Majorana Fermions in Strongly Interacting Helical Liquids

Majorana fermions were proposed to occur at edges and interfaces of gapped one-dimensional systems where phases with different topological character meet due to an interplay of spin-orbit coupling, proximity-induced superconductivity and external magnetic fields. Here we investigate the effect of strong particle interactions, and show that the helical liquid offers a mechanism that protects the very existence of Majorana edge states: whereas moderate interactions close the proximity gap which supports the edge states, in helical liquids the gap re-opens due to two-particle processes. However, gapless fermionic excitations occur at spatial proximity to the Majorana states at interfaces and may jeopardize their long term Majorana coherence.Comment: 7 pages, 4 figure

Orbital multicriticality in spin gapped quasi-1D antiferromagnets

Motivated by the quasi-1D antiferromagnet CaV$_2$O$_4$, we explore spin-orbital systems in which the spin modes are gapped but orbitals are near a macroscopically degenerate classical transition. Within a simplified model we show that gapless orbital liquid phases possessing power-law correlations may occur without the strict condition of a continuous orbital symmetry. For the model proposed for CaV$_2$O$_4$, we find that an orbital phase with coexisting order parameters emerges from a multicritical point. The effective orbital model consists of zigzag-coupled transverse field Ising chains. The corresponding global phase diagram is constructed using field theory methods and analyzed near the multicritical point with the aid of an exact solution of a zigzag XXZ model.Comment: 9 page

Application of the Fuzzy Inference System Method to Predict the Number of Weaving Fabric Production

In this study discusses the application of fuzzy logic in solving production problems using the Tsukamoto method and the Sugeno method. The problem that is solved is how to determine the production of woven fabric when using three variables as input data, namely: stock, demand and inventory of production costs. The first step is to solve the problem of woven fabric production using the Tsukamoto method which is to determine the input variables and output variables which are firm sets, the second step is to change the input variable into a fuzzy set with the fuzzification process, then the third step is processing the fuzzy set data with the maximum method. And the last or fourth step is to change the output into a firm set with the defuzzification process with a weighted average method, so that the desired results will be obtained in the output variable. The solution to the production problem using the Sugeno method is almost the same as using the Tsukamoto method, it\u27s just that the system output is not a fuzzy set, but rather a constant or a linear equation. The difference between the Tsukamoto Method and the Sugeno Method is in consequence. The Sugeno method uses constants or mathematical functions of the input variables

Local Magnetization in the Boundary Ising Chain at Finite Temperature

We study the local magnetization in the 2-D Ising model at its critical temperature on a semi-infinite cylinder geometry, and with a nonzero magnetic field $h$ applied at the circular boundary of circumference $\beta$. This model is equivalent to the semi-infinite quantum critical 1-D transverse field Ising model at temperature $T \propto \beta^{-1}$, with a symmetry-breaking field $\propto h$ applied at the point boundary. Using conformal field theory methods we obtain the full scaling function for the local magnetization analytically in the continuum limit, thereby refining the previous results of Leclair, Lesage and Saleur in Ref. \onlinecite{Leclair}. The validity of our result as the continuum limit of the 1-D lattice model is confirmed numerically, exploiting a modified Jordan-Wigner representation. Applications of the result are discussed.Comment: 9 pages, 3 figure

Low-temperature ordered phases of the spin-12\frac{1}{2} XXZ chain system Cs2_2CoCl4_4

In this study the magnetic order of the spin-1/2 XXZ chain system Cs$_2$CoCl$_4$ in a temperature range from 50 mK to 0.5 K and in applied magnetic fields up to 3.5 T is investigated by high-resolution measurements of the thermal expansion and the specific heat. Applying magnetic fields along a or c suppresses $T_\textrm{N}$ completely at about 2.1 T. In addition, we find an adjacent intermediate phase before the magnetization saturates close to 2.5 T. For magnetic fields applied along b, a surprisingly rich phase diagram arises. Two additional transitions are observed at critical fields $\mu_0 H_{SF1}\simeq 0.25$ T and $\mu_0 H_{SF2}\simeq 0.7$ T, which we propose to arise from a two-stage spin-flop transition.Comment: 10 pages, 10 figure

Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups

Given an automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-twisted conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-twisted conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that SL$(n,\mathbb{Z})$ and its congruence subgroups have the $R_\infty$-property. Further we show that any (countable) abelian extension of $\Gamma$ has the $R_\infty$-property where $\Gamma$ is a torsion free non-elementary hyperbolic group, or SL$(n,\mathbb{Z})$, Sp$(2n,\mathbb{Z})$ or a principal congruence subgroup of SL$(n,\mathbb{Z})$ or the fundamental group of a complete Riemannian manifold of constant negative curvature

Non-adiabatic pumping in an oscillating-piston model

We consider the prototypical "piston pump" operating on a ring, where a circulating current is induced by means of an AC driving. This can be regarded as a generalized Fermi-Ulam model, incorporating a finite-height moving wall (piston) and non trivial topology (ring). The amount of particles transported per cycle is determined by a layered structure of phase-space. Each layer is characterized by a different drift velocity. We discuss the differences compared with the adiabatic and Boltzmann pictures, and highlight the significance of the "diabatic" contribution that might lead to a counter-stirring effect.Comment: 6 pages, 4 figures, improved versio

ANALISIS PERKEMBANGAN KAWASAN PERMUKIMAN SEKITAR DANAU TONDANO KABUPATEN MINAHASA

Dalam RTRW Kabupaten Minahasa kawasan sekitar Danau Tondano ditetapkan sebagai kawasan lindung, kenyataannya kawasan lindung yang ada sudah dijadikan tempat bermukim dari masyarakat yang ada untuk memenuhi kepentingan manusia. Pertambahan jumlah penduduk lokal yang terjadi di daerah ini didukung juga oleh keadaan lokasinya yang strategis yaitu berada dekat Danau Tondano. Kebutuhan masyarakat untuk lahan sebagai tempat membangun rumah semakin berkurang karena pertambahan jumlah penduduk. Rumah-rumah  penduduk tidak lagi berada di sekitar danau, tapi sudah merambah  sampai perairannya. Oleh karena itu, maka dilakukan penelitian dengan tujuannya adalah mengidentifikasi perkembangan kawasan permukiman yang berada sekitar Danau Tondano dan menghitung luas perkembangan kawasan permukiman sekitar Danau Tondano. Metode penelitian yang digunakan dalam penelitian ini adalah analisis spasial time series untuk melihat perkembangan kawasan permukiman dan analisis deskriptif kuantitatif. Hasil penelitian menunjukkan bahwa kawasan sekitar danau Tondano mengalami perkembangan permukiman dari tahun 2003 sampai tahun 2019. Luas perkembangan permukiman dari tahun 2003 sampai tahun 2011 bertumbuh sebesar 87 ha sedangkan perkembangan permukiman pada tahun 2011 sampai 2019 bertambah sebesar 132,58 ha. Luas sebaran permukiman dari  tahun 2003-2019 yaitu 413,76 ha menjadi 633,81 ha.Kata Kunci : Perkembangan Kawasan, Permukiman, Danau Tondan

Dislocation-mediated melting of one-dimensional Rydberg crystals

We consider cold Rydberg atoms in a one-dimensional optical lattice in the Mott regime with a single atom per site at zero temperature. An external laser drive with Rabi frequency \Omega and laser detuning \Delta, creates Rydberg excitations whose dynamics is governed by an effective spin-chain model with (quasi) long-range interactions. This system possesses intrinsically a large degree of frustration resulting in a ground-state phase diagram in the (\Delta,\Omega) plane with a rich topology. As a function of \Delta, the Rydberg blockade effect gives rise to a series of crystalline phases commensurate with the optical lattice that form a so-called devil's staircase. The Rabi frequency, \Omega, on the other hand, creates quantum fluctuations that eventually lead to a quantum melting of the crystalline states. Upon increasing \Omega, we find that generically a commensurate-incommensurate transition to a floating Rydberg crystal occurs first, that supports gapless phonon excitations. For even larger \Omega, dislocations within the floating Rydberg crystal start to proliferate and a second, Kosterlitz-Thouless-Nelson-Halperin-Young dislocation-mediated melting transition finally destroys the crystalline arrangement of Rydberg excitations. This latter melting transition is generic for one-dimensional Rydberg crystals and persists even in the absence of an optical lattice. The floating phase and the concomitant transitions can, in principle, be detected by Bragg scattering of light.Comment: 21 pages, 9 figures; minor changes, published versio