1,171 research outputs found
Stability of a functional equation in complex banach spaces
Using fixed point technique, in the present paper , we wish to examine generalization of the Hyers-Ulam-Rassias stability theorem for the functional equations f ( 2 x + i y ) + f ( x + 2 i y ) = 4 f ( x + i y ) + f ( x ) + f ( y ) (0.1) and f ( 2 x + i y ) − f (i x − 2 y ) = − 4 f (i x − y ) + f ( x ) − f ( − y ) (0.2) in complex Banach spaces .Publisher's Versio
Frequency dependent superfluid stiffness in the pseudogap regime in strongly disordered NbN thin films
We measure the frequency dependence of the complex ac conductivity of NbN
films with different levels of disorder in frequency range 0.4-20 GHz. Films
with low disorder exhibit a narrow dynamic fluctuation regime above T_c as
expected for a conventional superconductor. However, for strongly disordered
samples, the fluctuation regime extends well above T_c, with a strongly
frequency-dependent superfluid stiffness which disappears only at a temperature
T* close to the pseudogap temperature obtained from scanning tunneling
measurements. Such a finite-frequency response is associated to a marked
slowing down of the superconducting fluctuations already below T*. The
corresponding large length-scale fluctuations suggest a scenario of thermal
phase fluctuations between superconducting domains in a strongly disordered
s-wave superconductor.Comment: pdf file: 18 pages including figure
On the stability of a Pexiderized functional equation in intuitionistic fuzzy Banach spaces
During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. The objective of the present paper is to determine the Hyers-Ulam-Rassias type stability concerning the Pexiderized functional equation in intuitionistic fuzzy Banach spaces. Under a few sufficient conditions, Hyers-Ulam-Rassias type stability of a Pexiderized functional equation has been established in intuitionistic fuzzy Banach spaces
Probing long-range correlations in the Berezinskii-Kosterlitz-Thouless fluctuation regime of ultra-thin NbN superconducting films using transport noise measurements
We probe the presence of long-range correlations in phase fluctuations by
analyzing the higher-order spectrum of resistance fluctuations in ultra-thin
NbN superconducting films. The non-Gaussian component of resistance
fluctuations is found to be sensitive to film thickness close to the
transition, which allows us to distinguish between mean field and
Berezinskii-Kosterlitz-Thouless (BKT) type superconducting transitions. The
extent of non-Gaussianity was found to be bounded by the BKT and mean field
transition temperatures and depend strongly on the roughness and structural
inhomogeneity of the superconducting films. Our experiment outlines a novel
fluctuation-based kinetic probe in detecting the nature of superconductivity in
disordered low-dimensional materials.Comment: submitted to PR
Two component quantum walk in one-dimensional lattice with hopping imbalance
We investigate the two-component quantum walk in one-dimensional lattice. We
show that the inter-component interaction strength together with the hopping
imbalance between the components exhibit distinct features in the quantum walk
for different initial states. When the walkers are initially on the same site,
both the slow and fast particles perform independent particle quantum walks
when the interaction between them is weak. However, stronger inter-particle
interactions result in quantum walks by the repulsively bound pair formed
between the two particles. For different initial states when the walkers are on
different sites initially, the quantum walk performed by the slow particle is
almost independent of that of the fast particle, which exhibits reflected and
transmitted components across the particle with large hopping strength for weak
interactions. Beyond a critical value of the interaction strength, the wave
function of the fast particle ceases to penetrate through the slow particle
signalling a spatial phase separation. However, when the two particles are
initially at the two opposite edges of the lattice, then the interaction
facilitates the complete reflection of both of them from each other. We analyze
the above mentioned features by examining various physical quantities such as
the on-site density evolution, two-particle correlation functions and
transmission coefficients.Comment: Accepted Version(Scientific Reports
Non-linear characteristics in two-dimensional superconductors: Berezinskii-Kosterlitz-Thouless physics vs inhomogeneity
One of the hallmarks of the Berezinskii-Kosterlitz-Thouless (BKT) transition
in two-dimensional (2D) superconductors is the universal jump of the superfluid
density, that can be indirectly probed via the non-linear exponent of the
current-voltage characteristics. Here, we compare the experimental
measurements of characteristics in two cases, namely NbN thin films and
SrTiO-based interfaces. While the former display a paradigmatic example of
BKT-like non-linear effects, the latter do not seem to justify a BKT analysis.
Rather, the observed characteristics can be well reproduced theoretically
by modelling the effect of mesoscopic inhomogeneity of the superconducting
state. Our results offer an alternative perspective on the spontaneous
fragmentation of the superconducting background in confined 2D systems.Comment: Final version, as publishe
Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces
In this paper we investigate Hyers-Ulam-Rassias stability of certain nonlinear functional equations. Considerations of such stabilities in different branches of mathematics have been very extensive. Again the fuzzy concepts along with their several extensions have appeared in almost all branches of mathematics. Here we work on intuitionistic fuzzy real Banach spaces, which is obtained by combining together the concepts of fuzzy Banach spaces with intuitionistic fuzzy sets. We establish that pexiderized quadratic functional equations defined on such spaces are stable in the sense of Hyers-Ulam-Rassias stability. We adopt a fixed point approach to the problem. Precisely, we use a generxalized contraction mapping principle. The result is illustrated with an example.This work was supported by the Basque Government under the Grant IT 1207-1
Penetration depth and tunneling studies in very thin epitaxial NbN films
We investigate evolution of the magnetic penetration depth and
superconducting energy gap in epitaxial NbN films using a low frequency mutual
inductance technique and tunneling spectroscopy using a low temperature
scanning tunneling microscope (STM). The superconducting transition temperature
(Tc) for films grown under optimal growth conditions decreases monotonically
from 15.87K to 9.16K as the film thickness is decreased from 50nm to 3nm. With
decrease in film thickness delta(0) monotonically decreases, whereas lambda(0)
monotonically increases. We observe that Tc, lambda(o) and delta(0) are well
described by Bardeen-Cooper-Schrieffer (BCS) theory in all films other than the
two thinnest ones where we see evidence of the Kosterlitz-Thouless-Berezinski
(KTB) transition close to Tc.Comment: Modified version with extensive analysis of the KTB transition. One
new author adde
Phase diagram of a strongly disordered s-wave superconductor, NbN, close to the metal-insulator transition
We present a phase diagram as a function of disorder in three-dimensional NbN
thin films, as the system enters the critical disorder for the destruction of
the superconducting state. The superconducting state is investigated using a
combination of magnetotransport and tunneling spectroscopy measurements. Our
studies reveal 3 different disorder regimes. At low disorder the (k_{F}l~10-4),
the system follows the mean field Bardeen-Cooper-Schrieffer behavior where the
superconducting energy gap vanishes at the temperature where electrical
resistance appears. For stronger disorder (k_{F}l<4) a "pseudogap" state
emerges where a gap in the electronic spectrum persists up to temperatures much
higher than Tc, suggesting that Cooper pairs continue to exist in the system
even after the zero resistance state is destroyed. Finally, very strongly
disordered samples (k_{F}l<1) exhibit a pronounced magnetoresistance peak at
low temperatures, suggesting that localized Cooper pairs continue to survive in
the system even after the global superconducting ground state is completely
destroyed.Comment: pdf file with figures (Modified Version
- …