145 research outputs found
Kink-antikink collisions in a weakly interacting model
We study kink-antikink scattering in a one-parameter variant of the
theory where the model parameter controls the static intersoliton force. We
interpolate between the limit of no static force (BPS limit) and the regime
where the static interaction is small (non-BPS). This allows us to study the
impact of the strength of the intersoliton static force on the soliton
dynamics.
In particular, we analyze how the transition of a bound mode through the mass
threshold affects the soliton dynamics in a generic process, i.e., when a
static intersoliton force shows up. We show that the thin, precisely localized
spectral wall which forms in the limit of no static force, broadens in a
well-defined manner when a static force is included, giving rise to what we
will call a thick spectral wall. This phenomenon just requires that a discrete
mode crosses into the continuum at some intermediate stage of the dynamics and,
therefore, should be observable in many soliton-antisoliton collisions.Comment: version accepted in Phys. Rev.
Sphaleron without shape mode and its oscillon
We find that an oscillon can possess a characteristic double oscillation
structure even though it results in a decay of a sphaleron which does not have
any positive energy vibrational mode. We show that dynamics of such an oscillon
can still be captured by collective coordinates provided by the sphaleron.
Namely, its unstable mode and its scaling deformation i.e., Derrick mode.Comment: 10 pages, 12 figure
Collective coordinate model of kink-antikink collisions in theory
The fractal velocity pattern in symmetric kink-antikink collisions in
theory is shown to emerge from a dynamical model with two effective
moduli, the kink-antikink separation and the internal shape mode amplitude. The
shape mode usefully approximates Lorentz contractions of the kink and antikink,
and the previously problematic null-vector in the shape mode amplitude at zero
separation is regularized.Comment: the metric and potential of the effective model are now include
Order parameters in the Verwey phase transition
The Verwey phase transition in magnetite is analyzed on the basis of the
Landau theory. The free energy functional is expanded in a series of components
belonging to the primary and secondary order parameters. A low-temperature
phase with the monoclinic P2/c symmetry is a result of condensation of two
order parameters X_3 and \Delta_5 . The temperature dependence of the shear
elastic constant C_44 is derived and the mechanism of its softening is
discussed.Comment: 4 pages, 1 figur
Solvable self-dual impurity models
We find a family of (half) self-dual impurity models such that the self-dual (BPS) sector is exactly solvable, for any spatial distribution of the impurity, both in the topologically trivial case and for kink (or antikink) configurations. This allows us to derive the metric on the corresponding one-dimensional moduli space in an analytical form. Also the generalized translational symmetry is found in an exact form. This symmetry provides a motion on moduli space which transforms one BPS solution into another. Finally, we analyse exactly how vibrational properties (spectral modes) of the BPS solutions depend on the actual position on moduli space. These results are obtained both for the nontrivial topological sector (kinks or antikinks) as well as for the topologically trivial sector, where the motion on moduli space represents a kink-antikink annihilation process
Metrizability of Clifford topological semigroups
We prove that a topological Clifford semigroup is metrizable if and only
if is an -space and the set of idempotents of is
a metrizable -set in . The same metrization criterion holds also
for any countably compact Clifford topological semigroup .Comment: 4 page
Constrained instantons and kink-antikink collisions
We show that constrained instantons, combined with the Relativistic
Moduli Space approach, can accurately describe kink-antikink collisions in the
model.Comment: 8 pages, 5 figure
Seeking for a fingerprint: analysis of point processes in actigraphy recording
Motor activity of humans displays complex temporal fluctuations which can be
characterized by scale-invariant statistics, thus documenting that structure
and fluctuations of such kinetics remain similar over a broad range of time
scales. Former studies on humans regularly deprived of sleep or suffering from
sleep disorders predicted change in the invariant scale parameters with respect
to those representative for healthy subjects. In this study we investigate the
signal patterns from actigraphy recordings by means of characteristic measures
of fractional point processes. We analyse spontaneous locomotor activity of
healthy individuals recorded during a week of regular sleep and a week of
chronic partial sleep deprivation. Behavioural symptoms of lack of sleep can be
evaluated by analysing statistics of duration times during active and resting
states, and alteration of behavioural organization can be assessed by analysis
of power laws detected in the event count distribution, distribution of waiting
times between consecutive movements and detrended fluctuation analysis of
recorded time series. We claim that among different measures characterizing
complexity of the actigraphy recordings and their variations implied by chronic
sleep distress, the exponents characterizing slopes of survival functions in
resting states are the most effective biomarkers distinguishing between healthy
and sleep-deprived groups.Comment: Communicated at UPON2015, 14-17 July 2015, Barcelona. 21 pages, 11
figures; updated: figures 4-7, text revised, expanded Sec. 1,3,
Semi-BPS sphaleron and its dynamics
We construct a simple field theory in which a sphaleron, i.e., a saddle-point
particle-like solution, forms a semi-BPS state with a background defect that is
an impurity. This means that there is no static force between the sphaleron and
the impurity. Therefore such a sphaleron-impurity system is very much like
usual BPS multi-solitons, however, still possessing an unstable direction
allowing for its decay. We study dynamics of the sphaleron in such a system.Comment: 13 pages, 12 figures, references added and improved discussio
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