Statistics of Transmission Eigenvalues for a Disordered Quantum Point Contact

We study the distribution of transmission eigenvalues of a quantum point contact with nearby impurities. In the semi-classical case (the chemical potential lies at the conductance plateau) we find that the transmission properties of this system are obtained from the ensemble of Gaussian random reflection matrices. The distribution only depends on the number of open transport channels and the average reflection eigenvalue and crosses over from the Poissonian for one open channel to the form predicted by the circuit theory in the limit of large number of open channels.Comment: 8 pages, 3 figure

Completely splittable representations of affine Hecke-Clifford algebras

We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.Comment: 39 pages, v2, added a new reference with comments in section 4.4, added two examples (Example 5.4 and Example 5.11) in section 5, mild corrections of some typos, to appear in J. Algebraic Combinatoric

From Luttinger liquid to Altshuler-Aronov anomaly in multi-channel quantum wires

A crossover theory connecting Altshuler-Aronov electron-electron interaction corrections and Luttinger liquid behavior in quasi-1D disordered conductors has been formulated. Based on an interacting non-linear sigma model, we compute the tunneling density of states and the interaction correction to the conductivity, covering the full crossover.Comment: 15 pages, 3 figures, revised version, accepted by PR

Random wave functions and percolation

Recently it was conjectured that nodal domains of random wave functions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wave function correlations decay slowly, a careful use of Harris' criterion confirms that these correlations are unessential and nodal domains of random wave functions belong to the same universality class as non critical percolation. Second, we argue that level domains of random wave functions are described by the non-critical percolation model.Comment: 13 page

Nonlinear statistics of quantum transport in chaotic cavities

Copyright © 2008 The American Physical Society.In the framework of the random matrix approach, we apply the theory of Selberg’s integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order. As a result, we derive exact explicit expressions for the skewness and kurtosis of the conductance and transmitted charge as well as for the variance of the shot-noise power in chaotic cavities. The obtained results are generally valid at arbitrary numbers of propagating channels in the two attached leads. In the particular limit of large (and equal) channel numbers, the shot-noise variance attends the universal value 1∕64β that determines a universal Gaussian statistics of shot-noise fluctuations in this case.DFG and BRIEF

Phonon-Coupled Electron Tunneling in Two and Three-Dimensional Tunneling Configurations

We treat a tunneling electron coupled to acoustical phonons through a realistic electron phonon interaction: deformation potential and piezoelectric, in two or three-dimensional tunneling configurations. Making use of slowness of the phonon system compared to electron tunneling, and using a Green function method for imaginary time, we are able to calculate the change in the transition probability due to the coupling to phonons. It is shown using standard renormalization procedure that, contrary to the one-dimensional case, second order perturbation theory is sufficient in order to treat the deformation potential coupling, which leads to a small correction to the transmission coefficient prefactor. In the case of piezoelectric coupling, which is found to be closely related to the piezoelectric polaron problem, vertex corrections need to be considered. Summing leading logarithmic terms, we show that the piezoelectric coupling leads to a significant change of the transmission coefficient.Comment: 17 pages, 4 figure

Ballistic transport in disordered graphene

An analytic theory of electron transport in disordered graphene in a ballistic geometry is developed. We consider a sample of a large width W and analyze the evolution of the conductance, the shot noise, and the full statistics of the charge transfer with increasing length L, both at the Dirac point and at a finite gate voltage. The transfer matrix approach combined with the disorder perturbation theory and the renormalization group is used. We also discuss the crossover to the diffusive regime and construct a ``phase diagram'' of various transport regimes in graphene.Comment: 23 pages, 10 figure

Measuring the distribution of current fluctuations through a Josephson junction with very short current pulses

We propose to probe the distribution of current fluctuations by means of the escape probability histogram of a Josephson junction (JJ), obtained using very short bias current pulses in the adiabatic regime, where the low-frequency component of the current fluctuations plays a crucial role. We analyze the effect of the third cumulant on the histogram in the small skewness limit, and address two concrete examples assuming realistic parameters for the JJ. In the first one we study the effects due to fluctuations produced by a tunnel junction, finding that the signature of higher cumulants can be detected by taking the derivative of the escape probability with respect to current. In such a realistic situation, though, the determination of the whole distribution of current fluctuations requires an amplification of the cumulants. As a second example we consider magnetic flux fluctuations acting on a SQUID produced by a random telegraph source of noise.Comment: 6 pages, 6 figures; final versio

The gl(M|N) Super Yangian and Its Finite Dimensional Representations

Methods are developed for systematically constructing the finite dimensional irreducible representations of the super Yangian Y(gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite dimensional irreducible representation of Y(gl(M|N)) is of highest weight type, and is uniquely characterized by a highest weight. The necessary and sufficient conditions for an irrep to be finite dimensional are given.Comment: 14 pages plain late