the Bell theorem, which implies that there is a class of games no classical (i.e., local and deterministic) strategy can ever win. On the other hand, a quantum strategy with an access to an ensemble of entangled spin-$\frac{1}{2}$ particles and circuits for local quantum spin measurement, can be used to win the game.