Cyclostationary measurement of low-frequency odd moments of current fluctuations

Measurement of odd moments of current fluctuations is difficult due to strict requirements for band-pass filtering. We propose how these requirements can be overcome using cyclostationary driving of the measured signal and indicate how the measurement accuracy can be tested through the phase dependence of the moments of the fluctuations. We consider two schemes, the mixing scheme and the statistics scheme, where the current statistics can be accessed. We also address the limitations of the schemes, due to excess noise and due to the effects of the environment, and, finally, discuss the required measurement times for typical setups.Comment: 13 pages, 3 figure

Full counting statistics of Luttinger liquid conductor

Non-equilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the full counting statistics of the transmitted charge is derived. It is given by Fredholm determinant of the counting operator with a time dependent scattering phase. The result has a form of counting statistics of non-interacting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the non-interacting leads.Comment: 5 pages, 2 figure

A simple mathematical model for the effect of benzoannelation on cyclic conjugation

In a series of earlier studies, it was established that benzoannelation in the angular (resp. linear) position relative to a ring R of a polycyclic conjugated π-electron system, increases (resp. decreases) the intensity of the cyclic conjugation in the ring R. Herein, it is shown how this regularity can be explained by means of a simple, Kekulé-structurebased argument, itself based on an idea of Randić from the 1970s

Theoretical Studies on Radialenes and Related Molecules

For certain classes of molecules it is possible to obtain a general solution ·of the Ruckel problem, i.e. to derive expressions for the orbital energy, orbital coefficients, total n-electron energy, etc. in a closed analytical form1-5• General solutions are important because a large amount of numerical labour can be saved. Besides, they show the dependence of HMO quantities on the molecular topology, which has been recently investigated by various authors

The maximal energy of classes of integral circulant graphs

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count $n$ and a set $\cal D$ of divisors of $n$ in such a way that they have vertex set $\mathbb{Z}_n$ and edge set ${{a,b}: a,b\in\mathbb{Z}_n, \gcd(a-b,n)\in {\cal D}}$. For a fixed prime power $n=p^s$ and a fixed divisor set size $|{\cal D}| =r$, we analyze the maximal energy among all matching integral circulant graphs. Let $p^{a_1} < p^{a_2} < ... < p^{a_r}$ be the elements of ${\cal D}$. It turns out that the differences $d_i=a_{i+1}-a_{i}$ between the exponents of an energy maximal divisor set must satisfy certain balance conditions: (i) either all $d_i$ equal $q:=\frac{s-1}{r-1}$, or at most the two differences $[q]$ and $[q+1]$ may occur; %(for a certain $d$ depending on $r$ and $s$) (ii) there are rules governing the sequence $d_1,...,d_{r-1}$ of consecutive differences. For particular choices of $s$ and $r$ these conditions already guarantee maximal energy and its value can be computed explicitly.Comment: Discrete Applied Mathematics (2012

Suppression of geometrical barrier in Bi2Sr2CaCu2O8+δBi_2Sr_2CaCu_2O_{8+\delta} crystals by Josephson vortex stacks

Differential magneto-optics are used to study the effect of dc in-plane magnetic field on hysteretic behavior due to geometrical barriers in $Bi_2Sr_2CaCu_2O_{8+\delta}$ crystals. In absence of in-plane field a vortex dome is visualized in the sample center surrounded by barrier-dominated flux-free regions. With in-plane field, stacks of Josephson vortices form vortex chains which are surprisingly found to protrude out of the dome into the vortex-free regions. The chains are imaged to extend up to the sample edges, thus providing easy channels for vortex entry and for drain of the dome through geometrical barrier, suppressing the magnetic hysteresis. Reduction of the vortex energy due to crossing with Josephson vortices is evaluated to be about two orders of magnitude too small to account for the formation of the protruding chains. We present a model and numerical calculations that qualitatively describe the observed phenomena by taking into account the demagnetization effects in which flux expulsion from the pristine regions results in vortex focusing and in the chain protrusion. Comparative measurements on a sample with narrow etched grooves provide further support to the proposed model.Comment: 12 figures (low res.) Higher resolution figures are available at the Phys Rev B version. Typos correcte

Elementary models of 3D topological insulators with chiral symmetry

We construct a set of lattice models of non-interacting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of $\mathbb{Z}$ classes. By coupling the two AIII models related by time-reversal symmetry we construct other chiral symmetric topological insulators that may also possess additional symmetries (the time-reversal and/or particle-hole). There are two different chiral symmetry operators for the coupled model, that correspond to two distinct ways of defining the sublattices. The integer topological invariant (the winding number) in case of weak coupling can be either the sum or difference of indices of the basic building blocks, dependent on the preserved chiral symmetry operator. The value of the topological index in case of weak coupling is determined by the chiral symmetry only and does not depend on the presence of other symmetries. For $\mathbb{Z}$ topological classes AIII, DIII, and CI with chiral symmetry are topologically equivalent, it implies that a smooth transition between the classes can be achieved if it connects the topological sectors with the same winding number. We demonstrate this explicitly by proving that the gapless surface states remain robust in $\mathbb{Z}$ classes as long as the chiral symmetry is preserved, and the coupling does not close the gap in the bulk. By studying the surface states in $\mathbb{Z}_2$ topological classes, we show that class CII and AII are distinct, and can not be adiabatically connected

Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.Comment: 20 pages, 13 figure

Integral circulant graphs of prime power order with maximal energy

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Zn and edge set {{a, b} : a, b in Zn; gcd(a - b, n) in D}. Using tools from convex optimization, we study the maximal energy among all integral circulant graphs of prime power order ps and varying divisor sets D. Our main result states that this maximal energy approximately lies between s(p - 1)p^(s-1) and twice this value. We construct suitable divisor sets for which the energy lies in this interval. We also characterize hyperenergetic integral circulant graphs of prime power order and exhibit an interesting topological property of their divisor sets.Comment: 25 page