We develop a general theory of electric polarization in crystals with inhomogeneous order. We show that the inhomogeneity-induced polarization can be classified into two parts: a perturbative contribution stemming from a correction to the basis functions and a topological contribution described in terms of the Chern-Simons form of the Berry gauge fields. The latter is determined up to an uncertainty quantum, which is the second Chern number in appropriate units. Our theory provides an exhaustive link between microscopic models and the macroscopic polarization.
Using variational mean-field theory, many-body dissipative effects on the threshold law for quantum sticking and reflection of neutral and charged particles are examined. For the case of an ohmic bosonic bath, we study the effects of the infrared divergence on the probability of sticking and obtain a non-perturbative expression for the sticking rate. We find that for weak dissipative coupling α, the low energy threshold laws for quantum sticking are modified by an infrared singularity in the bath. The sticking probability for a neutral particle with incident energy E → 0 behaves asymptotically as s ∼ E (1+α)/2(1−α) ; for a charged particle, we obtain s ∼ E α/2(1−α) . Thus, "quantum mirrors" -surfaces that become perfectly reflective to particles with incident energies asymptotically approaching zero-can also exist for charged particles.
We present an exact solution of a one-dimensional (1D) model: a particle of incident energy E colliding with a target which is a 1D harmonic "solid slab" with N atoms in its ground state; the Hilbert space of the target is restricted to the (N + 1) states with zero or one phonon present. For the case of a shortrange interaction V(z) between the particle and the surface atom supporting a bound state, an explicit nonperturbative solution of the collision problem is obtained. For finite and large N, there is no true sticking but only so-called Feshbach resonances. A finite sticking coefficient s(E) is obtained by introducing a small phonon decay rate g and letting N~00. Our main interest is in the behavior of s (E) as E~O. For a short-range V(z), we find s(E)-E' ', regardless of the strength of the particle-phonon coupling. However, if V(z) has a Coulomb z tail, we find s (E)~a, where 0 & a & 1. [A fully classical calculation gives s(E)~1 in both cases. ] We conclude that the same threshold laws apply to 3D systems of neutral and charged particles, respectively. In an appendix we elucidate the nature of sticking by the behavior of a wave packet incident on a finite N target. tion of a "compound nucleus"' in nucleon-nucleon collisions. We find that for an interaction potential of finite range or a z tail, regardless of its strength, s(E)~E ' for small E. However, for potentials with attractive Coulomb tails, we find, unlike Ref. 11 that, for small E, s (E)~a where 0 & a & 1. 46 4921
A continuum model for low-energy physisorption on a membrane under tension is proposed and studied with variational mean-field theory. A discontinuous change in the energy-dependent sticking coefficient is predicted under certain conditions. This singularity is a result of the bosonic orthogonality catastrophe of the vibrational states of the membrane. The energy-dependent sticking coefficient is predicted to have exponential scaling in 1/E above the singularity. The application of this model to the quantum sticking of cold hydrogen to suspended graphene is discussed. The model predicts that a beam of atomic hydrogen can be completely reflected by suspended graphene at ultralow energies.
We study the infrared dynamics of low-energy atoms interacting with a sample of suspended graphene at finite temperature. The dynamics exhibits severe infrared divergences order by order in perturbation theory as a result of the singular nature of low-energy flexural phonon emission. Our model can be viewed as a two-channel generalization of the independent boson model with asymmetric atom-phonon coupling. This allows us to take advantage of the exact non-perturbative solution of the independent boson model in the stronger channel while treating the weaker one perturbatively. In the low-energy limit, the exact solution can be viewed as a resummation (exponentiation) of the most divergent diagrams in the perturbative expansion. As a result of this procedure, we obtain the atom's Green function which we use to calculate the atom damping rate, a quantity equal to the quantum sticking rate. A characteristic feature of our results is that the Green's function retains a weak, infrared cutoff dependence that reflects the reduced dimensionality of the problem. As a consequence, we predict a measurable dependence of the sticking rate on graphene sample size. We provide detailed predictions for the sticking rate of atomic hydrogen as a function of temperature and sample size. The resummation yields an enhanced sticking rate relative to the conventional Fermi golden rule result (equivalent to the one-loop atom self-energy), as higher-order processes increase damping at finite temperature. arXiv:1603.03476v2 [cond-mat.mes-hall]
A definition for structure of atomic scale systems is introduced which extends the typical crystallographic description to include elements of the total charge density. We argue that the mechanical properties of intermetallic alloys are related to this extended structure. These relationships have their origin in the nature of the charge redistribution accompanying strain. The direction of this charge redistribution is determined solely by the extended structure, while its magnitude can be correlated with a quantification of this extended structure. We demonstrate these facts by determining the extended structure and nature of the charge redistribution resulting from uniaxial strain for two alloys with the L10 structure: CuAu and TiAl. While these alloys share the same crystallographic structure, their extended structures are different, with CuAu possessing the same extended structure as the allotropic fcc metals while TiAl does not. These different extended structures give rise to different charge redistributions, which are argued to be related to the intrinsically ductile behavior of CuAu and the tendency for TiAl to fail transgranularly.
The emerging discipline of computational materials design (CMD) seeks to speed materials development by using computers to calculate the properties of substances that have yet to be made in the laboratory. In this way, computation could one day supplant time-consuming experimental empiricism, greatly accelerating the pace of technological advancement [1]. Over the past twenty years, the potential of CMD has attracted hundreds of millions of dollars in investment. In some ways, this investment has paid dividends by providing the ability to perform computer simulations of ever-greater sophistication. However, these new capabilities have had less influence on materials development than its supporters might have predicted; other than a few small molecules [3], not a single material has been computer-designed. We suggest that the path towards achieving the ultimate goals of this still immature science is in need of a midcourse adjustment.Both scientists and society-at-large have a stake in seeing CMD reach its full potential. Such a science could dramatically and radically alter the way technologies develop, consequently liberating the pace of technological advance from its current dependence on the unpredictability of trial-and-error experiments. For millennia, technologies were born only when a new material with novel properties became available. During the past century, science developed a limited capability to design materials, but we are still too dependent on serendipity. In just the past twenty years, researchers have stumbled upon high-temperature superconductors, conducting polymers, quasicrystals, and nanotubes-all possessing properties that, before their discovery, conventional wisdom deemed impossible. Now, these materials are being explored as the foundation of a host of new twenty-firstcentury technologies. But a full science of materials design would enable materials such as these to be designed in response to the needs of technology-that is, the path should lead from properties to materials -instead of the reverse.Our primitive abilities to design materials have developed concurrently with a fundamental understanding of the laws of physics and chemistry that govern the properties of materials. Although these laws were fully elucidated more than seventy-five years ago, they gave rise to equations that-for any real-world material-were much too difficult to solve. Yet, two advances have now made numerical solutions practicable: (1) the relentless progress in digital computers that have boosted processing speed by more than five orders of magnitude over the past twenty years; and (2) the improvements in computational methods. Now, there is a growing consensus that a general science of CMD will one day be achievable.In the view of many, the structure for this new science will rest upon the foundation provided by solving the equations of quantum mechanics, which provide the thermodynamic rationale to account for all materials properties. Accordingly, beginning in the mid 1980s and continuing to this day, U....
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