Storage of classical information in quantum spins

Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and backaction of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both reading and recording classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where a spin-polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom.

The emergence of classical behaviour in magnetic adatoms

A wide class of nanomagnets shows striking quantum behaviour, known as quantum spin tunnelling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground-state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behaviour emerges in the case of magnetic adatoms, where, contrary to larger nanomagnets, the QST splitting is in some instances bigger than temperature and broadening. We analyze two different mechanisms for the renormalization of the QST splitting: Heisenberg exchange between different atoms, and Kondo exchange interaction with the substrate electrons. Sufficiently strong spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization. Importantly, we extract the strength of the Kondo exchange for various experiments on individual adatoms and construct a phase diagram for the classical to quantum transition.

Measuring the stellar wind parameters in IGR J17544-2619 and Vela X-1 constrains the accretion physics in supergiant fast X-ray transient and classical supergiant X-ray binaries

Context. Classical supergiant X-ray binaries (SGXBs) and supergiant fast X-ray transients (SFXTs) are two types of high-mass X-ray binaries (HMXBs) that present similar donors but, at the same time, show very different behavior in the X-rays. The reason for this dichotomy of wind-fed HMXBs is still a matter of debate. Among the several explanations that have been proposed, some of them invoke specific stellar wind properties of the donor stars. Only dedicated empiric analysis of the donors’ stellar wind can provide the required information to accomplish an adequate test of these theories. However, such analyses are scarce. Aims. To close this gap, we perform a comparative analysis of the optical companion in two important systems: IGR J17544-2619 (SFXT) and Vela X-1 (SGXB). We analyze the spectra of each star in detail and derive their stellar and wind properties. As a next step, we compare the wind parameters, giving us an excellent chance of recognizing key differences between donor winds in SFXTs and SGXBs. Methods. We use archival infrared, optical and ultraviolet observations, and analyze them with the non-local thermodynamic equilibrium (NLTE) Potsdam Wolf-Rayet model atmosphere code. We derive the physical properties of the stars and their stellar winds, accounting for the influence of X-rays on the stellar winds. Results. We find that the stellar parameters derived from the analysis generally agree well with the spectral types of the two donors: O9I (IGR J17544-2619) and B0.5Iae (Vela X-1). The distance to the sources have been revised and also agree well with the estimations already available in the literature. In IGR J17544-2619 we are able to narrow the uncertainty to d = 3.0 ± 0.2 kpc. From the stellar radius of the donor and its X-ray behavior, the eccentricity of IGR J17544-2619 is constrained to e< 0.25. The derived chemical abundances point to certain mixing during the lifetime of the donors. An important difference between the stellar winds of the two stars is their terminal velocities (ν∞ = 1500 km s-1 in IGR J17544-2619 and ν∞ = 700 km s-1 in Vela X-1), which have important consequences on the X-ray luminosity of these sources. Conclusions. The donors of IGR J17544-2619 and Vela X-1 have similar spectral types as well as similar parameters that physically characterize them and their spectra. In addition, the orbital parameters of the systems are similar too, with a nearly circular orbit and short orbital period. However, they show moderate differences in their stellar wind velocity and the spin period of their neutron star which has a strong impact on the X-ray luminosity of the sources. This specific combination of wind speed and pulsar spin favors an accretion regime with a persistently high luminosity in Vela X-1, while it favors an inhibiting accretion mechanism in IGR J17544-2619. Our study demonstrates that the relative wind velocity is critical in class determination for the HMXBs hosting a supergiant donor, given that it may shift the accretion mechanism from direct accretion to propeller regimes when combined with other parameters.

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.