## Quantum statistical mechanics of an array of resistively shunted Josephson junctions

- We have constructed a fully quantum-mechanical model of an ordered array of resistively shunted Josephson junctions, and have determined the nature of the phase diagram as a function of the Josephson coupling, V, the capacitance, C (or, equivalently, the charging energy E0=4e2/C), the shunt resistance, R, and the temperature, T. In order to treat the dissipative element (R) in a quantum system, we have modeled it by a heat bath with spectral weight chosen to reproduce Ohmic resistance in the classical limit. Among other results, we find that in the extreme quantum limit, E0≫V≫kBT, the onset of global phase coherence (superconductivity) in the array occurs only if R is less than a critical value Rc=Ah/e2, where A is a number of order 1 which depends on the dimension and the lattice structure. The fact that the dissipation enters the thermodynamics at all is a consequence of the quantum nature of the transition. This transition is reminiscent of the results of recent experiments on thinWe have constructed a fully quantum-mechanical model of an ordered array of resistively shunted Josephson junctions, and have determined the nature of the phase diagram as a function of the Josephson coupling, V, the capacitance, C (or, equivalently, the charging energy E0=4e2/C), the shunt resistance, R, and the temperature, T. In order to treat the dissipative element (R) in a quantum system, we have modeled it by a heat bath with spectral weight chosen to reproduce Ohmic resistance in the classical limit. Among other results, we find that in the extreme quantum limit, E0≫V≫kBT, the onset of global phase coherence (superconductivity) in the array occurs only if R is less than a critical value Rc=Ah/e2, where A is a number of order 1 which depends on the dimension and the lattice structure. The fact that the dissipation enters the thermodynamics at all is a consequence of the quantum nature of the transition. This transition is reminiscent of the results of recent experiments on thin films of granular superconductors.…

Author: | Sudip Chakravarty, Gert-Ludwig IngoldORCiDGND, Steven Kivelson, Gergely Zimanyi |
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URN: | urn:nbn:de:bvb:384-opus4-406432 |

Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/40643 |

ISSN: | 0163-1829OPAC |

Parent Title (English): | Physical Review B |

Publisher: | American Physical Society (APS) |

Type: | Article |

Language: | English |

Year of first Publication: | 1988 |

Publishing Institution: | Universität Augsburg |

Release Date: | 2018/09/11 |

Volume: | 37 |

Issue: | 7 |

First Page: | 3283 |

Last Page: | 3294 |

DOI: | https://doi.org/10.1103/physrevb.37.3283 |

Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |

Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik | |

Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik I | |

Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |

Licence (German): | Deutsches Urheberrecht |