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]
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