Kink-antikink collisions in a weakly interacting ϕ4\phi^4 model

We study kink-antikink scattering in a one-parameter variant of the $\phi^4$ 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 ϕ4\phi^4 theory

The fractal velocity pattern in symmetric kink-antikink collisions in $\phi^4$ 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 $S$ is metrizable if and only if $S$ is an $M$-space and the set $E=\{e\in S:ee=e\}$ of idempotents of $S$ is a metrizable $G_\delta$-set in $S$. The same metrization criterion holds also for any countably compact Clifford topological semigroup $S$.Comment: 4 page

Constrained instantons and kink-antikink collisions

We show that constrained $CP^1$ instantons, combined with the Relativistic Moduli Space approach, can accurately describe kink-antikink collisions in the $\phi^4$ 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