The stationary energy current <i>J</i>₂ as a function of the external magnetic flux Φ_<i>e</i>.

<p>Panel (a) for various temperatures of reservoirs: ({<i>θ</i>₁, <i>θ</i>₂} = {1, 10}, {1, 5}, {5, 10}. Panel (b) for = 0.1 and various Josephson energy: <i>ε_J</i> = 8, 10, 12, 14. Panel (c) for <i>ε_J</i> = 14 and various charging energy = 0.1, 0.15, 0.225, 0.25.</p

Schematic representation of an rf SQUID in contact with two thermal reservoirs of different temperature <i>T</i>₁ and <i>T</i>₂.

<p>The loop is threaded with a magnetic flux <i>ϕ</i>.</p

Short-time regime of (a) the total energy current <i>J</i>(<i>t</i>), (b) the energy current <i>J</i>₁(<i>t</i>) induced only by the reservoir of temperature <i>T</i>₁ and (c) the energy current <i>J</i>₂(<i>t</i>) induced by the reservoir of temperature <i>T</i>₂ for selected values of the rescaled external magnetic flux Φ_<i>e</i>.

<p>The reservoir rescaled temperatures are <i>θ</i>₁ = <i>k</i>_<i>B</i> <i>T</i>₁/ℏ<i>ω</i>_<i>B</i> = 1, <i>θ</i>₂ = <i>k</i>_<i>B</i> <i>T</i>₂/ℏ<i>ω</i>_<i>B</i> = 10. Remaining parameters are fixed as: <i>ε_J</i> = 10, = 0.1 and <i>γ</i>₁ = <i>γ</i>₂ = 0.05. The dimensionless time <i>t</i> is rescaled by the oscillator frequency <i>ω</i>.</p

Pulse regime.

<p>(a) The total energy current <i>J</i>(<i>t</i>) = <i>J</i>₁(<i>t</i>) + <i>J</i>₂(<i>t</i>) as a function of time for three values of the external magnetic flux Φ_<i>e</i> = 0, 0.25, 0.5. The reservoir rescaled temperatures are <i>θ</i>₁ = 1, <i>θ</i>₂ = 10. (b) <i>J</i>(<i>t</i>) is shown for three sets of reservoirs temperatures {<i>θ</i>₁, <i>θ</i>₂} = {1, 10}, {1, 5}, {5, 10}. (c) <i>J</i>₁(<i>t</i>) and (d) <i>J</i>₂(<i>t</i>) for the same set of temperatures as in panel (b). In panels (b)-(d) the flux Φ_<i>e</i> = 0. Remaining parameters are fixed as: <i>ε_J</i> = 4, = 1.5 and <i>γ</i>₁ = <i>γ</i>₂ = 0.05. The dimensionless time <i>t</i> is rescaled by the oscillator frequency <i>ω</i>.</p