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The physics of Josephson tunnel junctions drastically depends on their geometrical configurations. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the…
The high-Q harmonic oscillator mode of a Josephson junction can be used as a novel probe of spurious two-level systems (TLSs) inside the amorphous oxide tunnel barriers of the junction. In particular, we show that spectroscopic transmission…
We consider a Josephson junction system installed with a finite length inhomogeneity, either of microresistor or of microresonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent…
This paper applies recent results on the robust stability of nonlinear quantum systems to the case of a Josephson junction in a resonant cavity. The Josephson junction is characterized by a Hamiltonian operator which contains a…
Using highly efficient simulations of the tight-binding Bogoliubov-de Gennes model we solved self-consistently for the pair correlation and the Josephson current in a Superconducting-Bilayer graphene-Superconducting Josephson junction.…
We have carried out a detailed experimental investigation of the static properties of planar Josephson tunnel junctions in presence of a uniform external magnetic field applied in an arbitrary orientation with respect to the barrier plane.…
We derive microscopically the dynamics associated with the d.c. Josephson effect in a superconducting tunnel junction interacting with an arbitrary electromagnetic environment. To do so, we extend to superconducting junctions the so-called…
We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of…
A direct method for calculating the minimal length of ``one-dimensional'' Josephson junctions is proposed, in which the specific distribution of the magnetic flux retains its stability. Since the length of the junctions is a variable…
Josephson junctions with an intrinsic phase shift of pi, so-called pi Josephson junctions, can be realized by a weak link of a d-wave superconductor with an appropriate boundary geometry. A model for the pairing potential of an according…
The magnetic field distribution in the barrier of small planar Josephson tunnel junctions is numerically simulated in the case when an external magnetic field is applied perpendicular to the barrier plane. The simulations allow for…
Mathematical models related to some Josephson junctions are pointed out and attention is drawn to the solutions of certain initial boundary problems and to some of their estimates. In addition, results of rigorous analysis of the behaviour…
We prove that the equation modelling an annular Josephson junction has a rotating fluxon wave for all values of the parameters. We also obtain results on uniqueness of the rotating fluxon wave in some parameter regimes, and results on…
The $J(\phi)$ relation in SFIFS, SNINS and SIS tunnel junctions is studied. The method for analytical solution of linearized Usadel equations has been developed and applied to these structures. It is shown that the Josephson current across…
The fluxon solutions of a boundary problem for the sine-Gordon equation (SGE) are investigated numerically in dependence on the boundary conditions. Interconnection between fluxon and constant solutions is analyzed. Numerical results are…
Josephson effect in a planar graphene junction is studied by assuming that the coupling of a graphene sheet and two superconductors deposited on its top is described by a tunneling Hamiltonian. This model properly takes account of the…
The minimal length of ``one-dimensional'' Josephson junctions, in which the specific bound states of the magnetic flux retain their stability is discussed numerically. Thereby, we consider as ``long'' every Josephson junction, in which…
This is a detailed derivation of the equation for the voltage noise of a resistively shunted Josephson junction with non-sinusoidal current-phase relation, which was presented in Sov. Phys. JETP {\bf 67}, 579 (1988).
In parallel with Kibble's description of the onset of phase transitions in the early universe, Zurek has provided a simple picture for the onset of phase transitions in condensed matter systems, strongly supported by agreement with…
We study coherent phonon oscillations and tunneling between two coupled nonlinear nanomechanical resonators. We show that the coupling between two nanomechanical resonators creates an effective phonon Josephson junction which exhibits two…