Comment on "Magnetic response of Disordered Metallic Rings: Large Contributions of Far Levels"

Comment on cond-mat/0205390; PRL 90, 026805 (2003

Effective descriptions of complex quantum systems: path integrals and operator ordering problems

We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard Feynman-Vernon Caldeira-Leggett model to include a non-linear coupling between ``particle'' and environment, and considering a particular spectral density of the coupling, a coordinate-dependent mass (or velocity-dependent potential) is obtained. The related effective quantum theory, which depends on the proper discretisation of the path integral, is derived and discussed. As a result, we find that in general a simple effective low-energy Hamiltonian, in which only the coordinate-dependent mass enters, cannot be formulated. The quantum theory of weakly coupled superconductors and the quantum dynamics of vortices in Josephson junction arrays are physical examples where these considerations, in principle, are of relevance.Comment: 13 pages, no figure

Decoherence without dissipation?

In a recent article, Ford, Lewis and O'Connell (PRA 64, 032101 (2001)) discuss a thought experiment in which a Brownian particle is subjected to a double-slit measurement. Analyzing the decay of the emerging interference pattern, they derive a decoherence rate that is much faster than previous results and even persists in the limit of vanishing dissipation. This result is based on the definition of a certain attenuation factor, which they analyze for short times. In this note, we point out that this attenuation factor captures the physics of decoherence only for times larger than a certain time t_mix, which is the time it takes until the two emerging wave packets begin to overlap. Therefore, the strategy of Ford et al of extracting the decoherence time from the regime t < t_mix is in our opinion not meaningful. If one analyzes the attenuation factor for t > t_mix, one recovers familiar behaviour for the decoherence time; in particular, no decoherence is seen in the absence of dissipation. The latter conclusion is confirmed with a simple calculation of the off-diagonal elements of the reduced density matrix.Comment: 8 pages, 4 figure

Entropy and Time

The emergence of a direction of time in statistical mechanics from an underlying time-reversal-invariant dynamics is explained by examining a simple model. The manner in which time-reversal symmetry is preserved and the role of initial conditions are emphasized. An extension of the model to finite temperatures is also discussed.Comment: 9 pages, 8eps figures. To appear in the theme issue of the American Journal of Physics on Statistical Physic

Critical Current in the High-T_c Glass model

The high-T_c glass model can be combined with the repulsive tt'--Hubbard model as microscopic description of the striped domains found in the high-T_c materials. In this picture the finite Hubbard clusters are the origin of the d-wave pairing. In this paper we show, that the glass model can also explain the critical currents usually observed in the high-T_c materials. We use two different approaches to calculate the critical current densities of the high-T_c glass model. Both lead to a strongly anisotropic critical current. Finally we give an explanation, why we expect nonetheless a nearly perfect isotropic critical current in the high-T_c superconductors.Comment: 8 pages with 5 eps-figures, LaTeX using RevTeX, accepted by Int.J.Mod.Phys.

Width and Magnetic Field Dependence of Transition Temperature in Ultranarrow Superconducting Wires

We calculate the transition temperature in ultranarrow superconducting wires as a function of wire width, resistance and applied magnetic field. We compare the results of first-order perturbation theory and the non-perturbative resummation technique developed by Oreg and Finkel'stein. The latter technique is found to be superior as it is valid even in the strong disorder limit. In both cases the predicted additional suppression of the transition temperature due to the reduced dimensionality is strongly dependent upon the boundary conditions used. When we use the correct (zero-gradient) boundary conditions, we find that theory and experiment are consistent, although more experimental data is required to verify this systematically. We calculate the magnetic field dependence of the transition temperature for different wire widths and resistances in the hope that this will be measured in future experiments. The predicted results have a rich structure - in particular we find a dimensional crossover which can be tuned by varying either the width of the wire or its resistance per square.Comment: 12 pages, 1 table, 7 figures. The changes made to the paper are ones of emphasis. The comparison between theory and experiment has been altered, and detailed comparisons of various approximations have been omitted, although the results are summarised in the paper. Much more emphasis has been placed on the new predictions of the effect of an applied magnetic field on transition temperature in wires (Figs. 5-7