# Effect of quantum noise and tunneling on the fluctuational voltage-current characteristics and the lifetime of the zero-voltage state in Josephson junctions

## Abstract

The minima of the potential energy for the dynamical variable phi of a Josephson junction are separated by barriers of height h-dash-barI-italic/sub c-italic//e, where I-italic/sub c-italic/ is the critical current. At low temperatures, T-italic<h-dash-bar..cap omega../2..pi.. (..cap omega.. is the Josephson plasma frequency). We consider this problem for high-quality junctions (R-italicC-italic..cap omega..>>1, R-italic and C-italic are the resistance and the capacitance of the junction), accounting for the effect of a Johnson-Nyquist noise and quantum tunneling at the barrier top. With a simplifying assumption, we derive a pair of integral equations containing an e-italicn-italice-italicr-italicg-italicy-italic v-italica-italicr-italici-italica-italicb-italicl-italice-italic for the steady-state distribution of phi and phi-dot, and solve it by a modification of the Wiener-Hopf method. The result is a formula for the current dependence of the fluctuational voltage, valid for currents I-italic<4I-italic/sub c-italic//..pi..RC..cap omega... We discuss the ohmic resistance of the junction, the case of a relatively high damping (1<..0, and perturbative quantum corrections in (h-dash-bar..cap omega../T-italic)/sup 2/<<1.

- Authors:

- Publication Date:

- Research Org.:
- Landau Institute for Theoretical Physics, Moscow, U.S.S.R.

- OSTI Identifier:
- 5582225

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev. B: Condens. Matter; (United States)

- Additional Journal Information:
- Journal Volume: 34:3

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; JOSEPHSON JUNCTIONS; ELECTRIC CONDUCTIVITY; TEMPERATURE NOISE; DAMPING; FLUCTUATIONS; INTEGRAL EQUATIONS; QUANTUM MECHANICS; TUNNEL EFFECT; ELECTRICAL PROPERTIES; EQUATIONS; JUNCTIONS; MECHANICS; NOISE; PHYSICAL PROPERTIES; SUPERCONDUCTING JUNCTIONS; VARIATIONS; 420201* - Engineering- Cryogenic Equipment & Devices

### Citation Formats

```
Mel'nikov, V I, and Suetoe, A.
```*Effect of quantum noise and tunneling on the fluctuational voltage-current characteristics and the lifetime of the zero-voltage state in Josephson junctions*. United States: N. p., 1986.
Web. doi:10.1103/PhysRevB.34.1514.

```
Mel'nikov, V I, & Suetoe, A.
```*Effect of quantum noise and tunneling on the fluctuational voltage-current characteristics and the lifetime of the zero-voltage state in Josephson junctions*. United States. https://doi.org/10.1103/PhysRevB.34.1514

```
Mel'nikov, V I, and Suetoe, A. 1986.
"Effect of quantum noise and tunneling on the fluctuational voltage-current characteristics and the lifetime of the zero-voltage state in Josephson junctions". United States. https://doi.org/10.1103/PhysRevB.34.1514.
```

```
@article{osti_5582225,
```

title = {Effect of quantum noise and tunneling on the fluctuational voltage-current characteristics and the lifetime of the zero-voltage state in Josephson junctions},

author = {Mel'nikov, V I and Suetoe, A},

abstractNote = {The minima of the potential energy for the dynamical variable phi of a Josephson junction are separated by barriers of height h-dash-barI-italic/sub c-italic//e, where I-italic/sub c-italic/ is the critical current. At low temperatures, T-italic<h-dash-bar..cap omega../2..pi.. (..cap omega.. is the Josephson plasma frequency). We consider this problem for high-quality junctions (R-italicC-italic..cap omega..>>1, R-italic and C-italic are the resistance and the capacitance of the junction), accounting for the effect of a Johnson-Nyquist noise and quantum tunneling at the barrier top. With a simplifying assumption, we derive a pair of integral equations containing an e-italicn-italice-italicr-italicg-italicy-italic v-italica-italicr-italici-italica-italicb-italicl-italice-italic for the steady-state distribution of phi and phi-dot, and solve it by a modification of the Wiener-Hopf method. The result is a formula for the current dependence of the fluctuational voltage, valid for currents I-italic<4I-italic/sub c-italic//..pi..RC..cap omega... We discuss the ohmic resistance of the junction, the case of a relatively high damping (1<..0, and perturbative quantum corrections in (h-dash-bar..cap omega../T-italic)/sup 2/<<1.},

doi = {10.1103/PhysRevB.34.1514},

url = {https://www.osti.gov/biblio/5582225},
journal = {Phys. Rev. B: Condens. Matter; (United States)},

number = ,

volume = 34:3,

place = {United States},

year = {1986},

month = {8}

}