Periodic alternating 0,π0,\pi-junction structures as realization of ϕ\phi-Josephson junctions

We consider the properties of a periodic structure consisting of small alternating 0- and pi- Josephson junctions. We show that depending on the relation between the lengths of the individual junctions, this system can be either in the homogeneous or in the phase-modulated state. The modulated phase appears via a second order phase transition when the mismatch between the lengths of the individual junctions exceeds the critical value. The screening length diverges at the transition point. In the modulated state, the equilibrium phase difference in the structure can take any value from -pi to pi (phi-junction). The current-phase relation in this structure has very unusual shape with two maxima. As a consequence, the field dependence of the critical current in a small structure is very different from the standard Fraunhofer dependence. The Josephson vortex in a long structure carries partial magnetic flux, which is determined by the equilibrium phase.Comment: 4 pages, 3 figues, submitted to Phys. Rev.

An Intuitionistic Formula Hierarchy Based on High-School Identities

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal) propositional sequent calculi are formula (i.e. sequent) isomorphisms corresponding to the high-school identities, we show that one can obtain a more compact variant of a proof system, consisting of non-invertible proof rules only, and where the invertible proof rules have been replaced by a formula normalisation procedure. Moreover, for certain proof systems such as the G4ip sequent calculus of Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the non-invertible proof rules as strict inequalities between exponential polynomials; a careful combinatorial treatment is given in order to establish this fact. Finally, we extend the exponential polynomial analogy to the first-order quantifiers, showing that it gives rise to an intuitionistic hierarchy of formulas, resembling the classical arithmetical hierarchy, and the first one that classifies formulas while preserving isomorphism

Electromagnetic waves in a Josephson junction in a thin film

We consider a one-dimensional Josephson junction in a superconducting film with the thickness that is much less than the London penetration depth. We treat an electromagnetic wave propagating along this tunnel contact. We show that the electrodynamics of a Josephson junction in a thin film is nonlocal if the wave length is less than the Pearl penetration depth. We find the integro-differential equation determining the phase difference between the two superconductors forming the tunnel contact. We use this equation to calculate the dispersion relation for an electromagnetic wave propagating along the Josephson junction. We find that the frequency of this wave is proportional to the square root of the wave vector if the wave length is less than the Pearl penetration depth.Comment: 12 pages, a figure is included as a uuencodeded postscript file, ReVTe

Collapse of the critical state in superconducting niobium

Giant abrupt changes in the magnetic flux distribution in niobium foils were studied by using magneto-optical visualization, thermal and magnetic measurements. Uniform flux jumps and sometimes almost total catastrophic collapse of the critical state are reported. Results are discussed in terms of thermomagnetic instability mechanism with different development scenarios.Comment: arXiv.org produced artifacts in color images (three versions were attempts to make better images). Download clean PDF and watch video-figures at: "http://cmp.ameslab.gov/supermaglab/video/Nb.html

Flux Creep and Flux Jumping

We consider the flux jump instability of the Bean's critical state arising in the flux creep regime in type-II superconductors. We find the flux jump field, $B_j$, that determines the superconducting state stability criterion. We calculate the dependence of $B_j$ on the external magnetic field ramp rate, $\dot B_e$. We demonstrate that under the conditions typical for most of the magnetization experiments the slope of the current-voltage curve in the flux creep regime determines the stability of the Bean's critical state, {\it i.e.}, the value of $B_j$. We show that a flux jump can be preceded by the magneto-thermal oscillations and find the frequency of these oscillations as a function of $\dot B_e$.Comment: 7 pages, ReVTeX, 2 figures attached as postscript file

Suppression of surface barrier in superconductors by columnar defects

We investigate the influence of columnar defects in layered superconductors on the thermally activated penetration of pancake vortices through the surface barrier. Columnar defects, located near the surface, facilitate penetration of vortices through the surface barrier, by creating ``weak spots'', through which pancakes can penetrate into the superconductor. Penetration of a pancake mediated by an isolated column, located near the surface, is a two-stage process involving hopping from the surface to the column and the detachment from the column into the bulk; each stage is controlled by its own activation barrier. The resulting effective energy is equal to the maximum of those two barriers. For a given external field there exists an optimum location of the column for which the barriers for the both processes are equal and the reduction of the effective penetration barrier is maximal. At high fields the effective penetration field is approximately two times smaller than in unirradiated samples. We also estimate the suppression of the effective penetration field by column clusters. This mechanism provides further reduction of the penetration field at low temperatures.Comment: 8 pages, 9 figures, submitted to Phys. Rev.

Semantics and Proof Theory of the Epsilon Calculus

The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing the development of proof-theoretically well-behaved systems are outlined.Comment: arXiv admin note: substantial text overlap with arXiv:1411.362

Josephson Vortex Bloch Oscillations: Single Pair Tunneling Effect

We consider the Josephson vortex motion in a long one--dimensional Josephson junction in a thin film. We show that this Josephson vortex is similar to a mesoscopic capacitor. We demonstrate that a single Cooper pair tunneling results in nonlinear Bloch--type oscillations of a Josephson vortex in a current-biased Josephson junction. We find the frequency and the amplitude of this motion.Comment: 7 pages, 2 figures included as postscript files, LaTe

High-field vortices in Josephson junctions with alternating critical current density

We study long Josephson junctions with the critical current density alternating along the junction. New equilibrium states, which we call the field synchronized or FS states, are shown to exist if the applied field is from narrow intervals centered around equidistant series of resonant fields, $H_m$. The values of $H_m$ are much higher than the flux penetration field, $H_s$. The flux per period of the alternating critical current density, $\phi_i$, is fixed for each of the FS states. In the $m$-th FS state the value of $\phi_i$ is equal to an integer amount of flux quanta, $\phi_i =m\phi_0$. Two types of single Josephson vortices carrying fluxes $\phi_0$ or/and $\phi_0/2$ can exist in the FS states. Specific stepwise resonances in the current-voltage characteristics are caused by periodic motion of these vortices between the edges of the junction.Comment: 4 pages, 5 figure

The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p