Splitting electrons into quasiparticles with fractional edge-state Mach-Zehnder interferometer

We have studied theoretically the tunneling between two edges of Quantum Hall liquids (QHL) of different filling factors, $\nu_{0,1}=1/(2 m_{0,1}+1)$, with $m_0 \geq m_1\geq 0$, through two separate point contacts in the geometry of Mach-Zehnder interferometer [Y. Ji et al., Nature {\bf 422}, 415 (2003); I. Neder et al., Phys.\ Rev.\ Lett. {\bf 96}, 016804 (2006)]. The quasi-particle formulation of the interferometer model is derived as a dual to the initial electron model, in the limit of strong electron tunneling reached at large voltages or temperatures. For $m\equiv 1+m_{0}+m_{1}>1$, the tunneling of quasiparticles of fractional charge $e/m$ leads to non-trivial $m$-state dynamics of effective flux through the interferometer, which restores the regular "electron" periodicity of the current in flux despite the fractional charge and statistics of quasiparticles. The exact solution available for equal times of propagation between the contacts along the two edges demonstrates that the interference pattern of modulation of the tunneling current by flux depends on voltage and temperature only through a common amplitude.Comment: fourteen two-column pages in RevTex4, 4 eps figure, extended final verson as appeared in PR

Coulomb drag between one-dimensional conductors

We have analyzed Coulomb drag between currents of interacting electrons in two parallel one-dimensional conductors of finite length $L$ attached to external reservoirs. For strong coupling, the relative fluctuations of electron density in the conductors acquire energy gap $M$. At energies larger than $\Gamma = const \times v_- \exp (-LM/v_-)/L + \Gamma_{+}$, where $\Gamma_{+}$ is the impurity scattering rate, and for $L>v_-/M$, where $v_-$ is the fluctuation velocity, the gap leads to an ``ideal'' drag with almost equal currents in the conductors. At low energies the drag is suppressed by coherent instanton tunneling, and the zero-temperature transconductance vanishes, indicating the Fermi liquid behavior.Comment: 5 twocolumn pages in RevTex, added 1 eps-Figure and calculation of trans-resistanc

Mach-Zehnder interferometer in the Fractional Quantum Hall regime

We consider tunneling between two edges of Quantum Hall liquids (QHL) of filling factors $\nu_{0,1}=1/(2 m_{0,1}+1)$, with $m_0 \geq m_1\geq 0$, through two point contacts forming Mach-Zehnder interferometer. Quasi-particle description of the interferometer is derived explicitly through the instanton duality transformation of the initial electron model. For $m_{0}+m_{1}+1\equiv m>1$, tunneling of quasiparticles of charge $e/m$ leads to non-trivial $m$-state dynamics of effective flux through the interferometer, which restores the regular ``electron'' periodicity of the current in flux. The exact solution available for equal propagation times between the contacts along the two edges demonstrates that the interference pattern in the tunneling current depends on voltage and temperature only through a common amplitude.Comment: five two-column pages in RevTex4, 1 eps figur

Reply to Comment on "Strongly Correlated Fractional Quantum Hall Line Junctions"

In two recent articles [PRL 90, 026802 (2003); PRB 69, 085307 (2004)], we developed a transport theory for an extended tunnel junction between two interacting fractional-quantum-Hall edge channels, obtaining analytical results for the conductance. Ponomarenko and Averin (PA) have expressed disagreement with our theoretical approach and question the validity of our results (cond-mat/0602532). Here we show why PA's critique is unwarranted.Comment: 1 page, no figures, RevTex

Strong-coupling branching of FQHL edges

We have developed a theory of quasiparticle backscattering in a system of point contacts formed between single-mode edges of several Fractional Quantum Hall Liquids (FQHLs) with in general different filling factors $\nu_j$ and one common single-mode edge $\nu_0$ of another FQHL. In the strong-tunneling limit, the model of quasiparticle backscattering is obtained by the duality transformation of the electron tunneling model. The new physics introduced by the multi-point-contact geometry of the system is coherent splitting of backscattered quasiparticles at the point contacts in the course of propagation along the common edge $\nu_0$. The ``branching ratios'' characterizing the splitting determine the charge and exchange statistics of the edge quasiparticles that can be different from those of Laughlin's quasiparticles in the bulk of FQHLs. Accounting for the edge statistics is essential for the system of more than one point contact and requires the proper description of the flux attachement to tunneling electrons.Comment: 12 pages, 2 figure

Arithmetic of Semigroup Semirings

We define semigroup semirings by analogy with group rings and semigroup rings. We study the arithmetic properties and determine sufficient conditions under which a semigroup semiring is atomic, has finite factorization, or has bounded factorization. We also present a semigroup-semiring analog (although not a generalization) of the Gauss lemma on primitive polynomials.Напiвгруповi напiвкiльця визначаються по аналогiї з груповими кiльцями та напiвгруповими кiльцями. Вивчено арифметичнi властивостi та отримано достатнi умови, за яких напiвгрупове напiвкiльце є атомним, має скiнченну факторизацiю або має обмежену факторизацiю. Також наведено напiвгрупово-напiвкiльцевий аналог (хоча i не узагальнення) гауссiвської леми про примiтивнi полiноми

Epizootological monitoring studies on the spread of nematodirosis of cattle in the territory of Poltava region

The most common helminthiasis of cattle is strongylidosis of the digestive organs. This group of animal helminthiasis is widespread in Ukraine and is caused by nematodes of the Strongylida suborder, among which nematodirosis occupies a leading place. Invasion leads to a decrease in productivity, the quality of the obtained products, barrenness of the broodstock, and deterioration of the growth and development of the young. Invasion of definitive hosts occurs mostly passively; by alimentary means, the invasive is the larva of the third stage. The work aimed to conduct monitoring studies of the epizootic situation regarding the spread of nematodirosis of cattle in the territory of Poltava region based on the results of the analysis of statistical data of the reporting documentation of the Main Department of the State Production and Consumer Service in Poltava region for 2018–2022. It was established that the extent of nematodirosis infestation in cattle ranged from 0.81 % (in 2020) to 5.30 % (2022), with the average extensiveness of the invasion for the studied period at 1.36 %. At the same time, the share of nematodirosis among other nematode diseases of cattle was 18.37 %. Among other nematodes, neoascarosis, bunostomosis, esophagostomosis, dictyokaulosis, and trichurosis were diagnosed in the territory of the studied region, the share of which ranged from 1.51 to 51.51 %. Among the invasive diseases of cattle registered on the territory of the Poltava region, the share of trematodes (fasciolosis, dicroceliosis, paramphistomatosis) in the general parasitic pathology is 85.51 %, protozoans (eimeriosis, babesiosis) and nematodes – 8.67 and 5.78 %, respectively, for cestodoses (moniasis) – 0.04 %. The obtained data from monitoring studies indicate the relevance of a more in-depth study of the spread of nematodirosis infestation among cattle in farms of the Poltava region, taking into account the nematode fauna, the characteristics of the infestation of animals of different age groups, in different seasons of the year, and as part of mixed infestations with other parasites