Skip to main content
3 votes

Lagrangian for a non-linear wave equation

Here is one proposal in 1+1D: Define a Lagrangian density $$ {\cal L} ~=~ \frac{1}{2} (\partial_t\Phi)^2 +\cos(\partial_x\Phi).\tag{1}$$ Then the Euler-Lagrange (EL) equation is $$ \partial^2_t\Phi-\...
Qmechanic's user avatar
  • 205k
3 votes
Accepted

Resistively and Capacitively Shunted Junction (RCSJ) Model of Josephson Junction Numerical Solution

First, think about the point $U=0$. Any constant value of $\delta$ is a solution to the second equation. This means the current can take any value between $-I_0$ and $I_0$, as you see at $V=0$ in your ...
user34722's user avatar
  • 2,504
2 votes
Accepted

Josephson junction characteristics

Since $L_J=\frac{\Phi_0}{2\pi I_0}$ is the inductance of the junction, $1/\omega_c=L_J/R$ is just the $RL$ time constant of the junction. In the resistively-shunted junction model (RSJ), one can ...
Ofer Naaman's user avatar
2 votes
Accepted

What makes cooper pairs hop to another superconductor?

Hopping is a bad way to understand the physics of superconductors, because it implies movement of discrete charges, whereas the state of a superconductor has a definite phase and uncertain number of ...
Roger V.'s user avatar
  • 59.4k
1 vote

Thermal Smearing in Josephson Junction

This might be a helpful reference to point you in the right direction, although not entirely sure. It discusses a Josephson junction simulation it appears: https://arxiv.org/pdf/1909.12421 A quote ...
ad2004's user avatar
  • 1,136
1 vote

Resistively and Capacitively Shunted Junction (RCSJ) Model of Josephson Junction Numerical Solution

For your simulation, it’s best to start from the dimensionless equation (slide 29): $$ \beta_c\ddot\delta+\dot\delta+\sin\delta=i+i_N \tag{1} $$ In your problem, $i$ is imposed (DC, additional ...
LPZ's user avatar
  • 12.8k
1 vote

Questions about the SQUID (Superconducting Quantum Interference Device)

There is an (understandable) confusion here stemming from the fact that "critical current" gets used in a number of completely different, yet superconductor-adjacent ways. The important ...
J. Murray's user avatar
  • 70k
1 vote
Accepted

Unitary Transformation Taking a 4$\pi$ Periodic Wave Function to 2$\pi$ Periodic Wave Function

First note (I'm assuming there are no operator ordering issues) \begin{eqnarray} \Omega(\phi+2\pi) &=& \Omega(\phi) e^{i(1-\hat{P})\pi/2} = \Omega(\phi)\left(e^{i\pi}\right)^{(1-\hat{P})/2} = \...
Andrew's user avatar
  • 50.2k
1 vote
Accepted

Microscopic derivation of the Josephson effect

First, in the last equation of your problem, the $t$ there should be $te^{i\phi}$, then it's clear why the result only contains the anomalous Green's function $\mathcal{F}(\textbf{k},\tau)$: terms ...
Black Monolith's user avatar
1 vote

Questions regarding the pair of Josephson equations

The quantity $V$ is the potential difference across the junction. It does not matter where it comes from. The quantity $\varphi$ is the difference in phase of the order parameter $\langle\psi\psi \...
mike stone's user avatar
  • 53.9k
1 vote

Wavefunction used in Derivation of Josephson Effect

I guess the main point is that in some ordinary material you have no such collective behavior as in a superconductor, which allows you to describe all electrons within your material using only one ...
Milarepa's user avatar
  • 892
1 vote

Josephson junction: why do we need a capacitance in parallel to the inductance in the description?

As you pointed out, the small-signal model derived from the two Josephson relations is a perfect inductor. Any parallel capacitance in the model is not derived from the Josephson relations at all, ...
anonymous's user avatar
1 vote
Accepted

Computing flux modulation of the energy spectrum in a DC SQUID

After some more investigation with a friend who works with superconducting circuits I have the solution. The first mistake was I wasn't giving it the values I thought, so the peak frequency error was ...
Nathan Holman's user avatar
1 vote
Accepted

Why do excited states of charge qubits have higher charge sensitivity than the ground state?

I think it helps to analyze this problem in the following two limits: (i) when $E_C \gg E_J$ (the charge qubit limit) and (ii) when $E_J \gg E_C$ (the transmon limit). Since the charge qubit came ...
Alex Opremcak's user avatar
1 vote

The Hamiltonian for Josephson Junctions

In the physics of nanostructures one often uses something like: $$\hat{H} = -E_J \cos\hat{\varphi},$$ where $\hat{\varphi}=\hat{\varphi}_1 - \hat{\varphi}_2$ is the superconductor phase difference, ...
Roger V.'s user avatar
  • 59.4k
1 vote

The Hamiltonian for Josephson Junctions

In the same spirit as the tight-binding approach for atomic orbitals in a lattice, you assume that the spatial wavefunctions (let's call them $\phi_{1,2}(\mathbf{r})$ here) on either site of the ...
Naloo's user avatar
  • 13
1 vote

Is there net current through a Josephson junction at zero bias?

The direction and magnitude of the current depends on the difference in phase of the order parameter on the two sides of the junction. In the simplest case the current from the left to right right of ...
mike stone's user avatar
  • 53.9k
1 vote

What does the $I$-$V$ curve in josephson junction mean?

To me it seems like DanielSanks answer, while being correct, doesn't actually explain the picture at all. When looking at Josephson Junctions there are two models that can be applied. The first is to ...
1MegaMan1's user avatar
  • 340

Only top scored, non community-wiki answers of a minimum length are eligible