Origin of the anomalies: the modified Heisenberg equation

The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the non conservation of the charges. This explanation is equivalent to that of the Fujikawa in the path integral formalism. Finally, this approach is applied to the conformal symmetry breaking in two-dimensional quantum mechanics.Comment: 7 pages, LaTe

Density of states in a superconductor carrying a supercurrent

We have measured the tunneling density of states (DOS) in a superconductor carrying a supercurrent or exposed to an external magnetic field. The pair correlations are weakened by the supercurrent, leading to a modification of the DOS and to a reduction of the gap. As predicted by the theory of superconductivity in diffusive metals, we find that this effect is similar to that of an external magnetic field.Comment: To be published in Physical Review Letter

On the number of kk-cycles in the assignment problem for random matrices

We continue the study of the assignment problem for a random cost matrix. We analyse the number of $k$-cycles for the solution and their dependence on the symmetry of the random matrix. We observe that for a symmetric matrix one and two-cycles are dominant in the optimal solution. In the antisymmetric case the situation is the opposite and the one and two-cycles are suppressed. We solve the model for a pure random matrix (without correlations between its entries) and give analytic arguments to explain the numerical results in the symmetric and antisymmetric case. We show that the results can be explained to great accuracy by a simple ansatz that connects the expected number of $k$-cycles to that of one and two cycles.Comment: To appear in Journal of Statistical Mechanic

Effect of Magnetic Impurities on Energy Exchange between Electrons

In order to probe quantitatively the effect of Kondo impurities on energy exchange between electrons in metals, we have compared measurements on two silver wires with dilute magnetic impurities (manganese) introduced in one of them. The measurement of the temperature dependence of the electron phase coherence time on the wires provides an independent determination of the impurity concentration. Quantitative agreement on the energy exchange rate is found with a theory by G\"{o}ppert et al. that accounts for Kondo scattering of electrons on spin-1/2 impurities.Comment: 4 page

Transport in metallic multi-island Coulomb blockade systems: A systematic perturbative expansion in the junction transparency

We study electronic transport through metallic multi-island Coulomb-blockade systems. Based on a diagrammatic real-time approach, we develop a computer algorithm that generates and calculates all transport contributions up to second order in the tunnel-coupling strengths for arbitrary multi-island systems. This comprises sequential and cotunneling, as well as terms corresponding to a renormalization of charging energies and tunneling conductances. Multi-island cotunneling processes with energy transfer between different island are taken into account. To illustrate our approach we analyze the current through an island in Coulomb blockade, that is electrostatically coupled to a second island through which a large current is flowing. In this regime both cotunneling processes involving one island only as well as multi-island processes are important. The latter can be understood as photon-assisted sequential tunneling in the blockaded island, where the photons are provided by potential fluctuations due to sequential tunneling in the second island. We compare results of our approach to a P(E)-theory for photon-assisted tunneling in the weak coupling limit.Comment: 14 pages, 7 figures, published version; minor changes in Sec. IV

Charge Fluctuations in the Single Electron Box

Quantum fluctuations of the charge in the single electron box are investigated. Based on a diagrammatic expansion we calculate the average island charge number and the effective charging energy in third order in the tunneling conductance. Near the degeneracy point where the energy of two charge states coincides, the perturbative approach fails, and we explicitly resum the leading logarithmic divergencies to all orders. The predictions for zero temperature are compared with Monte Carlo data and with recent renormalization group results. While good agreement between the third order result and numerical data justifies the perturbative approach in most of the parameter regime relevant experimentally, near the degeneracy point and at zero temperature the resummation is shown to be insufficient to describe strong tunneling effects quantitatively. We also determine the charge noise spectrum employing a projection operator technique. Former perturbative and semiclassical results are extended by the approach.Comment: 20 pages, 15 figure

Bloch Oscillations in a Josephson Circuit

Bloch oscillations predicted to occur in current-biased single Josephson junctions have eluded direct observation up to now. Here, we demonstrate similar Bloch oscillations in a slightly richer Josephson circuit, the quantronium. The quantronium is a Bloch transistor with two small junctions in series, defining an island, in parallel with a larger junction. In the ground state, the microwave impedance of the device is modulated periodically with the charge on the gate capacitor coupled to the transistor island. When a current flows across this capacitor, the impedance modulation occurs at the Bloch frequency, which yields Bloch sidebands in the spectrum of a reflected continuous microwave signal. We have measured this spectrum, and compared it to predictions based on a simple model for the circuit. We discuss the interest of this experiment for metrology and for mesoscopic physics

Vacuum Energy and Renormalization on the Edge

The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective the renormalization prescriptions not only imply the renormalization of the couplings of the theory in the bulk but also the appearance of a flow in the space of boundary conditions. For regular boundaries this flow has a large variety of fixed points and no cyclic orbit. The family of fixed points includes Neumann and Dirichlet boundary conditions. In one-dimensional field theories pseudoperiodic and quasiperiodic boundary conditions are also RG fixed points. Under these conditions massless bosonic free field theories are conformally invariant. Among all fixed points only Neumann boundary conditions are infrared stable fixed points. All other conformal invariant boundary conditions become unstable under some relevant perturbations. In finite volumes we analyse the dependence of the vacuum energy along the trajectories of the renormalization group flow providing an interesting framework for dark energy evolution. On the contrary, the renormalization group flow on the boundary does not affect the leading behaviour of the entanglement entropy of the vacuum in one-dimensional conformally invariant bosonic theories.Comment: 10 pages, 1 eps figur

Exact renormalization-group analysis of first order phase transitions in clock models

We analyze the exact behavior of the renormalization group flow in one-dimensional clock-models which undergo first order phase transitions by the presence of complex interactions. The flow, defined by decimation, is shown to be single-valued and continuous throughout its domain of definition, which contains the transition points. This fact is in disagreement with a recently proposed scenario for first order phase transitions claiming the existence of discontinuities of the renormalization group. The results are in partial agreement with the standard scenario. However in the vicinity of some fixed points of the critical surface the renormalized measure does not correspond to a renormalized Hamiltonian for some choices of renormalization blocks. These pathologies although similar to Griffiths-Pearce pathologies have a different physical origin: the complex character of the interactions. We elucidate the dynamical reason for such a pathological behavior: entire regions of coupling constants blow up under the renormalization group transformation. The flows provide non-perturbative patterns for the renormalization group behavior of electric conductivities in the quantum Hall effect.Comment: 13 pages + 3 ps figures not included, TeX, DFTUZ 91.3