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

Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets

The manifestation of the spin-wave interaction in the low-temperature series of the partition function has been investigated extensively over more than seven decades in the case of the three-dimensional ferromagnet. Surprisingly, the same problem regarding ferromagnets in two spatial dimensions, to the best of our knowledge, has never been addressed in a systematic way so far. In the present paper the low-temperature properties of two-dimensional ideal ferromagnets are analyzed within the model-independent method of effective Lagrangians. The low-temperature expansion of the partition function is evaluated up to two-loop order and the general structure of this series is discussed, including the effect of a weak external magnetic field. Our results apply to two-dimensional ideal ferromagnets which exhibit a spontaneously broken spin rotation symmetry O(3) $\to$ O(2) and are defined on a square, honeycomb, triangular or Kagom\'e lattice. Remarkably, the spin-wave interaction only sets in at three-loop order. In particular, there is no interaction term of order $T^3$ in the low-temperature series for the free energy density. This is the analog of the statement that, in the case of three-dimensional ferromagnets, there is no interaction term of order $T^4$ in the free energy density. We also provide a careful discussion of the implications of the Mermin-Wagner theorem in the present context and thereby put our low-temperature expansions on safe grounds.Comment: 24 pages, 3 figure

Driven classical diffusion with strong correlated disorder

We analyze one-dimensional motion of an overdamped classical particle in the presence of external disorder potential and an arbitrary driving force F. In thermodynamical limit the effective force-dependent mobility mu(F) is self-averaging, although the required system size may be exponentially large for strong disorder. We calculate the mobility mu(F) exactly, generalizing the known results in linear response (weak driving force) and the perturbation theory in powers of the disorder amplitude. For a strong disorder potential with power-law correlations we identify a non-linear regime with a prominent power-law dependence of the logarithm of mu(F) on the driving force.Comment: 4 pages, 2 figures include

A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix

In time reversal symmetric systems with half integral spins (or more concretely, systems with an antiunitary symmetry that squares to -1 and commutes with the Hamiltonian) the transmission eigenvalues of the scattering matrix come in pairs. We present a proof of this fact that is valid both for even and odd number of modes and relies solely on the antisymmetry of the scattering matrix imposed by time reversal symmetry.Comment: 2 page

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.

Insight into Resonant Activation in Discrete Systems

The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a non-monotonic behavior of the frequency dependent first passage time probability density function (pdf). An analytical expression for the resonant frequency is introduced, which, together with numerical results, helps understand the RAP behavior in the space spanned by the transition rates for the case of reflecting and absorbing boundary conditions. The limited range of system parameters for which the RAP occurs is discussed. We show that a minimum and a maximum in the mean first passage time (MFPT) can be obtained when both boundaries are absorbing. Relationships to some biological systems are suggested.Comment: 5 pages, 5 figures, Phys. Rev. E., in pres

Significant g-factor values of a two-electron ground state in quantum dots with spin-orbit coupling

The magnetization of semiconductor quantum dots in the presence of spin-orbit coupling and interactions is investigated numerically. When the dot is occupied by two electrons we find that a level crossing between the two lowest many-body eigenstates may occur as a function of the spin-orbit coupling strength. This level crossing is accompanied by a non-vanishing magnetization of the ground-state. Using first order perturbation theory as well as exact numerical diagonalization of small clusters we show that the tendency of interactions to cause Stoner-like instability is enhanced by the SO coupling. The resulting g-factor can have a significant value, and thus may influence g-factor measurements. Finally we propose an experimental method by which the predicted phenomenon can be observed.Comment: 7+ pages, 7 figure

Teaching and learning problem solving in science. Part II: Learning problem solving in a thermodynamics course

This paper examines important new aspects and results related to an experimental new course

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