Point Charge Self-Energy in the General Relativity

Singularities in the metric of the classical solutions to the Einstein equations (Schwarzschild, Kerr, Reissner -- Nordstr\"om and Kerr -- Newman solutions) lead to appearance of generalized functions in the Einstein tensor that are not usually taken into consideration. The generalized functions can be of a more complex nature than the Dirac \d-function. To study them, a technique has been used based on a limiting solution sequence. The solutions are shown to satisfy the Einstein equations everywhere, if the energy-momentum tensor has a relevant singular addition of non-electromagnetic origin. When the addition is included, the total energy proves finite and equal to $mc^2$, while for the Kerr and Kerr--Newman solutions the angular momentum is $mc {\bf a}$. As the Reissner--Nordstr\"om and Kerr--Newman solutions correspond to the point charge in the classical electrodynamics, the result obtained allows us to view the point charge self-energy divergence problem in a new fashion.Comment: VI Fridmann Seminar, France, Corsica, Corgeze, 2004, LaTeX, 6 pages, 2 fige

Transport of interacting electrons in arrays of quantum dots and diffusive wires

We develop a detailed theoretical investigation of the effect of Coulomb interaction on electron transport in arrays of chaotic quantum dots and diffusive metallic wires. Employing the real time path integral technique we formulate a new Langevin-type of approach which exploits a direct relation between shot noise and interaction effects in mesoscopic conductors. With the aid of this approach we establish a general expression for the Fano factor of 1D quantum dot arrays and derive a complete formula for the interaction correction to the current which embraces all perturbative results previously obtained for various quasi-0D and quasi-1D disordered conductors and extends these results to yet unexplored regimes.Comment: 12 pages, 2 figure

Irreversibility on the Level of Single-Electron Tunneling

We present a low-temperature experimental test of the fluctuation theorem for electron transport through a double quantum dot. The rare entropy-consuming system trajectories are detected in the form of single charges flowing against the source-drain bias by using time-resolved charge detection with a quantum point contact. We find that these trajectories appear with a frequency that agrees with the theoretical predictions even under strong nonequilibrium conditions, when the finite bandwidth of the charge detection is taken into account

Nonequilibrium phenomena in multiple normal-superconducting tunnel heterostructures

Using the nonequilibrium theory of superconductivity with the tunnel Hamiltonian, we consider a mesoscopic NISINISIN heterostructure, i.e., a structure consisting of five intermittent normal-metal (N) and superconducting (S) regions separated by insulating tunnel barriers (I). Applying the bias voltage between the outer normal electrodes one can drive the central N island very far from equilibrium. Depending on the resistance ratio of outer and inner tunnel junctions, one can realize either effective electron cooling in the central N island or create highly nonequilibrium energy distributions of electrons in both S and N islands. These distributions exhibit multiple peaks at a distance of integer multiples of the superconducting chemical potential. In the latter case the superconducting gap in the S islands is strongly suppressed as compared to its equilibrium value

Decoherence of a particle in a ring

We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty metal environment. At low but finite temperatures we find a dephasing rate $\propto T^{3/2}$, and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass of the particle. At zero temperature we find that spatial fluctuations suppress the possibility of having a power law decay of coherence.Comment: 5 pages, 1 figure, proofed version to be published in EP

Comment on "Quantum Decoherence in Disordered Mesoscopic Systems"

In a recent paper, Phys. Rev. Lett. 81, 1074 (1998), Golubev and Zaikin (GZ) found that ``zero-point fluctuations of electrons'' contribute to the dephasing rate extracted from the magnetoresistance. As a result, the dephasing rate remains finite at zero temperature. GZ claimed that their results ``agree well with the experimental data''. We point out that the GZ results are incompatible with (i) conventional perturbation theory of the effects of interaction on weak localization (WL), and (ii) with the available experimental data. More detailed criticism of GZ findings can be found in cond-mat/9808053.Comment: 1 page, no figure

Parity-Affected Superconductivity in Ultrasmall Metallic Grains

We investigate the breakdown of BCS superconductivity in {\em ultra}\/small metallic grains as a function of particle size (characterized by the mean spacing $d$ between discrete electronic eigenstates), and the parity ($P$ = even/odd) of the number of electrons on the island. Assuming equally spaced levels, we solve the parity-dependent BCS gap equation for the order parameter $\Delta_P (d,T)$. Both the $T=0$ critical level spacing $d_{c,P}$ and the critical temperature $T_{c,P} (d)$ at which $\Delta_P = 0$ are parity dependent, and both are so much smaller in the odd than the even case that these differences should be measurable in current experiments.Comment: 4 pages RevTeX, 1 encapsulated postscript figure, submitted to Physical Review Letter