arXiv subjects
Publications and source records attributed to Vinay Ambegaokar.
The autocorrelation function of the Langevin force in the model introduced in the cited paper is calculated and verified to be correct.
Using the Ehrenfest urn model we illustrate the subtleties of error estimation in Monte Carlo simulations. We discuss how the smooth results of correlated sampling in Markov chains can fool one's perception of the accuracy of the data, and show (via numerical and analytical methods) how to obtain reliable error estimates from correlated samples.
An explicit demonstration is given of a harmonic oscillator in equilibrium approaching the equilibrium of a corresponding interacting system by coupling it to a thermal bath consisting of a continuum of harmonic oscillators.
This is the first in a series of two papers (I and II), in which we revisit the problem of decoherence in weak localization. The basic challenge addressed in our work is to calculate the decoherence of electrons interacting with a quantum-mechanical environment, while taking proper account of the Pauli principle. First, we review the usual influence functional approach valid for decoherence of electrons due to classical noise, showing along the way how the quantitative accuracy can be improved by properly averaging over closed (rather than unrestricted) random walks. We then use a heuristic approach to show how the Pauli principle may be incorporated into a path-integral description of decoherence in weak localization. This is accomplished by introducing an effective modification of the quantum noise spectrum, after which the calculation proceeds in analogy to the case of classical noise. Using this simple but efficient method, which is consistent with much more laborious diagrammatic calculations, we demonstrate how the Pauli principle serves to suppress the decohering effects of quantum fluctuations of the environment, and essentially confirm the classic result of Altshuler, Aronov and Khmelnitskii for the energy-averaged decoherence rate, which vanishes at zero temperature. Going beyond that, we employ our method to calculate explicitly the leading quantum corrections to the classical decoherence rates, and to provide a detailed analysis of the energy-dependence of the decoherence rate. The basic idea of our approach is general enough to be applicable to decoherence of degenerate Fermi systems in contexts other than weak localization as well. -- Paper II will provide a more rigorous diagrammatic basis for our results, by rederiving them from a Bethe-Salpeter equation for the Cooperon.
This is the second in a series of two papers (I and II) on the problem of decoherence in weak localization. In paper I, we discussed how the Pauli principle could be incorporated into an influence functional approach for calculating the Cooperon propagator and the magnetoconductivity. In the present paper II, we check and confirm the results so obtained by diagrammatically setting up a Bethe-Salpeter equation for the Cooperon, which includes self-energy and vertex terms on an equal footing and is free from both infrared and ultraviolet divergencies. We then approximately solve this Bethe-Salpeter equation by the Ansatz C(t) = C^0 (t) e^{-F(t)}, where the decay function F(t) determines the decoherence rate. We show that in order to obtain a divergence-free expression for the decay function F(t), it is sufficient to calculate C^1 (t), the Cooperon in the position-time representation to first order in the interaction. Paper II is independent of paper I and can be read without detailed knowledge of the latter.
The time development of the reduced density matrix for a quantum oscillator damped by coupling it to an ohmic environment is calculated via an identity of the Debye-Waller form. Results obtained some years ago by Hakim and the author in the free particle limit [1] are thus recovered. The evolution of a free particle in a prepared initial state is examined, and a previously published exchange [2,3] is illuminated with figures showing no decoherence without dissipation. [1] V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1985). [2] G.W. Ford and R.F. O'Connell, Phys. Rev. A 70, 026102 (2004). [3] D. Gobert, J. von Delft, and V. Ambegaokar, Phys. Rev. A 70, 0261001 (2004).
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.
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.
Using a generalization of the non-crossing approximation which incorporates Andreev reflection, we study the properties of an infinite-U Anderson impurity coupled to two superconducting leads. In the regime where $Δ$ and $T_K$ are comparable, we find that the position of the sub-gap resonance in the impurity spectral function develops a strong anomalous phase dependence-- its energy is a minimum when the phase difference between the superconductors is equal to $π$. Calculating the Josephson current through the impurity, we find that $π$-junction behaviour is lost as the position of the bound-state moves above the Fermi energy.
We calculate the first-order perturbative correction to the transition temperature $T_c$ in a superconductor with both non-magnetic and magnetic impurities. We do this by first evaluating the correction to the effective potential, $Ω(Δ)$, and then obtain the first-order correction to the order parameter, $Δ$, by finding the minimum of $Ω(Δ)$. Setting $Δ=0$ finally allows $T_c$ to be evaluated. $T_c$ is now a function of both the resistance per square, $R_\square$, a measure of the non-magnetic disorder, and the spin-flip scattering rate, $1/τ_s$, a measure of the magnetic disorder. We find that the effective pair-breaking rate per magnetic impurity is virtually independent of the resistance per square of the film, in agreement with an experiment of Chervenak and Valles. This conclusion is supported by both the perturbative calculation, and by a non-perturbative re-summation technique.
We examine the properties of an infinite-$U$ Anderson impurity coupled to both normal and superconducting metals. Both the cases of a quantum dot and a quantum point contact containing an impurity are considered; for the latter, we study both one and two-channel impurities. Using a generalization of the noncrossing approximation which incorporates multiple Andreev reflection, we compute the impurity spectral function and the linear-response conductance of these devices. We find generically that the Kondo resonance develops structure at energies corresponding to the superconducting gap, and that the magnitude of the resonance at the Fermi energy is altered. This leads to observable changes in the zero-bias conductance as compared to the case with no superconductivity.
Recent experiments by Ralph and Buhrman on zero-bias anomalies in quenched Cu nanoconstrictions (reviewed in the preceding paper, I), are in accord with the assumption that the interaction between electrons and nearly degenerate two-level systems in the constriction can be described, for sufficiently small voltages and temperatures ($V,T < \Tk$), by the 2-channel Kondo (2CK) model. Motivated by these experiments, we introduce a generalization of the 2CK model, which we call the nanoconstriction 2-channel Kondo model (NTKM), that takes into account the complications arising from the non-equilibrium electron distribution in the nanoconstriction. We calculate the conductance $G(V,T)$ of the constriction in the weakly non-equilibrium regime of $V,T \ll \Tk$ by combining concepts from Hershfield's $Y$-operator formulation of non-equilibrium problems and Affleck and Ludwig's exact conformal field theory (CFT) solution of the 2CK problem (CFT technicalities are discussed in a subsequent paper, III). Finally, we extract from the conductance a universal scaling curve $Γ(v)$ and compare it with experiment. Combining our results with those of Hettler, Kroha and Hershfield, we conclude that the NTKM achieves quantitative agreement with the experimental scaling data.
We present calculations of the upper critical field in superconducting films as a function of increasing disorder (as measured by the normal state resistance per square). In contradiction to previous work, we find that there is no anomalous low-temperature positive curvature in the upper critical field as disorder is increased. We show that the previous prediction of this effect is due to an unjustified analytical approximation of sums occuring in the perturbative calculation. Our treatment includes both a careful analysis of first-order perturbation theory, and a non-perturbative resummation technique. No anomalous curvature is found in either case. We present our results in graphical form.
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.
Assertions by Overhauser of error in accepted calculations of the temperature dependence of the Josephson current are shown to be without merit.
We discuss the influence of the electromagnetic environment and the electron-electron interaction on the weak localization correction to the conductivity of a disordered metal. The theory of this phenomenon for sufficiently high temperature, where the quantum nature of the interaction of electrons with the electromagnetic field can be disregarded, has been understood for some time. We consider the first order quantum correction to this semiclassical description and work out the temperature range in which this correction is small. No external low frequency cut-off is needed in our calculation. We conclude that in the whole region of temperature where the weak localization correction is much smaller than the Drude conductivity the classical treatment of the interaction is valid.
Certain zero-bias anomalies (ZBAs) in the voltage, temperature and magnetic field dependence of the conductance $G(V,T,H)$ of quenched Cu point contacts have previously been interpreted to be due to non-magnetic 2-channel Kondo (2CK) scattering from near-degenerate atomic two-level tunneling systems (Ralph and Buhrman, 1992; Ralph et al. 1994), and hence to represent an experimental realization of the non-Fermi-liquid physics of the T=0 fixed point of the 2-channel Kondo model. In this, the first in a series of three papers (I,II,III) devoted to 2-channel Kondo physics, we present a comprehensive review of the quenched Cu ZBA experiments and their 2CK interpretation, including new results on ZBAs in constrictions made from Ti or from metallic glasses. We first review the evidence that the ZBAs are due to electron scattering from stuctural defects that are not static, but possess internal dynamics. In order to distinguish between several mechanisms proposed to explain the experiments, we then analyze the scaling properties of the conductance at low temperature and voltage and extract from the data a universal scaling function $Γ(v)$. The theoretical calculation of the corresponding scaling function within the 2CK model is the subject of papers II and III. The main conclusion of our work is that the properties of the ZBAs, and most notably their scaling behavior, are in good agreement with the 2CK model and clearly different from several other proposed mechanisms.
We point out that even at the absolute zero of temperature environmental decoherence limits the destructive interference between time-reversed paths for an electron in a disordered metal, and thus causes the leading (`weak localization') quantum correction to the conductivity to saturate at T=0. Our calculation, which is intended to be illustrative rather than complete, uses a model in which an electron interacts with the fluctuations of the mean voltage in the sample. The average of the fluctuations produces the steady damping well known in Brownian motion, introduces a direction of time, ensures that arbitrarily long time-reversed electron paths lose phase coherence, and is consistent with the experimental observation of a finite low temperature phase-breaking lifetime.