We study the competition between Josephson and charging energies in twodimensional arrays of ultr... more We study the competition between Josephson and charging energies in twodimensional arrays of ultrasmall Josephson junctions, when the mutual capacitance is dominant over the self-capacitance. Our calculations involve a combination of an analytic WKB renormalization group approach plus nonperturbative Quantum Monte Carlo simulations. We consider the zero frustration case in detail and we are able to make a successful comparison between our results and those obtained experimentally. *
In a scattering problem where an incoming particle interacts elastically with more than one scatt... more In a scattering problem where an incoming particle interacts elastically with more than one scatterer the trajectories that the particle can follow can be quite complex, even in two dimensions. In this paper the elastic scattering of a particle from a two-disk system is ...
We present results from an extensive analytic and numerical study of a twodimensional model of a ... more We present results from an extensive analytic and numerical study of a twodimensional model of a square array of ultrasmall Josephson junctions. We include the ultrasmall self and mutual capacitances of the junctions, for the same parameter ranges as those produced in the experiments. The model Hamiltonian studied includes the Josephson, E J , as well as the charging, E C , energies between superconducting islands. The corresponding quantum partition function is expressed in different calculationally convenient ways within its path-integral representation. The phase diagram is analytically studied using a WKB renormalization group (WKB-RG) plus a self-consistent harmonic approximation (SCHA) analysis, together with non-perturbative quantum Monte Carlo simulations. Most of the results presented here pertain to the superconductor to normal (S-N) region, although some results for the insulating to normal (I-N) region are also included. We find very good agreement between the WKB-RG and QMC results when compared to the experimental data. To fit the data, we only used the experimentally determined capacitances as fitting parameters. The WKB-RG analysis in the S-N region predicts a low temperature instability i.e. a Quantum Induced Transition (QUIT). We carefully analyze the possible existence of the QUIT via the QMC simulations and carry out a finite size analysis of T QU IT as a function of the magnitude of imaginary time axis L τ . We find that for some relatively large values of α = E C E J (1 ≤ α ≤ 2.25), the L τ → ∞ limit does appear to give a non-zero T QU IT , while for α ≥ 2.5, T QU IT = 0. We use the SCHA to analytically understand the L τ dependence of the QMC results with good agreement between them. Finally, we also carried out a WKB-RG analysis in the I-N region and found no evidence of a low temperature QUIT, up to lowest order in α −1 .
Formulae relating the two-point, space time, vorticity correlation tensor to the intensity of ult... more Formulae relating the two-point, space time, vorticity correlation tensor to the intensity of ultrasound scattered by a bounded region of nonvanishing vorticity are given both in two and in three dimensions. The incident wave is supposed to be of low intensity and of frequency high in comparison with typical frequencies of the target flow, which is assumed to be of low Math number; viscosity is assumed not to affect sound propagation. This result suggests a non-intrusive, direct, way of measuring vorticity correlations. The derivation emphasizes the central role played by vorticity as the basic scattering mechanism of the incident sound.
We study the competition between Josephson and charging energies in twodimensional arrays of ultr... more We study the competition between Josephson and charging energies in twodimensional arrays of ultrasmall Josephson junctions, when the mutual capacitance is dominant over the self-capacitance. Our calculations involve a combination of an analytic WKB renormalization group approach plus nonperturbative Quantum Monte Carlo simulations. We consider the zero frustration case in detail and we are able to make a successful comparison between our results and those obtained experimentally. *
In a scattering problem where an incoming particle interacts elastically with more than one scatt... more In a scattering problem where an incoming particle interacts elastically with more than one scatterer the trajectories that the particle can follow can be quite complex, even in two dimensions. In this paper the elastic scattering of a particle from a two-disk system is ...
We present results from an extensive analytic and numerical study of a twodimensional model of a ... more We present results from an extensive analytic and numerical study of a twodimensional model of a square array of ultrasmall Josephson junctions. We include the ultrasmall self and mutual capacitances of the junctions, for the same parameter ranges as those produced in the experiments. The model Hamiltonian studied includes the Josephson, E J , as well as the charging, E C , energies between superconducting islands. The corresponding quantum partition function is expressed in different calculationally convenient ways within its path-integral representation. The phase diagram is analytically studied using a WKB renormalization group (WKB-RG) plus a self-consistent harmonic approximation (SCHA) analysis, together with non-perturbative quantum Monte Carlo simulations. Most of the results presented here pertain to the superconductor to normal (S-N) region, although some results for the insulating to normal (I-N) region are also included. We find very good agreement between the WKB-RG and QMC results when compared to the experimental data. To fit the data, we only used the experimentally determined capacitances as fitting parameters. The WKB-RG analysis in the S-N region predicts a low temperature instability i.e. a Quantum Induced Transition (QUIT). We carefully analyze the possible existence of the QUIT via the QMC simulations and carry out a finite size analysis of T QU IT as a function of the magnitude of imaginary time axis L τ . We find that for some relatively large values of α = E C E J (1 ≤ α ≤ 2.25), the L τ → ∞ limit does appear to give a non-zero T QU IT , while for α ≥ 2.5, T QU IT = 0. We use the SCHA to analytically understand the L τ dependence of the QMC results with good agreement between them. Finally, we also carried out a WKB-RG analysis in the I-N region and found no evidence of a low temperature QUIT, up to lowest order in α −1 .
Formulae relating the two-point, space time, vorticity correlation tensor to the intensity of ult... more Formulae relating the two-point, space time, vorticity correlation tensor to the intensity of ultrasound scattered by a bounded region of nonvanishing vorticity are given both in two and in three dimensions. The incident wave is supposed to be of low intensity and of frequency high in comparison with typical frequencies of the target flow, which is assumed to be of low Math number; viscosity is assumed not to affect sound propagation. This result suggests a non-intrusive, direct, way of measuring vorticity correlations. The derivation emphasizes the central role played by vorticity as the basic scattering mechanism of the incident sound.
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Papers by Cristian Rojas