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Volumn 54, Issue C, 2000, Pages 263-512

The Two-Dimensional Physics of Josephson Junction Arrays

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EID: 33749466593     PISSN: 00811947     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0081-1947(08)60250-7     Document Type: Chapter
Times cited : (133)

References (544)
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    • c is the energy cost to place a charge on an island in the array.
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    • The most weakly bound vortices are those with the greatest separation. These are also the ones most likely to have other, smaller pairs between them, reducing the interaction energy. It is the importance of these weakly bound vortices and interaction effects that leads to the need to look carefully at renormalization effects for exact results
    • The most weakly bound vortices are those with the greatest separation. These are also the ones most likely to have other, smaller pairs between them, reducing the interaction energy. It is the importance of these weakly bound vortices and interaction effects that leads to the need to look carefully at renormalization effects for exact results.
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    • Recall that we use the term dielectric constant to describe the screening of a particular pair of vortices by the other, smaller pairs because of the Coulomb gas analogy, wherein the vortices are treated as effective charges
    • Recall that we use the term dielectric constant to describe the screening of a particular pair of vortices by the other, smaller pairs because of the Coulomb gas analogy, wherein the vortices are treated as effective charges.
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    • This differs from the convention used for zero field defined by Eq, 9.6
    • This differs from the convention used for zero field defined by Eq. (9.6).
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    • Note that when we plot V versus I we refer to the step width; for I versus V we refer to the step height
    • Note that when we plot V versus I we refer to the step width; for I versus V we refer to the step height.
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    • We note that Straley; studied the motion of vortex superlattices with f=p/q and only a DC drive current. Interestingly, he found motion of the superlattice with a prominent frequency v= 2eVq/Nhp, a nearly correct result
    • We note that Straley; studied the motion of vortex superlattices with f=p/q and only a DC drive current. Interestingly, he found motion of the superlattice with a prominent frequency v= 2eVq/Nhp, a nearly correct result.
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    • It was assumed here that the matrix element of the Josephson coupling is not affected by charging effects. This assumption is correct if the superconductor's energy gap δ is large compared to the typical charging energy. Otherwise, the situation becomes more complicated; see, e.g
    • It was assumed here that the matrix element of the Josephson coupling is not affected by charging effects. This assumption is correct if the superconductor's energy gap δ is large compared to the typical charging energy. Otherwise, the situation becomes more complicated; see, e.g.
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    • Earlier, less systematic treatments of quantum corrections to the Kosterlitz-Thouless transition were given by Maekawa et al. (Ref. 259)
    • Earlier, less systematic treatments of quantum corrections to the Kosterlitz-Thouless transition were given by Maekawa et al. (Ref. 259)
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    • The results of these treatments differ from each other as well as from the quasi-classical expansion discussed here
    • The results of these treatments differ from each other as well as from the quasi-classical expansion discussed here.
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    • ij.
    • ij.
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    • KT, a quantum-induced transition (QUIT) by José. Of course, the quasi-classical approximation is not expected to be valid at low temperatures. Therefore, very extensive Monte-Carlo calculations were performed
    • KT, a quantum-induced transition (QUIT) by José. Of course, the quasi-classical approximation is not expected to be valid at low temperatures. Therefore, very extensive Monte-Carlo calculations were performed
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    • These qualitatively confirmed the existence of a second phase transition. The character and physical significance of that phase transition are not yet quite clear. Mikalopas et al.
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    • also studied quantum Josephson arrays with local charging energy. No QUIT was found, although metastable states associated with the phase boundary were. They speculated that these metastable states could be misidentified as a QUIT
    • also studied quantum Josephson arrays with local charging energy. No QUIT was found, although metastable states associated with the phase boundary were. They speculated that these metastable states could be misidentified as a QUIT.
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    • José and Rojas also corroborated the quasi-classical results by Monte-Carlo calculations
    • José and Rojas also corroborated the quasi-classical results by Monte-Carlo calculations.
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    • This last reference is usually more readily available than Peierls' original articles on the matter
    • This last reference is usually more readily available than Peierls' original articles on the matter.
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    • See, for example, Sec. 12.1.
    • See, for example, Sec. 12.1.
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    • 0=0, was proposed by)) and by Ferrell and Mirashem(Ref. 289). These authors considered small clusters of islands and treated both the Josephson coupling and the electrostatic coupling to islands outside the cluster in an average way.
    • 0=0, was proposed by)) and by Ferrell and Mirashem(Ref. 289). These authors considered small clusters of islands and treated both the Josephson coupling and the electrostatic coupling to islands outside the cluster in an average way.
    • (1984) Z. Phys. B , vol.51 , pp. 193
    • Mirashem, B.1    Ferrell, R.2
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    • 0=0 it is a factor of 2 smaller than the result of the variationally enhanced mean-field theory (cf. Section 33.b.5).
    • 0=0 it is a factor of 2 smaller than the result of the variationally enhanced mean-field theory (cf. Section 33.b.5).
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    • This section is a listing of papers that we did not reference in the main text but that are germaine to the subjects covered, or were published after our cut-off dates on the various topics, as well as papers on several topics we were not able to discuss-e.g, chaos, turbulence, and the quantized Hall effect. The papers are roughly divided by areas
    • This section is a listing of papers that we did not reference in the main text but that are germaine to the subjects covered, or were published after our cut-off dates on the various topics, as well as papers on several topics we were not able to discuss-e.g., chaos, turbulence, and the quantized Hall effect. The papers are roughly divided by areas.
  • 333
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    • The Topological Phase Transition
    • The Topological Phase Transition
  • 349
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    • Series in Sol. State Phys
    • Series in Sol. State Phys.
  • 389
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    • Frustration and Magnetic Field Effects
    • Frustration and Magnetic Field Effects
  • 435
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    • Giant Shapiro Steps
    • Giant Shapiro Steps
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    • Quantum Arrays
    • Quantum Arrays
  • 491
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    • Dynamical Effects, Chaos, and Turbulence
    • Dynamical Effects, Chaos, and Turbulence
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    • Miscellaneous Articles
    • Miscellaneous Articles


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