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

On non-abelian homomorphic public-key cryptosystems

An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f:G --> H, where G, H are (publically known) groups and H is finite. A letter of a message to be encrypted is an element h element of H, while its encryption g element of G is such that f(g)=h. A homomorphic cryptosystem allows one to perform computations (operating in a group G) with encrypted information (without knowing the original message over H). In this paper certain homomorphic cryptosystems are constructed for the first time for non-abelian groups H (earlier, homomorphic cryptosystems were known only in the Abelian case). In fact, we present such a system for any solvable (fixed) group H.Comment: 15 pages, LaTe

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

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

Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime

High-field magnetotransport experiments provide an excellent tool to investigate the plateau-insulator phase transition in the integral quantum Hall effect. Here we review recent low-temperature high-field magnetotransport studies carried out on several InGaAs/InP heterostructures and an InGaAs/GaAs quantum well. We find that the longitudinal resistivity $\rho_{xx}$ near the critical filling factor $\nu_{c}$ ~ 0.5 follows the universal scaling law $\rho_{xx}(\nu, T) \propto exp[-\Delta \nu/(T/T_{0})^{\kappa}]$, where $\Delta \nu =\nu -\nu_{c}$. The critical exponent $\kappa$ equals $0.56 \pm 0.02$, which indicates that the plateau-insulator transition falls in a non-Fermi liquid universality class.Comment: 8 pages, accepted for publication in Proceedings of the Yamada Conference LX on Research in High Magnetic Fields (August 16-19, 2006, Sendai

Threshold features in transport through a 1D constriction

Suppression of electron current $\Delta I$ through a 1D channel of length $L$ connecting two Fermi liquid reservoirs is studied taking into account the Umklapp electron-electron interaction induced by a periodic potential. This interaction causes Hubbard gaps $E_H$ for $L \to \infty$. In the perturbative regime where $E_H \ll v_c/L$ ($v_c:$ charge velocity), and for small deviations $\delta n$ of the electron density from its commensurate values $- \Delta I/V$ can diverge with some exponent as voltage or temperature $V,T$ decreases above $E_c=max(v_c/L,v_c \delta n)$, while it goes to zero below $E_c$. This results in a nonmonotonous behavior of the conductance.Comment: Final variant published in PRL, 79, 1714; minor correction

Fractional charge in transport through a 1D correlated insulator of finite length

Transport through a one channel wire of length $L$ confined between two leads is examined when the 1D electron system has an energy gap $2M$: $M > T_L \equiv v_c/L$ induced by the interaction in charge mode ($v_c$: charge velocity in the wire). In spinless case the transformation of the leads electrons into the charge density wave solitons of fractional charge $q$ entails a non-trivial low energy crossover from the Fermi liquid behavior below the crossover energy $T_x \propto \sqrt{T_L M} e^{-M /[T_L(1-q^2)]}$ to the insulator one with the fractional charge in current vs. voltage, conductance vs. temperature, and in shot noise. Similar behavior is predicted for the Mott insulator of filling factor $\nu = integer/(2 m')$.Comment: 5 twocolumn pages in RevTex, no figure

Conductance of a Mott Quantum Wire

We consider transport through a one-dimensional conductor subject to an external periodic potential and connected to non-interacting leads (a "Mott quantum wire"). For the case of a strong periodic potential, the conductance is shown to jump from zero, for the chemical potential lying within the Mott-Hubbard gap, to the non-interacting value of 2e^2/h, as soon as the chemical potential crosses the gap edge. This behavior is strikingly different from that of an optical conductivity, which varies continuously with the carrier concentration. For the case of a weak potential, the perturbative correction to the conductance due to Umklapp scattering is absent away from half-filling.Comment: 4 pages, RevTex, 1 ps figure included; published versio

Current noise spectrum in a solvable model of tunneling Fermi-edge singularity

We consider tunneling of spinless electrons from a single-channel emitter into an empty collector through an interacting resonant level of the quantum dot (QD). When all Coulomb screening of sudden charge variations of the dot during the tunneling is realized by the emitter channel, the system is mapped onto an exactly solvable model of a dissipative qubit. The qubit density matrix evolution is described with a generalized Bloch equation which permits us to count the tunneling electrons and find the charge transfer statistics. The two generating functions of the counting statistics of the charge transferred during the QD evolutions from its stationary and empty state have been expressed through each other. It is used to calculate the spectrum of the steady current noise and to demonstrate the occurrence of the bifurcation of its single zero-frequency minimum into two finite-frequency dips due to the qubit coherent dynamics

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.Comment: 9 pages, 7 figure