161 research outputs found
Variational principle for non-linear wave propagation in dissipative systems
The dynamics of many natural systems is dominated by non-linear waves
propagating through the medium. We show that the dynamics of non-linear wave
fronts with positive surface tension can be formulated as a gradient system.
The variational potential is simply given by a linear combination of the
occupied volume and surface area of the wave front, and changes monotonically
in time. Finally, we demonstrate that vortex filaments can be written as a
gradient system only if their binormal velocity component vanishes, which
occurs in chemical system with equal diffusion of reactants
Effective dynamics of twisted and curved scroll waves using virtual filaments
Scroll waves are three-dimensional excitation patterns that rotate around a
central filament curve; they occur in many physical, biological and chemical
systems. We explicitly derive the equations of motion for scroll wave filaments
in reaction-diffusion systems with isotropic diffusion up to third order in the
filament's twist and curvature. The net drift components define at every
instance of time a virtual filament which lies close to the instantaneous
filament. Importantly, virtual filaments obey simpler, time-independent laws of
motion which we analytically derive here and illustrate with numerical
examples. Stability analysis of scroll waves is performed using virtual
filaments, showing that filament curvature and twist add as quadratic terms to
the nominal filament tension. Applications to oscillating chemical reactions
and cardiac tissue are discussed.Comment: 28 page
On the fidelity of mixed states of two qubits
We consider a single copy of a mixed state of two qubits and show how its
fidelity or maximal singlet fraction is related to the entanglement measures
concurrence and negativity. We characterize the extreme points of the convex
set of states with constant fidelity, and use this to prove tight lower and
upper bounds on the fidelity for a given amount of entanglement.Comment: 4 pages; part I of quant-ph/0203073v2; see quant-ph/0303007 for part
I
QCD perturbation theory at large orders with large renormalization scales in the large beta(0) limit
Resolving the instability of the Savvidy vacuum by dynamical gluon mass
In this paper we apply the formalism of local composite operators as
developed by Verschelde et al. in combination with a constant chromomagnetic
field as considered in the seventies by Savvidy and others. We find that a
nonzero minimizes the vacuum energy, as in the case with no
chromomagnetic field, and that the chromomagnetic field itself is near-to zero.
The Nielsen-Olesen instability, caused by the imaginary part in the action,
also vanishes. We further investigate the effect of an external chromomagnetic
field on the value of , finding that this condensate is destroyed by
sufficiently strong fields. The inverse scenario, where is considered
as external, results in analogous findings: when this condensate is
sufficiently large, the induced chromomagnetic field is lowered to a
perturbative value slightly below the applied .Comment: 11 pages, 8 figure
The Schwarzian Theory - A Wilson Line Perspective
We provide a holographic perspective on correlation functions in Schwarzian
quantum mechanics, as boundary-anchored Wilson line correlators in
Jackiw-Teitelboim gravity. We first study compact groups and identify the
diagrammatic representation of bilocal correlators of the particle-on-a-group
model as Wilson line correlators in its 2d holographic BF description. We
generalize to the Hamiltonian reduction of SL(2,R) and derive the Schwarzian
correlation functions. Out-of-time ordered correlators are determined by
crossing Wilson lines, giving a 6j-symbol, in agreement with 2d CFT results.Comment: 28 pages + appendices, v3: corrected discussion on representation
theory and improved discussion on higher-point functions in appendices,
references added, typos corrected, matches published versio
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