Subleading Shape Functions in Inclusive B Decays

The contributions of subleading shape functions to inclusive decay distributions of B mesons are derived from a systematic two-step matching of QCD current correlators onto soft-collinear and heavy-quark effective theory. At tree-level, the results can be expressed in terms of forward matrix elements of bi-local light-cone operators. Four-quark operators, which arise at O(g^2), are included. Their effects can be absorbed entirely into a redefinition of other shape functions. Our results are in disagreement with some previous studies of subleading shape-function effects in the literature. A numerical analysis of B->X_u+l+nu decay distributions suggests that power corrections are small, with the possible exception of the endpoint region of the charged-lepton energy spectrum.Comment: 22 pages, 2 figures; several typos corrected; version published in JHE

Evidence of two-electron tunneling interference in Nb/InAs junctions

The impact of junction transparency in driving phase-coherent charge transfer across diffusive semiconductor-superconductor junctions is demonstrated. We present conductivity data for a set of Nb-InAs junctions differing only in interface transparency. Our experimental findings are analyzed within the quasi-classical Green-function approach and unambiguously show the physical processes giving rise to the observed excess zero-bias conductivity.Comment: 10 pages (RevTex), 4 figures (PostScript), accepted for pubblication in Physical Review

DC and AC Josephson Effect in a Superconductor-Luttinger Liquid-Superconductor System

We calculate both the DC and the AC Josephson current through a one-dimensional system of interacting electrons, connected to two superconductors by tunnel junctions. We treat the (repulsive) Coulomb interaction in the framework of the one-channel, spin-$1/2$ Luttinger model. The Josephson current is obtained for two geometries of experimental relevance: a quantum wire and a ring. At zero temperature, the critical current is found to decay algebraically with increasing distance $d$ between the junctions. The decay is characterized by an exponent which depends on the strength of the interaction. At finite temperatures $T$, lower than the superconducting transition temperature $T_c$, there is a crossover from algebraic to exponential decay of the critical current as a function of $d$, at a distance of the order of $\hbar v_F/k_B T$. Moreover, the dependence of critical current on temperature shows non-monotonic behavior. If the Luttinger liquid is confined to a ring of circumference $L$, coupled capacitively to a gate voltage and threaded by a magnetic flux, the Josephson current shows remarkable parity effects under the variation of these parameters. For some values of the gate voltage and applied flux, the ring acts as a $\pi$-junction. These features are robust against thermal fluctuations up to temperatures on the order of $\hbar v_F/k_B L$. For the wire-geometry, we have also studied the AC-Josephson effect. The amplitude and the phase of the time-dependent Josephson current are affected by electron-electron interactions. Specifically, the amplitude shows pronounced oscillations as a function of the bias voltage due to the difference between the velocities of spin and charge excitations in the Luttinger liquid. Therefore, the AC Josephson effect can be used as a tool for the observation o

Strong coupling of excited heavy mesons

We compute the strong coupling constant $G_{B^{**} B \pi} \; (G_{D^{**} D \pi})$, where $B^{**}$ ($D^{**}$) is the $0^+$ $P-$wave $b \bar q \; (c \bar q)$ state, by QCD sum rules and by light-cone sum rules. The two methods give compatible results in the limit $m_Q \to \infty$, with a rather large value of the coupling constant. We apply the results to the calculation of the hadronic widths of the positive parity $B$ and $D$ states and to the chiral loop contribution to the ratio $f_{D_s}/f_D$.Comment: 31 pages, RevTeX, 4 figures appended as uuencoded fil

Superconductor coupled to two Luttinger liquids as an entangler for electron spins

We consider an s-wave superconductor (SC) which is tunnel-coupled to two spatially separated Luttinger liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e. it creates spin-singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin density fluctuations produced by the injected spin-entangled electrons.Comment: 15 pages, 2 figure

Time dependent mean field theory of the superfluid-insulator phase transition

We develop a time-dependent mean field approach, within the time-dependent variational principle, to describe the Superfluid-Insulator quantum phase transition. We construct the zero temperature phase diagram both of the Bose-Hubbard model (BHM), and of a spin-S Heisenberg model (SHM) with the XXZ anisotropy. The phase diagram of the BHM indicates a phase transition from a Mott insulator to a compressibile superfluid phase, and shows the expected lobe-like structure. The SHM phase diagram displays a quantum phase transition between a paramagnetic and a canted phases showing as well a lobe-like structure. We show how the BHM and Quantum Phase model (QPM) can be rigorously derived from the SHM. Based on such results, the phase boundaries of the SHM are mapped to the BHM ones, while the phase diagram of the QPM is related to that of the SHM. The QPM's phase diagram obtained through the application of our approach to the SHM, describes the known onset of the macroscopic phase coherence from the Coulomb blockade regime for increasing Josephson coupling constant. The BHM and the QPM phase diagrams are in good agreement with Quantum Monte Carlo results, and with the third order strong coupling perturbative expansion.Comment: 15 pages, 8 figures. To be published in Phys. Rev.

Non-zero temperature transport near quantum critical points

We describe the nature of charge transport at non-zero temperatures ($T$) above the two-dimensional ($d$) superfluid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order $k_B T/\hbar$. This implies that the transport at frequencies $\omega \ll k_B T/\hbar$ is in the hydrodynamic, collision-dominated (or `incoherent') regime, while $\omega \gg k_B T/\hbar$ is the collisionless (or `phase-coherent') regime. The conductivity is argued to be $e^2 / h$ times a non-trivial universal scaling function of $\hbar \omega / k_B T$, and not independent of $\hbar \omega/k_B T$, as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic $\hbar \omega/k_B T \to 0$ limit of this function, and is a universal number times $e^2 / h$, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless $\hbar \omega/k_B T \to \infty$ limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times $e^2 / h$. We provide the first computation of the universal d.c. conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in $\epsilon=3-d$. The case of spin transport near quantum critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a new route to self-duality at two-dimensional quantum critical points.Comment: Feedback incorporated into numerous clarifying remarks; additional appendix discusses relationship to transport in dissipative quantum mechanics and quantum Hall edge state tunnelling problems, stimulated by discussions with E. Fradki

Analysis of the Three-Body B→D+D−π0B \to D^+ D^- \pi^0 Decay

The decay process $B\to D^+ D^- \pi^0$ is an interesting channel for the investigation of CP violating effects in the $b-$ sector. We write down a decay amplitude constrained by a low-energy theorem, which also includes the contribution of resonant $S-$ and $P-$wave beauty and charmed mesons, and we determine the relevant matrix elements in the infinite heavy quark mass limit, assuming the factorization ansatz. We estimate the rate of the decay: ${\cal B}(B \to D^+ D^- \pi^0)\simeq 1 \times 10^{-3}$. We also analyze the time-independent and time-dependent differential decay distributions, concluding that a signal for this process should be observed at the B-factories. Finally, we give an estimate of the decay rate of the Cabibbo-favoured process $B\to D^+ D^- K_S$.Comment: LaTex, 20 pages, 4 figure

Electronic Transport in Hybrid Mesoscopic Structures: A Nonequilibrium Green Function Approach

We present a unified transport theory of hybrid structures, in which a confined normal state ($N$) sample is sandwiched between two leads each of which can be either a ferromagnet ($F$) or a superconductor ($S$) via tunnel barriers. By introducing a four-dimensional Nambu-spinor space, a general current formula is derived within the Keldysh nonequilibrium Green function formalism, which can be applied to various kinds of hybrid mesoscopic systems with strong correlations even in the nonequilibrium situation. Such a formula is gauge invariant. We also demonstrate analytically for some quantities, such as the difference between chemical potentials, superconductor order parameter phases and ferromagnetic magnetization orientations, that only their relative value appears explicitly in the current expression. When applied to specific structures, the formula becomes of the Meir-Wingreen-type favoring strong correlation effects, and reduces to the Landauer-B\"uttiker-type in noninteracting systems such as the double-barrier resonant structures, which we study in detail beyond the wide-band approximation.Comment: 24 pages, 12 eps figures, Revtex

Metamorphosis and Taxonomy of Andreev Bound States

We analyze the spatial and energy dependence of the local density of states in a SNS junction. We model our system as a one-dimensional tight-binding chain which we solve exactly by numerical diagonalization. We calculate the dependence of the Andreev bound states on position, phase difference, gate voltage, and coupling with the superconducting leads. Our results confirm the physics predicted by certain analytical approximations, but reveal a much richer set of phenomena beyond the grasp of these approximations, such as the metamorphosis of the discrete states of the normal link (the normal bound states) into Andreev bound states as the leads become superconducting.Comment: 23 pages, 15 figure