24,393 research outputs found
A systematic stability analysis of the renormalisation group flow for the normal-superconductor-normal junction of Luttinger liquid wires
We study the renormalization group flows of the two terminal conductance of a
superconducting junction of two Luttinger liquid wires. We compute the power
laws associated with the renormalization group flow around the various fixed
points of this system using the generators of the SU(4) group to generate the
appropriate parameterization of a S-matrix representing small deviations from a
given fixed point S-matrix (obtained earlier in Phys. Rev. B 77, 155418
(2008)), and we then perform a comprehensive stability analysis. In particular,
for the non-trivial fixed point which has intermediate values of transmission,
reflection, Andreev reflection and crossed Andreev reflection, we show that
there are eleven independent directions in which the system can be perturbed,
which are relevant or irrelevant, and five directions which are marginal. We
obtain power laws associated with these relevant and irrelevant perturbations.
Unlike the case of the two-wire charge-conserving junction, here we show that
there are power laws which are non-linear functions of V(0) and V(2k_{F})
(where V(k) represents the Fourier transform of the inter-electron interaction
potential at momentum k). We also obtain the power law dependence of linear
response conductance on voltage bias or temperature around this fixed point.Comment: Final version to appear in Phys. Rev.
Manifestly Supersymmetric RG Flows
Renormalisation group (RG) equations in two-dimensional N=1 supersymmetric
field theories with boundary are studied. It is explained how a manifestly N=1
supersymmetric scheme can be chosen, and within this scheme the RG equations
are determined to next-to-leading order. We also use these results to revisit
the question of how brane obstructions and lines of marginal stability appear
from a world-sheet perspective.Comment: 22 pages; references added, minor change
Front propagation into unstable and metastable states in Smectic C* liquid crystals: linear and nonlinear marginal stability analysis
We discuss the front propagation in ferroelectric chiral smectics (SmC*)
subjected to electric and magnetic fields applied parallel to smectic layers.
The reversal of the electric field induces the motion of domain walls or fronts
that propagate into either an unstable or a metastable state. In both regimes,
the front velocity is calculated exactly. Depending on the field, the speed of
a front propagating into the unstable state is given either by the so-called
linear marginal stability velocity or by the nonlinear marginal stability
expression. The cross-over between these two regimes can be tuned by a magnetic
field. The influence of initial conditions on the velocity selection problem
can also be studied in such experiments. SmC therefore offers a unique
opportunity to study different aspects of front propagation in an experimental
system
A characterization of switched linear control systems with finite L 2 -gain
Motivated by an open problem posed by J.P. Hespanha, we extend the notion of
Barabanov norm and extremal trajectory to classes of switching signals that are
not closed under concatenation. We use these tools to prove that the finiteness
of the L2-gain is equivalent, for a large set of switched linear control
systems, to the condition that the generalized spectral radius associated with
any minimal realization of the original switched system is smaller than one
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