Spin Trajectories Research Articles

Towards a holistic magnetic braking model from the evolution of cataclysmic variables to stellar spin-down – I: the spin-down of fully convective M-dwarfs

ABSTRACT We extend a magnetic braking (MB) model, which has been used earlier to address the evolution of cataclysmic variables, to address the spin period Pspin evolution of fully convective M-dwarf (FCMD) stars. The MB mechanism is an α–Ω dynamo, which leads to stellar winds that carry away angular momentum. We model our MB torque such that the FCMDs experience an MB torque, approximately scaling as $P_\mathrm{spin}^{-1}$ at shorter periods, before transitioning into a Skumanich-type MB torque, scaling as $P_\mathrm{spin}^{-3}$. We also implement a parametrized reduction in the wind mass-loss owing to the entrapment of winds in dead zones. We choose a set of initial conditions and vary the two free parameters in our model to find a good match of our spin trajectories with open clusters containing FCMDs such as NGC2547, Pleiades, NGC2516, and Praesepe. We find that our model can explain the long spin periods of field stars and that a spread in spin distribution persists till over 3 Gyr. An advantage of our model is in relating physically motivated estimations of the magnetic field strength and stellar wind to properties of the stellar dynamo, which other models often remain agnostic about. We track the spin dependence of the wind mass-losses, Alfvén radii, and surface magnetic fields and find good agreement with observations. We discuss the implications of our results on the effect of the host FCMD on any orbiting exoplanets and our plans to extend this model to explain solar-like stars in the future.

Non-Hermitian dynamics for a two-spin system with PT symmetry

A system of interacting spins that are under the influence of spin-polarized currents can be described using a complex functional, or a non-Hermitian (NH) Hamiltonian. We study the dynamics of two exchange-coupled spins on the Bloch sphere. In the case of currents leading to PT symmetry, an exceptional point that survives also in the nonlinear system is identified. The nonlinear system is bistable for small currents and it exhibits stable oscillating motion or it can relax to a fixed point. The oscillating motion of the two spins is akin to synchronized spin-torque oscillators. For the full nonlinear system, we derive two conserved quantities that furnish a geometric description of the spin trajectories in phase space and indicate stability of the oscillating motion. Our analytical results provide tools for the description of the dynamics of NH systems that are defined on the Bloch sphere.

Ricochets on asteroids: Experimental study of low velocity grazing impacts into granular media

Spin off events and impacts can eject boulders from an asteroid surface and rubble pile asteroids can accumulate from debris following a collision between large asteroids. These processes produce a population of gravitational bound objects in orbit that can impact an asteroid surface at low velocity and with a distribution of impact angles. We present laboratory experiments of low velocity spherical projectiles into a fine granular medium, sand. We delineate velocity and impact angles giving ricochets, those giving projectiles that roll-out from the impact crater and those that stop within their impact crater. With high speed camera images and fluorescent markers on the projectiles we track spin and projectile trajectories during impact. We find that the projectile only reaches a rolling without slipping condition well after the marble has reached peak penetration depth. The required friction coefficient during the penetration phase of impact is 4–5 times lower than that of the sand suggesting that the sand is fluidized near the projectile surface during penetration. We find that the critical grazing impact critical angle dividing ricochets from roll-outs, increases with increasing impact velocity. The critical angles for ricochet and for roll-out as a function of velocity can be matched by an empirical model during the rebound phase that balances a lift force against gravity. We estimate constraints on projectile radius, velocity and impact angle that would allow projectiles on asteroids to ricochet or roll away from impact, finally coming to rest distant from their initial impact sites.

Geometric driving of two-level quantum systems

We investigate a class of cyclic evolutions for %the cyclic evolution of driven two-level quantum systems (effective spin-1/2) with a particular focus on the geometric characteristics of the driving and their specific imprints on the quantum dynamics. By introducing the concept of geometric field curvature for any field trajectory in the parameter space we are able to unveil underlying patterns in the overall quantum behavior: the knowledge of the field curvature provides a non-standard and fresh access to the interrelation between field and spin trajectories, and the corresponding quantum phases acquired in non-adiabatic cyclic evolutions. In this context, we single out setups in which the driving field curvature can be employed to demonstrate a pure geometric control of the quantum phases. Furthermore, the driving field curvature can be naturally exploited to introduce the geometrical torque and derive a general expression for the total quantum phase acquired in a cycle. Remarkably, such relation allows to access the mechanisms controlling the changeover of the quantum phase across a topological transition and to disentangle the role of the spin and field topological windings. As for implementations, we discuss a series of physical systems and platforms to demonstrate how the geometric control of the quantum phases can be realized for pendular field drivings. This includes setups based on superconducting islands coupled to a Josephson junction and inversion asymmetric nanochannels with suitably tailored geometric shapes.

Molecular velocity auto-correlations in glycerol/water mixtures studied by NMR MGSE method

Molecular dynamics in binary mixtures of water and glycerol was studied by measuring the spectrum of water velocity auto-correlation in the frequency range from 0.05−10 kHz by using the NMR method of modulated gradient spin echo. The method shows that the diversity of diffusion signature in the short spin trajectories provides information about heterogeneity of molecular motion due to the motion in the micro-vortexes of hydrodynamic fluctuation, which is especially pronounced for the mixtures with low glycerol content. As concentration of glycerol increases above 10vol%, a new feature of spectrum appears due to interaction of water molecules with the clusters formed around hydrophilic glycerol molecules. New spectrum exposes a rate thickening of molecular friction, according to Einstein–Smoluchowski–Kubo formula, which inhibits rapid molecular motions and creates the conditions for a slow process of spontaneously folding of disordered poly-peptides into biologically active protein molecules when immersed in such a mixture.

Optimized quantification of spin relaxation times in the hybrid state.

The optimization and analysis of spin ensemble trajectories in the hybrid state-a state in which the direction of the magnetization adiabatically follows the steady state while the magnitude remains in a transient state. Numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for -encoding, -encoding, and their weighted sum, respectively, followed by a comparison between the Cramér-Rao bounds obtained with our optimized spin-trajectories, Look-Locker sequences, and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. After a nonrecurring inversion segment on the southern half of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern hemisphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance - and -encoding still result in near optimal signal-to-noise efficiency for each relaxation time. Thus, the second parameter can be encoded at virtually no extra cost. We provided new insights into the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We found that joint acquisitions of and in the hybrid state are substantially more efficient than sequential encoding techniques.

Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method

The velocity auto-correlation spectra of simple liquids obtained by the NMR method of modulated gradient spin echo show features in the low frequency range up to a few kHz, which can be explained reasonably well by a t−3∕2 long-time tail decay only for non-polar liquid toluene, while the spectra of polar liquids, such as ethanol, water and glycerol, are more congruent with the model of diffusion of particles temporarily trapped in potential wells created by their neighbors. As the method provides the spectrum averaged over ensemble of particle trajectories, the initial non-exponential decay of spin echoes is attributed to a spatial heterogeneity of molecular motion in a bulk of liquid, reflected in distribution of the echo decays for short spin trajectories. While at longer time intervals, and thus with longer trajectories, heterogeneity is averaged out, giving rise to a spectrum which is explained as a combination of molecular self-diffusion and eddy diffusion within the vortexes of hydrodynamic fluctuations.

Effect of synchrotron radiation on the dynamics of electron spin precession in the process of laser-plasma acceleration

A model was developed and tested for studying the dynamics of spin precession and trajectories of charged particles in the wake fields generated in a laser-plasma accelerator. The model takes into account the radiation reaction force in the Landau – Lifshits form. An investigation is made of the effect of synchrotron radiation on the dynamics of energy gaining and spin precession of electrons accelerated in model constant fields as well as on the particle beam polarisation in the acceleration at a separate acceleration stage in the case of self-consistent description of the nonlinear dynamics of a laser pulse and its generated accelerating and focusing plasma wake fields. It is shown that synchrotron radiation hardly affects the energy gain rate and polarisation of the electrons that are accelerated in the fields characteristic for a moderately nonlinear mode of laser-plasma acceleration up to an energy of 3.8 TeV.

Inverse Ising problem in continuous time: A latent variable approach.

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Inferring hidden states in a random kinetic Ising model: replica analysis

We consider the problem of predicting the spin states in a kinetic Ising model when spin trajectories are observed for only a finite fraction of sites. In a Bayesian setting, where the probabilistic model of the spin dynamics is assumed to be known, the optimal prediction can be computed from the conditional (posterior) distribution of unobserved spins given the observed ones. Using the replica method, we compute the error of the Bayes optimal predictor for parallel discrete time dynamics in a fully connected spin system with non-symmetric random couplings. The results, exact in the thermodynamic limit, agree very well with simulations of finite spin systems.

Numerically optimized band-selective pulses in SOFAST-HMQC experiments for biomolecular NMR

This work demonstrates the efficacy of numerically optimized band-selective pulses in 2D fast-pulsing NMR pulse sequences of the SOFAST-HMQC variety. In order to achieve robust band selectivity the amplitude and phase of the shaped RF pulses are modulated according to a numerically optimized function. During the pulse duration, the spin trajectories evolve along complex and often unexpected pathways. The pulses have been designed using the GRAPE algorithm and are experimentally implemented on a model protein ubiquitin (13C, 15N labeled). Signal to noise ratios of peaks have been computed and compared for the different experiments performed using both numerically optimized band-selective pulses and standard pulse shapes. The numerically optimized pulses perform better in terms of signal enhancement and phase, as compared to standard pulse shapes.

Path-integral representation for quantum spin models: Application to the quantum cavity method and Monte Carlo simulations

The cavity method is a well-established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [Phys. Rev. B 78, 134424 (2008)] proposed recently an extension of this method to quantum spin-1/2 models in a transverse field, using a discretized Suzuki-Trotter imaginary-time formalism. Here we show how to take analytically the continuous imaginary-time limit. Our main technical contribution is an explicit procedure to generate the spin trajectories in a path-integral representation of the imaginary-time dynamics. As a side result we also show how this procedure can be used in simple heat bath Monte Carlo simulations of generic quantum spin models. The replica symmetric continuous-time quantum cavity method is formulated for a wide class of models and applied as a simple example on the Bethe lattice ferromagnet in a transverse field. The results of the methods are confronted with various approximation schemes in this particular case. On this system we performed quantum Monte Carlo simulations that confirm the exactness of the cavity method in the thermodynamic limit.

Spin precession in an adiabatically rotating electric field

Due to spin-orbit coupling, the adiabatic perturbation of an electron's orbital motion induced by a revolving external electric field lead to the electron spin-precession. The obtained results describe both transverse and longitudinal dynamics of an effective spin, for conical and figure-8 trajectories of a driving electric field, and elucidate the link between the quantum-mechanical, geometrical, and classical pictures of spin rotation. Within the limit of adiabatic approximation the derived formulas are valid regardless of whether eigenvectors of the total Hamiltonian of the problem are explicitly available or not, and are convenient for approximate calculations. The main expression for the time evolution of the Bloch vector has pure geometric character and is independent of the physical context.

Spin surfaces and trajectories in valence bands of tetrahedral semiconductors

AbstractSurfaces and trajectories traced out by spin vectors in spin space are calculated and systematized for holes in tetrahedral semiconductors. It is shown how various trajectories are related to the wave‐function phases and amplitudes of the doubly degenerated heavy‐mass, light‐mass, or split‐off bands. Relations between hole wave vectors and spin surface shapes are examined for high symmetry directions. The presented results may be useful in ultrafast spintronics, where both the spin state and the wave vector of a hole should be taken into account simultaneously in the description of the hole spin dynamics. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Exceptional orbits: a new class of spin trajectories in circular accelerators

We claim there is a new class of spin trajectories in circular accelerators, which are not accounted for in current theories of spin dynamics. We call them exceptional orbits. On such orbits the spin motion drives a secular growth of the orbital amplitude(s). Our results do not by themselves prove the spatial separation of spin states of a relativistic charged particle beam, but our findings are consistent with those of other workers. Our findings do invalidate the unconditional use of the semiclassical approximation to treat the orbital motion, to diagonalize the spin–orbit Hamiltonian. We analyze a simple model in detail to demonstrate our ideas. We review the canonical transformation theory of spin dynamics in storage rings, and extend it to account for exceptional orbits. We also examine how exceptional orbits affect map-based algorithms. We show that the algorithms can sometimes break down, in ways not hitherto suspected. We show that on an exceptional orbit the secular rate of spin phase advance depends explicitly on the orbital arc-length, in contradiction to claims that the spin tune depends only on the orbital amplitudes.

Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics

This is the first of three papers on the Glauber evolution of Ising spin systems with Kac potentials. We begin with the analysis of the mesoscopic limit, where space scales like the diverging range, gamma -1, of the interaction while time is kept finite: we prove that in this limit the magnetization density converges to the solution of a deterministic, nonlinear, nonlocal evolution equation. We also show that the long time behaviour of this equation describes correctly the evolution of the spin system till times which diverge as gamma to 0 but are small in units log gamma -1. In this time regime we can give a very precise description of the evolution and a sharp characterization of the spin trajectories. As an application of the general theory, we then prove that for ferromagnetic interactions, in the absence of external magnetic fields and below the critical temperature, on a suitable macroscopic limit, an interface between two stable phases moves by mean curvature. All the proofs are consequence of sharp estimates on special correlation functions, the v-functions, whose analysis is reminiscent of the cluster expansion in equilibrium statistical mechanics.

Relaxation and dynamics of coupled spin systems subjected to continuous radio frequency fields

A computational method for the prediction of spin trajectories in systems of two or more spins evolving under the influence of the static field, an applied radio frequency field, chemical shifts, spin–spin couplings, and magnetic dipolar relaxation has been described. The program has been tested to establish its correct operation by calculation of limiting cases with known solutions. It is shown that it is necessary to retain the nonsecular elements of the relaxation matrix in order to obtain correct results, primarily elements controlling cross relaxation between transverse components of magnetization of different spin states belonging to the same quantum number of the total magnetization along the axis of the static field. As a result of the retention of these terms, two unexpected features are predicted: frequency and phase shifts in spectra of two non-spin-coupled nuclei with relaxation rate comparable to frequency separation and unusually intense magnetizations in the locked state of two spins with the radio frequency applied at the center of the spectrum.

Passage of polarized neutrons through magnetic media. Depolarization by magnetized inhomogeneities

The behavior of a neutron polarization vector for neutrons passing through magnetic media characterized by a magnetic fluctuation tensor is described by Bloch-type equation. Coherent and incoherent spin flow motions on the surface of an unit three-dimension sphere are reflected by the equation. The applicability of the equation is based on two factors: (a) the SU(2) group analysis of the neutron spin behaviour in a magnetic field; and (b) consecutive averaging of spin trajectories in the SU(2) group manifold over all neutrons passing through a thin sample layer. Halpern-Holstein's and Maleyev-Ruban's depolarizations are discussed.

Islands of high-spin yrast isomers

The variation in nuclear deformation with angular momentum is considered in a wide region of nucleides, 34 ≦ Z ≦ 94. Cases of spin trajectories involving rotation around a symmetry axis, oblate or prolate, are surveyed as likely candidates for yrast traps. A few representative yrast spectra are also given and trap mechanisms discussed.