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

Evolution of a localized electron spin in a nuclear spin environment

Motivated by recent interest in the role of the hyperfine interaction in quantum dots we study the dynamics of a localized electron spin coupled to many nuclei. An important feature of the model is that the coupling to an individual nuclear spin depends on its position in the quantum dot. We introduce a semi-classical description of the system valid in the limit of a large number of nuclei and analyze the resulting classical dynamics. Contrary to a natural assumption, the correlation functions of electron spin with an arbitrary initial condition show no decay in time. Rather, they exhibit complicated undamped oscillations. This may be attributed to the fact that the system has many integrals of motion and is close to an integrable one. The ensemble averaged correlation functions do exhibit a slow decay (1/ln(t)) for t -> \infty.Comment: 11 pages, 11 figures, revtex4 styl

Tunnelling density of states at Coulomb blockade peaks

We calculate the tunnelling density of states (TDoS) for a quantum dot in the Coulomb blockade regime, using a functional integral representation with allowing correctly for the charge quantisation. We show that in addition to the well-known gap in the TDoS in the Coulomb-blockade valleys, there is a suppression of the TDoS at the peaks. We show that such a suppression is necessary in order to get the correct result for the peak of the differential conductance through an almost close quantum dot.Comment: 6 pages, 2 figure

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

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

Josephson effect in SF_{\rm F}XSF_{\rm F} junctions

We investigate the Josephson effect in S$_{\rm F}$XS$_{\rm F}$ junctions, where S$_{\rm F}$ is a superconducting material with a ferromagnetic exchange field, and X a weak link. The critical current $I_c$ increases with the (antiparallel) exchange fields if the distribution of transmission eigenvalues of the X-layer has its maximum weight at small values. This exchange field enhancement of the supercurrent does not exist if X is a diffusive normal metal. At low temperatures, there is a correspondence between the critical current in an S$_{\rm F}$IS$_{\rm F}$ junction with collinear orientations of the two exchange fields, and the AC supercurrent amplitude in an SIS tunnel junction. The difference of the exchange fields $h_1-h_2$ in an S$_{\rm F}$IS$_{\rm F}$ junction corresponds to the potential difference $V_1-V_2$ in an SIS junction; i.e., the singularity in $I_c$ [in an S$_{\rm F}$IS$_{\rm F}$ junction] at $|h_1-h_2|=\Delta_1+\Delta_2$ is the analogue of the Riedel peak. We also discuss the AC Josephson effect in S$_{\rm F}$IS$_{\rm F}$ junctions.Comment: 5 pages, 5 figure

Weak Charge Quantization as an Instanton of Interacting sigma-model

Coulomb blockade in a quantum dot attached to a diffusive conductor is considered in the framework of the non-linear sigma-model. It is shown that the weak charge quantization on the dot is associated with instanton configurations of the Q-field in the conductor. The instantons have a finite action and are replica non--symmetric. It is argued that such instantons may play a role in the transition regime to the interacting insulator.Comment: 4 pages. The 2D case substantially modifie

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

Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras

This paper completes a series devoted to explicit constructions of finite-dimensional irreducible representations of the classical Lie algebras. Here the case of odd orthogonal Lie algebras (of type B) is considered (two previous papers dealt with C and D types). A weight basis for each representation of the Lie algebra o(2n+1) is constructed. The basis vectors are parametrized by Gelfand--Tsetlin-type patterns. Explicit formulas for the matrix elements of generators of o(2n+1) in this basis are given. The construction is based on the representation theory of the Yangians. A similar approach is applied to the A type case where the well-known formulas due to Gelfand and Tsetlin are reproduced.Comment: 29 pages, Late

Phase dependent current statistics in short-arm Andreev interferometer

We calculate analytically the current statistics for a short diffusive wire between the normal reservoir and a short superconductor-normal metal-superconductor (SNS) junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference $\phi$ across the junction, approaching the normal-state value at $\phi=\pi$. At T=0 and at the applied voltage much smaller than the proximity gap $\Delta_\phi$, the current noise $P_I$ doubles and the third current cumulant $C_3$ is 4 times larger with respect to their values in the normal state; at $eV \gg \Delta_\phi$ they acquire large excess components. At the gap edge, $eV = \Delta_\phi$, the effective transferred charge defined through $dP_I/dI$ and $dP_I/dV$ approaches $0e$ and $3e$, respectively, which makes doubtful the interpretation of these quantities as physical elementary transferred charge. At $T \neq 0$, $C_3$ shows a non-monotonous voltage dependence with a dip near $eV = \Delta_\phi$.Comment: 13 pages, to be published in Proc. NATO ARW "Quantum Transport in Metallic and Hybrid Nanostructures", StPetersburg, 200