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## Voltage Noise in a Superconducting Wire with a Constriction

We analyze voltage fluctuations in superconducting nanowires with constrictions. We argue that quantum phase slips occurring in the constriction area are responsible for both equilibrium and non-equilibrium voltage noise in such systems. We evaluate the power spectrum of the voltage noise identifying its non-trivial dependence on both frequency and external bias.

Quantum phase slips (QPSs) generate voltage fluctuations in superconducting nanowires. Employing the Keldysh technique and making use of the phase-charge duality arguments, we develop a theory of QPS-induced voltage noise in such nanowires. We demonstrate that quantum tunneling of the magnetic flux quanta across the wire yields quantum shot noise which obeys Poisson statistics and is characterized by a power-law dependence of its spectrum SΩ on the external bias. In long wires, SΩdecreases with increasing frequency Ω and vanishes beyond a threshold value of Ω at T→0. The quantum coherent nature of QPS noise yields nonmonotonous dependence of SΩ on T at small Ω.

With rapid development of nanotechnology it became realistic to fabricate artificial nanostructures with dimensions in sub-50 nm scales. The physics of quasi-one-dimensional superconductors of corresponding dimensions is rather interesting [1]. The particular manifestation of size-dependent quantum fluctuations of superconducting order parameter - the quantum phase slip (QPS) – appeared capable to suppress such ‘text-book’ properties of superconductivity as zero resistivity [2] and persistent currents [3].

Here we demonstrate that one can build a superconducting analogue of a single-electron transistor (Cooper pair transistor) without any tunnel junctions. Instead a pair of thin superconducting wires in QPS regime - the quantum phase slip junctions (QPSJ) - can be used (Fig. 1). At sufficiently low temperatures, well below the critical temperature of the superconductor, the clear Coulomb blockade develops at the I-V characteristic of such a system [4,5]. Application of static gate potential efficiently modulates the amplitude of the Coulomb gap. The same device can be considered as the potential candidate for building a quantum standard of electric current [6].

The topic of superconductivity in strongly disordered materials has attractedsignificant attention. These materials appear to be rather promising for fabrication of various nanoscale devices such as bolometers and transition edge sensors of electromagnetic radiation. The vividly debated subject of intrinsic spatial inhomogeneity responsible for thenon-Bardeen–Cooper–Schrieffer relation between the superconducting gap and the pairing potential is crucial both for understanding the fundamental issues of superconductivity in highly disordered superconductors, and for theoperation of corresponding nanoelectronic devices. Here we report an experimental study of theelectron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. The temperature dependence of the critical current follows the textbook Ginzburg–Landau prediction for thequasi-one-dimensional superconducting channel Ic∼(1-T/Tc)3/2. We find that conventional models based on the thephase slip mechanism provide reasonable fits for the shape of R(T) transitions. Better agreement with R(T) data can be achieved assuming theexistence of short ‘weak links’ with slightly reduced local critical temperature Tc. Hence, one may conclude that an ‘exotic’ intrinsic electronic inhomogeneity either does not exist in our structures, or, if it doesexist, itdoes not affect their resistive state properties, or does not provide any specific impact distinguishablefrom conventional weak links.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.