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

Braiding of anyonic quasiparticles in the charge transfer statistics of symmetric fractional edge-state Mach-Zehnder interferometer

We have studied the zero-temperature statistics of the charge transfer between the two edges of Quantum Hall liquids of, in general, different filling factors, $\nu_{0,1}=1/(2 m_{0,1}+1)$, with $m_0 \geq m_1\geq 0$, forming Mach-Zehnder interferometer. General expression for the cumulant generating function in the large-time limit is obtained for symmetric interferometer with equal propagation times along the two edges between the contacts and constant bias voltage. The low-voltage limit of the generating function can be interpreted in terms of the regular Poisson process of electron tunneling, while its leading large-voltage asymptotics is proven to coincide with the solution of kinetic equation describing quasiparticle transitions between the $m$ states of the interferometer with different effective flux through it, where $m\equiv 1+m_{0}+m_{1}$. For $m>1$, this dynamics reflects both the fractional charge $e/m$ and the fractional statistical angle $\pi /m$ of the tunneling quasiparticles. Explicit expressions for the second (shot noise) and third cumulants are obtained, and their voltage dependence is analyzed.Comment: 11 two-column pages, 4 figure

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

New beetles (Insecta: Coleoptera) from the Lower Cretaceous of Spain

Three beetles remains from the Lower Cretaceous lithographic limestones of Spain are described. We classified them into two new genus and three new species. One specimen named Tetraphalerus brevicapitis n.sp. was placed in the Cupedidae, and both Megacoptoclava longiurogomphia n.gen., n.sp. and Bolbonectus lithographicus n.gen., n.sp. in Coptoclavidae.Three beetles remains from the Lower Cretaceous lithographic limestones of Spain are described. We classified them into two new genus and three new species. One specimen named Tetraphalerus brevicapitis n.sp. was placed in the Cupedidae, and both Megacoptoclava longiurogomphia n.gen., n.sp. and Bolbonectus lithographicus n.gen., n.sp. in Coptoclavidae

Charge transfer statistics and qubit dynamics at the tunneling Fermi-edge singularity

Tunneling of spinless electrons from a single-channel emitter into an empty collector through an interacting resonant level of the quantum dot (QD) is studied, when all Coulomb screening of charge variations on the dot is realized by the emitter channel and the system is mapped onto an exactly solvable model of a dissipative qubit. In this model we describe the qubit density matrix evolution with a generalized Lindblad equation, which permits us to count the tunneling electrons and therefore relate the qubit dynamics to the charge transfer statistics. In particular, the coefficients of its generating function equal to the time-dependent probabilities to have the fixed number of electrons tunneled into the collector are expressed through the parameters of a non-Hermitian Hamiltonian evolution of the qubit pure states in-between the successive electron tunneling events. From the leading asymptotics of the cumulant generating function (CGF) linear in time we calculate the Fano factor and the skewness and establish their relation to the extra average and the second cumulants, respectively, of the charge accumulated during the QD evolution from its empty and stationary states, which are defined by the next-to-leading term of the CGF asymptotics. The relation explains the origin of the sub-Poisson and super-Poisson shot noise in this system and shows that the super-Poisson signals existence of a nonmonotonous oscillating transient current and the qubit coherent dynamics. The mechanism is illustrated with particular examples of the generating functions, one of which coincides in the large time limit with the generating function of the 13 fractional Poisson distribution realized without the fractional charge tunneling

Transport properties of single channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise

The inhomogeneous Tomonaga Luttinger liquid model describing an interacting quantum wire adiabatically coupled to non-interacting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic non-monotonic parameter dependencies of the average current. We discuss oscillations of the non-linear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $\omega$ relative to $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Tomonaga Luttinger interaction parameter, and $L$ the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is non-vanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.Comment: 28 pages, 19 figures, published version with minor change