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 back-action of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both, read and record classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where spin polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom

Activated escape of periodically modulated systems

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor $\nu$ in the period-averaged escape rate depends on $A$ nonmonotonically. Near the bifurcation amplitude $A_c$ it scales as $\nu\propto (A_c-A)^{\zeta}$. We identify three scaling regimes, with $\zeta = 1/4, -1$, and 1/2

Kramers-Kronig, Bode, and the meaning of zero

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea

Topological Modes in Dual Lattice Models

Lattice gauge theory with gauge group $Z_{P}$ is reconsidered in four dimensions on a simplicial complex $K$. One finds that the dual theory, formulated on the dual block complex $\hat{K}$, contains topological modes which are in correspondence with the cohomology group $H^{2}(\hat{K},Z_{P})$, in addition to the usual dynamical link variables. This is a general phenomenon in all models with single plaquette based actions; the action of the dual theory becomes twisted with a field representing the above cohomology class. A similar observation is made about the dual version of the three dimensional Ising model. The importance of distinct topological sectors is confirmed numerically in the two dimensional Ising model where they are parameterized by $H^{1}(\hat{K},Z_{2})$.Comment: 10 pages, DIAS 94-3

Berry phase, topology, and diabolicity in quantum nano-magnets

A topological theory of the diabolical points (degeneracies) of quantum magnets is presented. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the the missing diabolical points for Fe8 molecular magnets is clarified. A new method is also developed to provide a simple interpretation, in terms of destructive interferences due to the Berry phase, of the complete set of diabolical points found in biaxial systems such as Fe8.Comment: 4 pages, 3 figure

Systematic computation of crystal field multiplets for X-ray core spectroscopies

We present a new approach to computing multiplets for core spectroscopies, whereby the crystal field is constructed explicitly from the positions and charges of surrounding atoms. The simplicity of the input allows the consideration of crystal fields of any symmetry, and in particular facilitates the study of spectroscopic effects arising from low symmetry environments. The interplay between polarization directions and crystal field can also be conveniently investigated. The determination of the multiplets proceeds from a Dirac density functional atomic calculation, followed by the exact diagonalization of the Coulomb, spin-orbit and crystal field interactions for the electrons in the open shells. The eigenstates are then used to simulate X-ray Absorption Spectroscopy and Resonant Inelastic X-ray Scattering spectra. In examples ranging from high symmetry down to low symmetry environment, comparisons with experiments are done with unadjusted model parameters as well as with semi-empirically optimized ones. Furthermore, predictions for the RIXS of low-temperature MnO and for Dy in a molecular complex are proposed.Comment: Accepted for publication in Phys. Rev.

Nonequilibrium fluctuation induced escape from a metastable state

Based on a simple microscopic model where the bath is in a non-equilibrium state we study the escape from a metastable state in the over-damped limit. Making use of Fokker-Planck-Smoluchowski description we derive the time dependent escape rate in the non-stationary regime in closed analytical form which brings on to fore a strong non-exponential kinetic of the system mode.Comment: 4 pages, no figures, EPJ class file include

Духовне життя українців-галичан часів ІІ Речі Посполитої

У статті висвітлюється суспільно-політичне становище в Західній Україні міжвоєнного періоду, дається оцінка тогочасним українським релігійним течіям, які проявлялися, з одно- го боку, у подальшому розмежуванні сил, а з іншого, – у їх консолідації на ґрунті духовності за допомогою Греко-католицької церкви. Протистояння полонізації та асиміляції викристалізовувало в менталітеті українців-галичан духовність, яка згуртовувала мільйонні селянські маси.The article analyses social and political life in Western Ukraine within the inter-war period. Ukrainian religious movements of the period are being evaluated. The author concludes that on the one hand those movements resulted in separation of forces, but on the other hand they caused consolidation of efforts on the basis of Greek Catholic religious principles. The opposition of expansion and assimilation have molded spiritual basis of the Galician Ukrainian mentality that have joined millions of rural citizens together

The WKB Approximation without Divergences

In this paper, the WKB approximation to the scattering problem is developed without the divergences which usually appear at the classical turning points. A detailed procedure of complexification is shown to generate results identical to the usual WKB prescription but without the cumbersome connection formulas.Comment: 13 pages, TeX file, to appear in Int. J. Theor. Phy

Nonequilibrium Atom-Dielectric Forces Mediated by a Quantum Field

In this paper we give a first principles microphysics derivation of the nonequilibrium forces between an atom, treated as a three dimensional harmonic oscillator, and a bulk dielectric medium modeled as a continuous lattice of oscillators coupled to a reservoir. We assume no direct interaction between the atom and the medium but there exist mutual influences transmitted via a common electromagnetic field. By employing concepts and techniques of open quantum systems we introduce coarse-graining to the physical variables - the medium, the quantum field and the atom's internal degrees of freedom, in that order - to extract their averaged effects from the lowest tier progressively to the top tier. The first tier of coarse-graining provides the averaged effect of the medium upon the field, quantified by a complex permittivity (in the frequency domain) describing the response of the dielectric to the field in addition to its back action on the field through a stochastic forcing term. The last tier of coarse- graining over the atom's internal degrees of freedom results in an equation of motion for the atom's center of mass from which we can derive the force on the atom. Our nonequilibrium formulation provides a fully dynamical description of the atom's motion including back action effects from all other relevant variables concerned. In the long-time limit we recover the known results for the atom-dielectric force when the combined system is in equilibrium or in a nonequilibrium stationary state.Comment: 24 pages, 2 figure