07-01-2012, 04:48 PM
Current responses and voltage fluctuations
in Josephson-junction systems
M.-S. Choi1, M. Y. Choi2 and S.-I. Lee1
1 Department of Physics, Pohang University of Science and Technology
Pohang 790-784, Korea
2 Department of Physics and Center for Theoretical Physics, Seoul National University
Seoul 151-742, Korea
(received 30 March 1998; accepted in nal form 23 June 1998)
PACS. 74.50+r { Proximity e ects, weak links, tunneling phenomena, and Josephson e ects.
PACS. 74.25Nf { Response to electromagnetic elds (nuclear magnetic resonance, surface
impedance, etc.).
PACS. 74.40+k { Fluctuations (noise, chaos, nonequilibrium superconductivity, localization,
etc.).
Abstract. { We consider arrays of Josephson junctions as well as single junctions in both the
classical and quantum-mechanical regimes, and examine the generalized (frequency-dependent)
resistance, which describes the dynamic responses of such Josephson-junction systems to external
currents. It is shown that the generalized resistance and the power spectrum of voltage
fluctuations are related via the fluctuation-dissipation theorem. Implications of the obtained
relations are also discussed in various experimental situations.
There has been much interest in the dynamics of Josephson junctions [1] and Josephsonjunction
arrays [2], e.g., current-voltage characteristics, dynamic resistivity, and voltage fluctuations.
Among these, the voltage fluctuations provide direct information about the dynamic
correlations in equilibrium [3, 4], whereas the resistivity probes the response to external currents
[5]. The latter is also closely related to the relaxation function, which describes the relaxation
behavior towards the equilibrium state. These two probes are therefore complementary to
each other, and one may expect, in view of the general idea of the fluctuation-dissipation (FD)
theorem, that there exists a FD relation between them. Nevertheless most existing studies have
been devoted either to the resistivity or to the voltage fluctuations, and the relation between
the two has hardly been investigated. Here we thus make use of the linear-response theory to
derive the generalized frequency-dependent resistance, and examine the relation between the
generalized resistance and the power spectrum of the voltage fluctuations in Josephson-junction
systems.
There are three energy scales in a Josephson-junction system: the Josephson coupling
energy EJ hIJ=2jej, the self-charging energy E0 e2=2C0, and the junction-charging energy
EC e2=2C, where IJ is the Josephson critical current and C0 and C are the self-capacitance
c EDP Sciences
in Josephson-junction systems
M.-S. Choi1, M. Y. Choi2 and S.-I. Lee1
1 Department of Physics, Pohang University of Science and Technology
Pohang 790-784, Korea
2 Department of Physics and Center for Theoretical Physics, Seoul National University
Seoul 151-742, Korea
(received 30 March 1998; accepted in nal form 23 June 1998)
PACS. 74.50+r { Proximity e ects, weak links, tunneling phenomena, and Josephson e ects.
PACS. 74.25Nf { Response to electromagnetic elds (nuclear magnetic resonance, surface
impedance, etc.).
PACS. 74.40+k { Fluctuations (noise, chaos, nonequilibrium superconductivity, localization,
etc.).
Abstract. { We consider arrays of Josephson junctions as well as single junctions in both the
classical and quantum-mechanical regimes, and examine the generalized (frequency-dependent)
resistance, which describes the dynamic responses of such Josephson-junction systems to external
currents. It is shown that the generalized resistance and the power spectrum of voltage
fluctuations are related via the fluctuation-dissipation theorem. Implications of the obtained
relations are also discussed in various experimental situations.
There has been much interest in the dynamics of Josephson junctions [1] and Josephsonjunction
arrays [2], e.g., current-voltage characteristics, dynamic resistivity, and voltage fluctuations.
Among these, the voltage fluctuations provide direct information about the dynamic
correlations in equilibrium [3, 4], whereas the resistivity probes the response to external currents
[5]. The latter is also closely related to the relaxation function, which describes the relaxation
behavior towards the equilibrium state. These two probes are therefore complementary to
each other, and one may expect, in view of the general idea of the fluctuation-dissipation (FD)
theorem, that there exists a FD relation between them. Nevertheless most existing studies have
been devoted either to the resistivity or to the voltage fluctuations, and the relation between
the two has hardly been investigated. Here we thus make use of the linear-response theory to
derive the generalized frequency-dependent resistance, and examine the relation between the
generalized resistance and the power spectrum of the voltage fluctuations in Josephson-junction
systems.
There are three energy scales in a Josephson-junction system: the Josephson coupling
energy EJ hIJ=2jej, the self-charging energy E0 e2=2C0, and the junction-charging energy
EC e2=2C, where IJ is the Josephson critical current and C0 and C are the self-capacitance
c EDP Sciences
