The comment by O. Entin-Wohlman, A. Aharony, and Y. Utsumi, on our paper S. Varela, I. Zambrano, B. Berche, V. Mujica, and E. Medina, Phys. Rev. B 101, 241410(R) (2020) makes a few points related to the validity of our model, especially in the light
of the interpretation of Bardarsons theorem: in the presence of time reversal symmetry and for half-integral spin the transmission eigenvalues of the two terminal scattering matrix come in (Kramers) degenerate pairs. The authors of the comment first propose an ansatz for the wave function in the spin active region and go on to show that the resulting transmission does not show spin dependence, reasoning that spin dependence would violate Bardarsons assertion. Here we clearly show that the ansatz presented assumes spin-momentum independence from the outset and thus just addresses the spinless particle problem. We then find the appropriate eigenfunction contemplating spin-momentum coupling and show that the resulting spectrum obeys Bardarsons theorem. Finally we show that the allowed wavevectors are the ones assumed in the original paper and thus the original conclusions follow. We recognize that the Hamiltonian in our paper written in local coordinates on a helix was deceptively simple and offer the expressions of how it should be written to more overtly convey the physics involved. The relation between spin polarization and torque becomes clear, as described in our paper. This response is a very important clarification in relation to the implications of Bardarsons theorem concerning the possibility of spin polarization in one dimensional systems in the linear regime.
The illuminating role of differential forms in electromagnetism is seldom discussed in the classroom. It is the aim of this article to bring forth some of the relevant insights that can be learnt from a differential forms approach to E&M. The article
is self-contained in that no previous knowledge of forms is needed to follow it through. The effective polarization of the classical vacuum due to a uniform gravitational field and of the quantum vacuum in the Casimir effect are used to illustrate the power and easiness of interpretation of differential forms in dealing with electromagnetism in nontrivial situations. We hope that this article motivates the physics teacher to bring the subject of differential forms to the classroom.
Electron transfer (ET) in biological molecules such as peptides and proteins consists of electrons moving between well defined localized states (donors to acceptors) through a tunneling process. Here we present an analytical model for ET by tunneling
in DNA, in the presence of Spin-Orbit (SO) interaction, to produce a strong spin asymmetry with the intrinsic atomic SO strength in meV range. We obtain a Hamiltonian consistent with charge transport through $pi$ orbitals on the DNA bases and derive the behavior of ET as a function of the injection state momentum, the spin-orbit coupling and barrier length and strength. A highly consistent scenario arises where two concomitant mechanisms for spin selection arises; spin interference and differential spin amplitude decay. High spin filtering can take place at the cost of reduced amplitude transmission assuming realistic values for the spin-orbit coupling. The spin filtering scenario is completed by addressing the spin dependent torque under the barrier, with a consistent conserved definition for the spin current.
Tracing the evolution of specific topics is a subject area which belongs to the general problem of mapping the structure of scientific knowledge. Often bibliometric data bases are used to study the history of scientific topic evolution from its appea
rance to its extinction or merger with other topics. In this chapter the authors present an analysis of the academic response to the disaster that occurred in 1986 in Chornobyl (Chernobyl), Ukraine, considered as one of the most devastating nuclear power plant accidents in history. Using a bibliographic database the distributions of Chornobyl-related papers in different scientific fields are analysed, as are their growth rates and properties of co-authorship networks. Elements of descriptive statistics and tools of complex-network theory are used to highlight interdisciplinary as well as international effects. In particular, tools of complex-network science enable information visualization complemented by further quantitative analysis. A further goal of the chapter is to provide a simple pedagogical introduction to the application of complex-network analysis for visual data representation and interdisciplinary communication.
We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length $xi_parallel$ in the direction along defec
ts, and a perpendicular correlation length $xi_perp$ in the direction perpendicular to the lines. Both $xi_parallel$ and $xi_perp$ diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents $ u_parallel$ and $ u_perp$ take different values. This property is specific for anisotropic scaling and the ratio $ u_parallel/ u_perp$ defines the anisotropy exponent $theta$. Estimates of quantitative characteristics of the critical behaviour for such systems were only obtained up to now within the renormalization group approach. We report a study of the anisotropic scaling in this system via Monte Carlo simulation of the three-dimensional system with Ising spins and non-magnetic impurities arranged into randomly distributed parallel lines. Several independent estimates for the anisotropy exponent $theta$ of the system are obtained, as well as an estimate of the susceptibility exponent $gamma$. Our results corroborate the renormalization group predictions obtained earlier.
We discuss the Pauli Hamiltonian within a ${SU(2)}$ gauge theory interpretation, where the gauge symmetry is broken. This interpretation carries directly over to the structural inversion asymmetric spin-orbit interactions in semiconductors and offers
new insight into the problem of spin currents in the condensed matter environment. The central results is that symmetry breaking leads to zero spin conductivity in contrast to predictions of Gauge symmetric treatments. Computing the translation operator commutation relations comprising the simplest possible structural inversion asymmetry due to an external electric field, we derive a new condition for orbit quantization. The relation between the topological nature of this effect is consistent with our non-Abelian gauge symmetry breaking scenario.
