1,786,527 research outputs found
Birman-Schwinger and the number of Andreev states in BCS superconductors
The number of bound states due to inhomogeneities in a BCS superconductor is
usually established either by variational means or via exact solutions of
particularly simple, symmetric perturbations. Here we propose estimating the
number of sub-gap states using the Birman-Schwinger principle. We show how to
obtain upper bounds on the number of sub-gap states for small normal regions
and derive a suitable Cwikel-Lieb-Rozenblum inequality. We also estimate the
number of such states for large normal regions using high dimensional
generalizations of the Szego theorem. The method works equally well for local
inhomogeneities of the order parameter and for external potentials.Comment: Final version to appear in Phys Rev
2D-Drop model applied to the calculation of step formation energies on a (111) substrate
A model is presented for obtaining the step formation energy for metallic
islands on (111) surfaces from Monte Carlo simulations. This model is applied
to homo (Cu/Cu(111), Ag/Ag(111)) and heteroepitaxy (Ag/Pt(111)) systems. The
embedded atom method is used to represent the interaction between the particles
of the system, but any other type of potential could be used as well. The
formulation can also be employed to consider the case of other single crystal
surfaces, since the higher barriers for atom motion on other surfaces are not a
hindrance for the simulation scheme proposed.Comment: 12 pages, LaTeX2e, 2 included EPS figures, submitted to Surface
Science Subj-clas
Multi-normed spaces
We modify the very well known theory of normed spaces (E, \norm) within
functional analysis by considering a sequence (\norm_n : n\in\N) of norms,
where \norm_n is defined on the product space for each .
Our theory is analogous to, but distinct from, an existing theory of
`operator spaces'; it is designed to relate to general spaces for , and in particular to -spaces, rather than to -spaces.
After recalling in Chapter 1 some results in functional analysis, especially
in Banach space, Hilbert space, Banach algebra, and Banach lattice theory that
we shall use, we shall present in Chapter 2 our axiomatic definition of a
`multi-normed space' ((E^n, \norm_n) : n\in \N), where (E, \norm) is a
normed space. Several different, equivalent, characterizations of multi-normed
spaces are given, some involving the theory of tensor products; key examples of
multi-norms are the minimum and maximum multi-norm based on a given space.
Multi-norms measure `geometrical features' of normed spaces, in particular by
considering their `rate of growth'. There is a strong connection between
multi-normed spaces and the theory of absolutely summing operators.
A substantial number of examples of multi-norms will be presented.
Following the pattern of standard presentations of the foundations of
functional analysis, we consider generalizations to `multi-topological linear
spaces' through `multi-null sequences', and to `multi-bounded' linear
operators, which are exactly the `multi-continuous' operators. We define a new
Banach space of multi-bounded operators, and show that it
generalizes well-known spaces, especially in the theory of Banach lattices.
We conclude with a theory of `orthogonal decompositions' of a normed space
with respect to a multi-norm, and apply this to construct a `multi-dual' space.Comment: Many update
Fermions on half-quantum vortex
The spectrum of the fermion zero modes in the vicinity of the vortex with
fractional winding number is discussed. This is inspired by the observation of
the 1/2 vortex in high-temperature superconductors (Kirtley, et al, Phys. Rev.
Lett. 76 (1996) 1336). The fractional value of the winding number leads to the
fractional value of the invariant, which describes the topology of the energy
spectrum of fermions. This results in the phenomenon of the "half-crossing":
the spectrum approaches zero but does not cross it, being captured at the zero
energy level. The similarity with the phenomenon of the fermion condensation is
discussed.Comment: In revised version the discussion is extended and 4 references are
added. The paper is accepted for publication in JETP Letters. 10 pages, LaTeX
file, 3 figures are available at
ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-96004.p
Conductance enhancement due to the resonant tunneling into the subgap vortex core states in normal metal/superconductor ballistic junctions
We investigate the low-energy quantum transport in the ballistic normal
metal-insulator -superconductor junction in the presence of magnetic field
creating Abrikosov vortices in the superconductor. Within the Bogolubov- de
Gennes theory we show that the presence of the subgap quasiparticle states
localized within the vortex cores near the junction interface leads to the
strong resonant enhancement of the Andreev reflection probability, and the
normal-to supercurrent conversion. The corresponding increase of the charge
conductance of the junction is determined by the distance from the vortex chain
to the junction interface, which can be controlled by the applied magnetic
field. The effect that we study provides a tool for probing the vortex core
states by the measurements of charge transport across the applied magnetic
field.Comment: 8 pages, 3 figure
Coexistence of different vacua in the effective quantum field theory and Multiple Point Principle
According to the Multiple Point Principle our Universe is on the coexistence
curve of two or more phases of the quantum vacuum. The coexistence of different
quantum vacua can be regulated by the exchange of the global fermionic charges
between the vacua, such as baryonic, leptonic or family charge. If the
coexistence is regulated by the baryonic charge, all the coexisting vacua
exhibit the baryonic asymmetry. Due to the exchange of the baryonic charge
between the vacuum and matter which occurs above the electroweak transition,
the baryonic asymmetry of the vacuum induces the baryonic asymmetry of matter
in our Standard-Model phase of the quantum vacuum. The present baryonic
asymmetry of the Universe indicates that the characteristic energy scale which
regulates the equilibrium coexistence of different phases of quantum vacua is
about 10^6 GeV.Comment: 12 pages, 1 figure, modified version submitted to JETP letter
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