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Conceptualizing planetary habitability depends on understanding how living organisms originated and what features of environments are essential to foster abiogenesis. Estimates of the abundance of life's building blocks are confounded by incomplete knowledge of the role of chirality and racemization in organic compounds in the origination of living organisms. Chirality is an essential feature of enzymes as well as many lock-and-key type structures. There are four known processes that can act on complex organic molecules to promote racemization for abiogenesis: quantum-tunneling effects; selection via interaction with circularly polarized light (CPL); templating processes; and interactions with electrical and magnetic (EM) fields. These occur in different places, respectively: cold interstellar space; regions of space with energetic photons, dust and/or magnetic fields; and mineral surfaces (for both templating and EM fields). Chirality as a feature of terrestrial life suggests neither a special place for local development of homochirality nor for extra-terrestrial enrichment and delivery. The presence of these molecules in three competing scenarios for life's origin - chemical gardens, geothermal fields, and ice substrates - relies on a framework of hypothesis and estimation. An easily-modified worksheet is included in the supplemental material that allows a user to generate different scenarios and data related to the distribution of chiral organic molecules as building blocks for living organisms within the galaxy. A simple hypothetical mechanism for planetary magnetic field reversals, based on a high-density plasma inner core, is also presented as a means to aid in estimating field polarity and hence the orientation of racemization processes based on planetary magnetic fields., Originally written in consultation with Richard Gordon and Alexei Sharov who were putting together the Elsevier volume "Habitability of the Universe Before Earth."

A magnetic plane, exchange coupled to an electron gas, generates a spin polarization and in the nonlinear theory also a charge distribution. The corresponding electrostatic energy per unit surface is evaluated. For an electron gas at metallic densities this turns out to be negligible, while it must be taken into account in dilute degenerate semiconductors.

Using planar Dirac \ensuremath{\delta} functions to describe the coupling of magnetic layers to an electron gas, the interaction between the layers is calculated. Both the bound and free states give contributions which are shaped by the range of the bound states. Due to a remarkable cancellation of terms the combined result does not show this shape. In fact, it differs appreciably from the weak-coupling limit only when the binding energy of the bound states is comparable or larger than the Fermi energy. \textcopyright{} 1996 The American Physical Society.

Exact expressions for the spin polarization due to a point field have been obtained for various inhomogeneous situations. The presence of boundaries or potentials modifies the nodes and amplitudes of the polarization, which determines the coupling between ion spins or nuclear magnetic moments in metals. For the half-space both in three and one dimensions, the analytic solution contains the usual Ruderman-Kittel-Kasuya-Yosida polarization around the source plus a polarization wave originating from the mirror point, although with the same phase at the border; there both are canceled by a third term. The case of a slab in three and one dimensions has been treated. A one-dimensional model with a reflectionsless localized potential with one bound state proved to be tractable. It is shown that the integrated polarization is given by the probability densities of the electron states at the position of the field summed over the Fermi surface.

The basis of dry friction is discussed using an independent oscillator model with longitudinal motion. This sample system is treated both numerically and with analytical methods. At vanishing velocity a sliding dry friction force is calculated which is smaller than the pinning force. At finite but not too large velocities the system displays bifurcation, chaotic motion, resonances at fractional and multiple frequencies of the oscillator, and hysteresis. Dry friction results from these complicated features. This force varies rapidly with velocity within this range, however, with a roughly constant mean value.

It is shown that the spin polarization of the electron cloud in thermal equilibrium with a ferromagnetic surface decays within a few Angstroms from the surface. This explains the vanishing spin polarization found in thermoemission from Ni and Fe by Vaterlaus et al. [Phys. Rev. Letters 65, 3041 (1990)].

The fluorescence lifetime of ${\mathrm{Cr}}^{3+}$ in ${\mathrm{GdAlO}}_{3}$ was measured in the range 1.8\char21{}4.2 K in magnetic fields up to 6 T. The results show a remarkable dependence of the transition probabilities on magnetic order. A model based on the exchange interaction between ${\mathrm{Cr}}^{3+}$ in highly excited states and the ${\mathrm{Gd}}^{3+}$ ions is proposed.

The exact static solutions of the Landau-Lifshitz equations for the magnetization, which have been identified as describing nucleation centers for the magnetization reversal in ferromagnets, are compared with those of phenomenological models of spherical and cylindrical symmetry. It is found that the latter have higher critical fields.

On etablit une solution plane generale de ces equations. De la, on evalue l'evolution dans le temps de petites deviations planes de forme arbitraire. On developpe en detail l'exemple d'une paroi se deplacant dans un champ magnetique brusquement eteint. Analyse des effets d'un champ magnetique dependant de l'espace et du temps et des modifications de l'anisotropie

Since dissipation requires motion, the velocity‐independent friction of macroscopic systems must result from quick motions of some of its components. A model of coupled spins, some of which have irregular anisotropy directions, presents velocity independent loss. During a collective motion of the spin ensemble, an irregular spin can fall into its potential minimum, from which it is subsequently dragged out again. The effect is pronounced for a range of the ratio between the anisotropy and interatomic exchange coupling constants which is typical for rare‐earth ions.

Dry friction is introduced into the Landau-Lifshitz equations. Numerical simulations show sustained motions or transitions to rest in a critical state. Hysteresis and Barkhausen noise can be modeled with simple structures. Dry friction in the Landau-Lifshitz equation can be a useful element in the modeling of ferromagnets. >

The relation between the potential r −β and the asymptotic behavior of the eigenvalues of the ordinary wave equation for space dimension N → ∞ is found. An analogous relation is discussed when the wave equation involves an iterated Laplacian. A criterion is given to determine when a potential should be considered singular, depending on the space dimension and the degree of iteration of the Laplacian. Finally, a modification is suggested for the approximation proposed by Witten which sensibly improves the results for the ground state energy of the hydrogen and helium atoms.

The Ruderman-Kittel interaction in one dimension is presented for an arbitrary coupling constant, as a by-product of previous considerations for a problem with planar symmetry in three dimensions. For coupling constants which are smaller than or even comparable to the Fermi energy, the interaction oscillates as a function of distance like the perturbation result, however, with a reduced amplitude. The interaction between two parallel magnetic lines in two dimensions is also discussed. \textcopyright{} 1996 The American Physical Society.

For a ferromagnet with exchange, uniaxial anisotropy, demagnetizing field, and an external magnetic field directed oppositely to the magnetization, the Landau-Lifshitz equations have time-independent, planar, local solutions of the Bloch and N\'eel type. These solutions are unstable. Analogous to a water droplet in supersaturated vapor for which a radius of unstable equilibrium exists, the solution for a given magnetic field is the configuration of smallest energy through which a magnetization reversal can nucleate.

The effect of critical fluctuations on the resistivity near magnetic and order-disorder phase transitions is discussed. It is shown that in all magnetic and electronic systems the asymptotic high-momentum spin correlation functions dominate the temperature dependence of the resistivity sufficiently close to the transition. The dependence on the parameters of the system of the critical behavior and the way in which this behavior is approached is discussed in detail. In particular, the importance of the transition from a classical to a proper critical behavior, for the interpretation of experimental results, is emphasized, and recent renormalization-group results for the form of the correlation functions are utilized. For semiconductors the effects of fluctuations on the band gap are also calculated. It is suggested that the Fisher-Langer relation between the temperature derivative of the resistivity and the specific heat should be valid over a considerable temperature range outside the critical region. Theoretical predictions are compared with available experimental results on the resistivity and band gaps. It is shown that these results can all be understood, at least qualitatively, in the Born approximation by using only the most general known properties of the system.

Films consisting of fine Ni grains (\ensuremath{\sim}50 \AA{}) dispersed in ${\mathrm{SiO}}_{2}$ exhibit a large negative magnetoresistance. The effect is accounted for by the field dependence of the magnetic exchange energy, associated with tunneling of electrons between neighboring grains whose magnetic moments are not parallel.

Scattering experiments with spin-polarized electron beams of 100-1000 eV on magnetic materials are now feasible. In view of this the spin-dependent part of the scattering cross section is calculated in the Born approximation for a ferromagnet in the spin-wave regime. It is evaluated as a function of momentum transfer for Ni and Fe using self-consistent potentials.

The anisotropy of the $^{19}\mathrm{F}$ nuclear-spin-lattice relaxation time in Ca${\mathrm{F}}_{2}$: ${\mathrm{U}}^{3+}$ has been measured at 300 and 77 K. The results are accounted for in terms of a proposed model which incorporates the anisotropic nature of the coupling between the nuclei and the impurity spin. This model applies, in the fast-diffusion regime, to those cases in which the usually defined diffusion radius is so small that nuclear-spin diffusion can proceed up to the nearest neighbors to the impurity.

The effect of critical fluctuations on the electrical resistivity of magnetic materials is discussed in detail. The temperature and magnetic field dependences of this critical resistivity $\ensuremath{\rho}(T, H)$ are given for both cases: when the critical temperature ${T}_{c}$ is approached from above and when it is approached from below. The results obtained apply to the two basic classes of magnetic materials: ferromagnets and antiferromagnets, as well as to the two basic electronic systems: metals and semiconductors. The present work is founded on the conclusion that close enough to ${T}_{c}$ the critical resistivity of all systems has a magnetic-energy-like behavior. This behavior extends father away from ${T}_{c}$ for all systems except for ferromagnetic semiconductors. It is shown that the critical magnetoresistance, $\ensuremath{\Delta}\ensuremath{\rho}=\ensuremath{\rho}(T, H)\ensuremath{-}\ensuremath{\rho}(T, 0)$ is negative except for antiferromagnetic semiconductors. $\ensuremath{\Delta}\ensuremath{\rho}$ is found to be peaked at ${T}_{c}$ for all systems but it never diverges as a function of temperature or field. The results are expressed in terms of power-law dependences of $\ensuremath{\Delta}\ensuremath{\rho}$ on $T\ensuremath{-}{T}_{c}$ and $H$ for all the different material classes and for all interesting temperature regions. The corresponding powers, under various conditions, are combinations of the well-known critical exponents, $\ensuremath{\alpha}$, $\ensuremath{\beta}$, $\ensuremath{\gamma}$, $\ensuremath{\delta}$, and $\ensuremath{\nu}$. In the mean-field regime the powers are predicted to be those of the critical regime except that the classical values of these exponents have to be used. The present results predict more details of the critical resistivity than can be deduced from the existing experimental data. However, the experimental data available are in accord with the results. In the case of antiferromagnetic metals, the present work explains the features of the magnetoresistance in the rare-earth metals, features that have not been understood before. It is suggested that by proper fit of critical resistance and magnetoresistance data to the power-law behaviors predicted here, critical exponents can be deduced. Recent demonstrations of such fits show that this is indeed feasible.

For a ferromagnet without anisotropy, which may be a spin-(1/2 lattice or an amorphous substance, the distribution of magnetization depends on the shape of the sample. The phenomenological equations of micromagnetics which contain the exchange energy and the magnetic energy are generalized to allow for a change in the magnitude of the magnetization. This permits the treatment of line singularities in the field-free configurations with circular concentric magnetization lines. For an ellipsoid with a rotation axis the free energy of such an arrangement is compared with that of the homogeneously magnetized sample, which is the stable form for a sufficiently small sample (roughly with a radius \ensuremath{\le}20 lattice constants).

The spin-lattice relaxation of a Kramer's doublet arising from as-like ground state in any crystal symmetry is discussed. It is shown that in the cubic case the relaxation rate for one-phonon processes can be expressed in terms of the staticg value and its rate of change under dilatation. A general formalism and its application to the case ofF centres in alkali halides are given.

When a ferromagnetic is heated from a temperature T0 to T in a time which is short compared to the relaxation time of the magnetisation, the work function of the majority carriers is smaller than that of the minority carriers by u mu B. mu B is the Bohr magneton and u is a magnetic field obtained from the magnetisation state function through M(T0,0)=M(T,u).

Fowler's hypothesis commonly used to interpret results of photoemission into the vacuum has been extended to deal with the problem of internal photoemission. This leads to the empirical relation $Y\ensuremath{\propto}{(E\ensuremath{-}{E}_{t})}^{2}$ between the quantum efficiency $Y$ and the photon energy $E$, currently used to interpret hole photoemission experiments. ${E}_{t}$ is the threshold energy for photoemission. Various cases of internal electron and hole photoemission between metals and semiconductors are discussed.

The dielectric constant of a liquid metal is calculated with the temperature Green's functions technique in the frequency rangeωPOpen image in new windowΩ≫ξ0 andΩOpen image in new windowξ0, whereξ0 is the resistivity relaxation frequency, andωP the plasma frequency. The electron scattering is described in the Born approximation using the empirical dynamical structure factor ofVan Hove and a screened electron-ion pseudopotential. At low frequencies (ħΩOpen image in new windowℰF=Fermi energy) the result can be identified with Drude's classical formula introducing an effective number of electrons per ion. ForħΩ∼ℰF, however, the result differs in form.

The equation for the quasistatic image potential induced by a charge is derived for a semiinfinite medium with wavevector and frequency dependent dielectric function. The equation is solved exactly for a dielectric function which is local in the direction perpendicular to the surface. This result is applied to the case of a metal, semiconductor and insulator; the Schottky effect is discussed.

The reduction of the Pauli susceptibility due to a perturbing Hamiltonian which allows for spin-flip processes is calculated. The results are applied to the spin-orbit coupling in liquid metals, and the exchange interaction in magnetic metals at high temperatures and near the Curie point. The corrections are small.

It is shown that, contrary to what had been found-owing to an excessive simplification of Fowler's hypothesis on photoemission-the behavior of the quantum yield $Y$ versus photon energy $E$ for internal photoemission from a semiconductor into a semiconductor has the same power-law dependence close to the threshold ${E}_{t}$ for electron and hole injection, namely, $Y \ensuremath{\propto} {(E\ensuremath{-}{E}_{t})}^{\frac{3}{2}}$.

We show that a proper description of the temperature dependence of the spin-lattice relaxation rate of low-spin hemoproteins and ferredoxin requires that both the fractal structure of the protein backbone (polypeptide chain) and the cross connections (H bridges) between segments of the folded chain be taken into account. Within this picture the fracton dimensionality ${d}_{\mathrm{fr}}$ (recently introduced by Alexander and Orbach), the fractal dimensionality ${d}_{f}$, and the experimental noninteger exponent $n$ of Stapleton et al. (spin-lattice relaxation rate $\frac{1}{{T}_{1}}\ensuremath{\propto}{T}^{n}$) become satisfactorily consistent.

High-spin metastable atomic beams of high density and extremely small divergence can be produced by electron capture during grazing-angle scattering of ion beams at ferromagnetic surfaces. This can be used to generate a long-lived reservoir of Li 1s2s2p /sup 4/P/sub 5/2//sup ts0/ with enough density of metastables so that after laser-induced transfer to Li 1s2p/sup ts2/P strong lasing at 207 A should occur. This novel technique can also be used to produce a variety of other metastables known as potential candidates for lasing at shorter wavelengths.

The spin flip cross section for an electron which interacts by exchange in going through a layer of magnetic impurities can be greatly enhanced in a situation of resonant transmission. We describe this effect by a one‐dimensional model which contains the essential physics and can be exactly solved. Besides its eventual application in problems related to the emission and reflection of spin polarized electrons, this model provides a nice and instructive quantum mechanical example.

The shift of the band gap in ferromagnetic semiconductors due to magnetization and critical fluctuations is determined in detail using recent results of the theory of critical phenomena. The band shift ΔE is expressed in terms of the reduced magnetic field h and the reduced temperature t. The dominant contributions to ΔE are found to be the following: In the critical region, both above and below the critical temperture Tc, ΔE∝−h1/δ−Bh1−α)/βδ for large h. For small h, ΔE∝ (−‖t‖β−b0‖t‖1−α) for T

As suggested by an extension of the supersymmetric Wess-Zumino model to higher dimensions we consider the eigenvalue problem for the Hamiltonian p4+V(r), where V is either a δ function or the Coulomb potential (which happens to be the Green's function for the bilaplacian in five dimensions)., Facultad de Ciencias Exactas

Recently it has been shown that the most efficient conduction-electron-spin relaxation mechanism in Al is associated with scattering events to and from certain portions (ridges) of the Fermi surface where the spin-orbit interaction leads to electron wave functions which have a substantial admixture of spin-up and spin-down components. Those ridges arise from intersections of the Fermi surface with Brillouin boundaries and therefore this relaxation mechanism must be common to and prevail in the simple (nontransition) polyvalent metals. Here, we show that in fact this mechanism accounts for the spin-flip processes responsible for the finite Knight shift observed in small Sn and Pb superconducting particles.