Fixed-point elimination in the intuitionistic propositional calculus

It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras are not complete as lattices. The reason is that these extremal fixed-points are definable by formulas of the IPC. Consequently, the $\mu$-calculus based on intuitionistic logic is trivial, every $\mu$-formula being equivalent to a fixed-point free formula. We give in this paper an axiomatization of least and greatest fixed-points of formulas, and an algorithm to compute a fixed-point free formula equivalent to a given $\mu$-formula. The axiomatization of the greatest fixed-point is simple. The axiomatization of the least fixed-point is more complex, in particular every monotone formula converges to its least fixed-point by Kleene's iteration in a finite number of steps, but there is no uniform upper bound on the number of iterations. We extract, out of the algorithm, upper bounds for such n, depending on the size of the formula. For some formulas, we show that these upper bounds are polynomial and optimal

Kondo Insulator to Semimetal Transformation Tuned by Spin-Orbit Coupling

Recent theoretical studies of topologically nontrivial electronic states in Kondo insulators have pointed to the importance of spin-orbit coupling (SOC) for stabilizing these states. However, systematic experimental studies that tune the SOC parameter $\lambda_{\rm{SOC}}$ in Kondo insulators remain elusive. The main reason is that variations of (chemical) pressure or doping strongly influence the Kondo coupling $J_{\text{K}}$ and the chemical potential $\mu$ -- both essential parameters determining the ground state of the material -- and thus possible $\lambda_{\rm{SOC}}$ tuning effects have remained unnoticed. Here we present the successful growth of the substitution series Ce$_3$Bi$_4$(Pt$_{1-x}$Pd$_x$)$_3$ ($0 \le x \le 1$) of the archetypal (noncentrosymmetric) Kondo insulator Ce$_3$Bi$_4$Pt$_3$. The Pt-Pd substitution is isostructural, isoelectronic, and isosize, and therefore likely to leave $J_{\text{K}}$ and $\mu$ essentially unchanged. By contrast, the large mass difference between the $5d$ element Pt and the $4d$ element Pd leads to a large difference in $\lambda_{\rm{SOC}}$, which thus is the dominating tuning parameter in the series. Surprisingly, with increasing $x$ (decreasing $\lambda_{\rm{SOC}}$), we observe a Kondo insulator to semimetal transition, demonstrating an unprecedented drastic influence of the SOC. The fully substituted end compound Ce$_3$Bi$_4$Pd$_3$ shows thermodynamic signatures of a recently predicted Weyl-Kondo semimetal.Comment: 6 pages, 5 figures plus Supplemental Materia

Surface effects on the Mott-Hubbard transition in archetypal V2_2O3_3

We present an experimental and theoretical study exploring surface effects on the evolution of the metal-insulator transition in the model Mott-Hubbard compound Cr-doped V$_2$O$_3$. We find a microscopic domain formation that is clearly affected by the surface crystallographic orientation. Using scanning photoelectron microscopy and X-ray diffraction, we find that surface defects act as nucleation centers for the formation of domains at the temperature-induced isostructural transition and favor the formation of microscopic metallic regions. A density functional theory plus dynamical mean field theory study of different surface terminations shows that the surface reconstruction with excess vanadyl cations leads to doped, and hence more metallic surface states, explaining our experimental observations.Comment: 5 pages, 4 figure

Unification Theory of Angular Magnetoresistance Oscillations in Quasi-One-Dimensional Conductors

We present a unification theory of angular magnetoresistance oscillations, experimentally observed in quasi-one-dimensional organic conductors, by solving the Boltzmann kinetic equation in the extended Brillouin zone. We find that, at commensurate directions of a magnetic field, resistivity exhibits strong minima. In two limiting cases, our general solution reduces to the results, previously obtained for the Lebed Magic Angles and Lee-Naughton-Lebed oscillations. We demonstrate that our theoretical results are in good qualitative and quantitative agreement with the existing measurements of resistivity in (TMTSF)$_2$ClO$_4$ conductor.Comment: 6 pages, 2 figure

Non-Fermi Liquids in the Extended Hubbard Model

I summarize recent work on non-Fermi liquids within certain generalized Anderson impurity model as well as in the large dimensionality ($D$) limit of the two-band extended Hubbard model. The competition between local charge and spin fluctuations leads either to a Fermi liquid with renormalized quasiparticle excitations, or to non-Fermi liquids with spin-charge separation. These results provide new insights into the phenomenological similarities and differences between different correlated metals. While presenting these results, I outline a general strategy of local approach to non-Fermi liquids in correlated electron systems.Comment: 30 pages, REVTEX, 14 figures included. To appear in ``Non Fermi Liquid Physics'', J. Phys: Cond. Matt. (1997

Early reionization by decaying particles in the light of three year WMAP data

We study the reionization histories where ionizing UV photons are emitted from decaying particles, in addition to usual contributions from stars and quasars, taking account of the fact that the universe is not fully ionized until z = 6 as observed by Sloan Digital Sky Survey. Likelihood analysis of the three-year data from the WMAP (Wilkinson Microwave Anisotropy Probe) severely constrains the decaying particle scenario.In particular, the decaying particle with relatively short lifetime is not favored by the polarization data.Comment: 9 pages, 11 figure

Inversion symmetry breaking induced triply degenerate points in orderly arranged PtSeTe family materials

$k$ paths exactly with $C_{3v}$ symmetry allow to find triply degenerate points (TDPs) in band structures. The paths that host the type-II Dirac points in PtSe$_2$ family materials also have the $C_{3v}$ spatial symmetry. However, due to Kramers degeneracy (the systems have both inversion symmetry and time reversal symmetry), the crossing points in them are Dirac ones. In this work, based on symmetry analysis, first-principles calculations, and $k\cdot p$ method, we predict that PtSe$_2$ family materials should undergo topological transitions if the inversion symmetry is broken, \emph{i.e.} the Dirac fermions in PtSe$_2$ family materials split into TDPs in PtSeTe family materials (PtSSe, PtSeTe, and PdSeTe) with orderly arranged S/Se (Se/Te). It is different from the case in high-energy physics that breaking inversion symmetry $I$ leads to the splitting of Dirac fermion into Weyl fermions. We also address a possible method to achieve the orderly arranged in PtSeTe family materials in experiments. Our study provides a real example that Dirac points transform into TDPs, and is helpful to investigate the topological transition between Dirac fermions and TDP fermions

Andreev Reflection and Spin Injection into s−s- and d−d-wave Superconductors

We study the effect of spin injection into $s-$ and $d-$wave superconductors, with an emphasis on the interplay between boundary and bulk spin transport properties. The quantities of interest include the amount of non-equilibrium magnetization ($m$), as well as the induced spin-dependent current ($I_s$) and boundary voltage ($V_s$). In general, the Andreev reflection makes each of the three quantities depend on a different combination of the boundary and bulk contributions. The situation simplifies either for half-metallic ferromagnets or in the strong barrier limit, where both $V_s$ and $m$ depend solely on the bulk spin transport/relaxation properties. The implications of our results for the on-going spin injection experiments in high $T_c$ cuprates are discussed.Comment: 4 pages, REVTEX, 1 figure included; typos correcte

Spin Injection into a Luttinger Liquid

We study the effect of spin injection into a Luttinger liquid. The spin-injection-detection setup of Johnson and Silsbee is considered; here spins injected into the Luttinger liquid induce, across an interface with a ferromagnetic metal, either a spin-dependent current ($I_s$) or a spin-dependent boundary voltage ($V_s$). We find that the spin-charge separation nature of the Luttinger liquid affects $I_s$ and $V_s$ in a very different fashion. In particular, in the Ohmic regime, $V_s$ depends on the spin transport properties of the Luttinger liquid in essentially the same way as it would in the case of a Fermi liquid. The implications of our results for the spin-injection-detection experiments in the high $T_c$ cuprates are discussed.Comment: 4 pages, REVTEX, 2 figures. Minor changes and corrections to typos. To appear in Phys. Rev. Let

A Tale of Two Animats: What does it take to have goals?

What does it take for a system, biological or not, to have goals? Here, this question is approached in the context of in silico artificial evolution. By examining the informational and causal properties of artificial organisms ('animats') controlled by small, adaptive neural networks (Markov Brains), this essay discusses necessary requirements for intrinsic information, autonomy, and meaning. The focus lies on comparing two types of Markov Brains that evolved in the same simple environment: one with purely feedforward connections between its elements, the other with an integrated set of elements that causally constrain each other. While both types of brains 'process' information about their environment and are equally fit, only the integrated one forms a causally autonomous entity above a background of external influences. This suggests that to assess whether goals are meaningful for a system itself, it is important to understand what the system is, rather than what it does.Comment: This article is a contribution to the FQXi 2016-2017 essay contest "Wandering Towards a Goal