Spin-½

About: Spin-½ is a research topic. Over the lifetime, 40423 publications have been published within this topic receiving 796639 citations.

Viewing the proton through 'color' filters

Abstract: While the form factors and parton distributions provide separately the shape of the proton in coordinate and momentum spaces, a more powerful imaging of the proton structure can be obtained through phase-space distributions. Here we introduce the Wigner-type quark and gluon distributions which depict a full-3D proton at every fixed light-cone momentum, like what is seen through momentum ("color") filters. After appropriate phase-space reductions, the Wigner distributions are related to the generalized parton distributions (GPDs) and transverse-momentum dependent parton distributions, which are measurable in high-energy experiments. The new interpretation of GPDs provides a classical way to visualize the orbital motion of the quarks, which is known to be the key to the spin and magnetic moment of the proton.

Dynamics of spin systems with randomly asymmetric bonds: Langevin dynamics and a spherical model

Abstract: Neural networks contain, very often, asymmetric bonds. The interactions J;, and J,; between the ith and the jth neurons are not identical. In this paper we study the Langevin dynamics of fully connected spin systems whose interaction matrix contains a random antisymmetrie part. The symmetric part consists of independent random bonds whose mean is either zero or ferromagnetic. We also consider a more general class of systems such as the asymmetric Hopfield model and other neural-network models. Within the framework of mean-field theory, the spin fluctuations are viewed as local, thermally averaged, time-dependent magnetic moments. These moments are induced by excess (i.e., nonthermal) internal noise which, in the presence of asymmetry, is time dependent and does not vanish even in the high-temperature phase. The mean-field equations are solved using a simplified, spherical model, in which the spins are linear variables except for a global constraint on the total level of their fluctuations. Random asymmetry of arbitrary strength destroys spin-glass freezing. Ferromagnetic phases, as well as "retrieval" states in neural networks, are affected only slightly by weak random asymmetry, in agreement with the conclusions of Hertz et al. The dynamical behavior of a system with weak asymmetry is studied in some detail. In the spin-glass case at low temperatures, when the strength of the asymmetry decreases, the internal excess noise does not vanish but slows down with a characteristic correlation time ~ ~ k The parameter k denotes the relative strength of the antisymmetric components of the bonds. The system behaves as a frozen symmetric spin glass on time scales t &&~ and as a paramagnet on scales t &&~. The thermal fluctuations decay with a characteristic time ~T ~ k . The spherical model exhibits a completely frozen spin-glass state at zero temperature. As T~O, fluctuations exhibit a critical slowing down with time ~~ T for all values of k ~0. This T =0 spin-glass transition is probably an artifact of the spherical model and is not expected to exist in nonlinear systems. The relevance of the results to the performance of neural networks is discussed.

General formulae for f1 --> f2 gamma

Abstract: At one-loop level the decay f1 --> f2 gamma, where f1 and f2 are two spin-1/2 particles with the same electric charge, is mediated by a boson B and a spin-1/2 fermion F. The boson B may have either spin 0 - interacting with the fermions through Dirac matrices 1 and gamma5 - or spin 1 - with V+A and V-A couplings to the fermions. I give general formulae for the one-loop electroweak amplitude of f1 --> f2 gamma in all these cases.

Spinning strings in AdS5 × S5: one-loop correction to energy in SL(2) sector

Abstract: We consider a circular string with spin S in AdS5 wrapped around big circle of S5 and carrying also momentum J. The corresponding N = 4 SYM operator belongs to the SL(2) sector, i.e. has tr(DSZJ)+... structure. The leading large J term in its 1-loop anomalous dimension can be computed using Bethe ansatz for the SL(2) spin chain and was previously found to match the leading term in the classical string energy. The string solution is stable at large J, and the Lagrangian for string fluctuations has constant coefficients, so that the 1-loop string correction to the energy E1 is given simply by the sum of characteristic frequencies. Curiously, we find that the leading term in the zero-mode part of E1 is the same as a 1/J correction to the one-loop anomalous dimension on the gauge theory (spin chain) side that was found in [1]. However, the contribution of non-zero string modes does not vanish. We also discuss the ``fast string'' expansion of the classical string action which coincides with the coherent state action of the SL(2) spin chain at the first order in λ, and extend this expansion to higher orders clarifying the role of the S5 winding number.

Observation of two types of fractional excitation in the Kitaev honeycomb magnet

Abstract: Quantum spin liquid is a disordered but highly entangled magnetic state with fractional spin excitations1. The ground state of an exactly solved Kitaev honeycomb model is perhaps its clearest example2. Under a magnetic field, a spin flip in this model fractionalizes into two types of anyon, a quasiparticle with more complex exchange statistics than standard fermions or bosons: a pair of gauge fluxes and a Majorana fermion2,3. Here, we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet α-RuCl3. The spin excitation gap determined by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magnetic field2,4,5, and a finite zero-field contribution matching the predicted size of the gauge flux gap2,6. The observed fractionalization into gapped anyons survives in a broad range of temperatures and magnetic fields, which establishes α-RuCl3 as a unique platform for future investigations of anyons.