Multi-soliton dynamics in the Skyrme model

We exhibit the dynamical scattering of multi-solitons in the Skyrme model for configurations with charge two, three and four. First, we construct maximally attractive configurations from a simple profile function and the product ansatz. Then using a sophisticated numerical algorithm, initially well-separated skyrmions in approximately symmetric configurations are shown to scatter through the known minimum energy configurations. These scattering events illustrate a number of similarities to BPS monopole configurations of the same charge. A simple modification of the dynamics to a dissipative regime, allows us to compute the minimal energy skyrmions for baryon numbers one to four to within a few percent.Comment: latex, 10 pages, plus 5 figures (as gif files

A Dynamical Model of Color Confinement

A dynamical model of confinement based on a transport theoretical description of the Friedberg-Lee model is extended to explicit color degrees of freedom. The string tension is reproduced by an adiabatic string formation from the nucleon ground state. Color isovector oscillation modes of a $q\bar{q}$-system are investigated for a wide range of relative $q\bar{q}$-momenta and the dynamical impact of color confinement on the quark motion is shown.Comment: 12 pages plus 5 figure

Scattering of Skyrmions

In this paper, we present a detailed study of Skyrmion-Skyrmion scattering for two B=1 Skyrmions in the attractive channel where we observe two different scattering regimes. For large separation, the scattering can be approximated as interacting dipoles. We give a qualitative estimate when this approximation breaks down. For small separations we observe an additional short-range repulsion which is qualitatively similar to monopole scattering. We also observe the interesting effect of "rotation without rotating" whereby two Skyrmions, whose orientations remain constant while well-separated, change their orientation after scattering. We can explain this effect by following preimages through the scattering process, thereby measuring which part of an in-coming Skyrmion forms part of an out-going Skyrmion. This leads to a new way of visualising Skyrmions. Furthermore, we consider spinning Skyrmions and find interesting trajectories

Two Skyrmion Dynamics with Omega Mesons

We present our first results of numerical simulations of two skyrmion dynamics using an $\omega$-meson stabilized effective Lagrangian. We consider skyrmion-skyrmion scattering with a fixed initial velocity of $\beta=0.5$, for various impact parameters and groomings. The physical picture that emerges is surprisingly rich, while consistent with previous results and general conservation laws. We find meson radiation, skyrmion scattering out of the scattering plane, orbiting and capture to bound states.Comment: 19 pages, 22 figure

Stability of the B=2 hedgehog in the Skyrme model

We study the unstable modes of the baryon number two hedgehog of the Skyrme model on a three dimensional spatial lattice. An expansion of the Skyrme Lagrangian around the hedgehog configuration provides the equations of motion for the fluctuation fields solvable numerically via a relaxation method. We find the negative energy modes and, by evolving the excited hedgehog in time, a breakup into two separated solitonic configurations is obtained. Different paths of descent for the receding Skyrmions are presented and the possibility of determining the metric structure of the collective-coordinate manifold is discussed.Comment: 22 pages Latex, 9 uuencoded figures include

Collision-Induced Decay of Metastable Baby Skyrmions

Many extensions of the standard model predict heavy metastable particles which may be modeled as solitons (skyrmions of the Higgs field), relating their particle number to a winding number. Previous work has shown that the electroweak interactions admit processes in which these solitons decay, violating standard model baryon number. We motivate the hypothesis that baryon-number-violating decay is a generic outcome of collisions between these heavy particles. We do so by exploring a 2+1 dimensional theory which also possesses metastable skyrmions. We use relaxation techniques to determine the size, shape and energy of static solitons in their ground state. These solitons could decay by quantum mechanical tunneling. Classically, they are metastable: only a finite excitation energy is required to induce their decay. We attempt to induce soliton decay in a classical simulation by colliding pairs of solitons. We analyze the collision of solitons with varying inherent stabilities and varying incident velocities and orientations. Our results suggest that winding-number violating decay is a generic outcome of collisions. All that is required is sufficient (not necessarily very large) incident velocity; no fine-tuning of initial conditions is required.Comment: 24 pages, 7 figures, latex. Very small changes onl

Skyrmion-anti-Skyrmion Annihilation with Omega Mesons

We study numerically the annihilation of an omega-stabilized Skyrmion and an anti-Skyrmion in three spatial dimensions. To our knowledge this is a first successful simulation of Skyrmion-anti-Skyrmion annihilation which follows through to the point where the energy is carried by outgoing meson waves. We encounter instabilities similar to those encountered is earlier calculations, but in our case these are not fatal and we are able to simulate through this process with a global energy loss of less than 8%, and to identify robust features of the final radiation pattern. The system passes through a singular configuration at the time of half-annihilation. This is followed by the onset of fast oscillations which are superimposed on the smoother process which leads to the appearence of outgoing spherical waves. We investigate the two prominent features of this process, the proliferation of small, fast oscillations, and the singular intermediate configuration. We find that our equations of motion allow for a regime in which the amplitude of certain small perturbations increases exponentially. This regime is similar but not identical to the situation pointed out earlier regarding the original Skyrme model. We argue that the singularity may be seen as the result of a pinch effect similar to that encountered in plasmas.Comment: 26 pages, 15 figure

Classical Skyrmions -- Static Solutions and Dynamics

Skyrmions with a realistic value of the pion mass parameter are expected to be quite compact structures, but beyond baryon number B=8 only a few examples are known. The largest of these is the cubically symmetric B=32 Skyrmion which is a truncated piece of the Skyrme crystal. Here it is proposed that many more such Skyrmions could be found, without any restriction on the baryon number, as pieces of the Skyrme crystal. Particular attention is given to the possibility of reducing B by 1 by chopping a corner off a cubic crystal chunk. Nuclei are modelled by Skyrmions with quantised spin and isospin. Here it is argued that these quantised states can be approximated by classically spinning Skyrmions. The orientations of the spinning Skyrmions corresponding to polarised protons, neutrons and deuterons are identified. Nuclear collisions and the nuclear spin-orbit force are discussed in terms of classically spinning Skyrmions. Going beyond the rigid collective motions of Skyrmions, there are spatially modulated collective motions, which are oscillatory in time. They are argued to describe not just vibrational excitations of nuclei, but also giant resonance states. A speculative proposal for identifying quarks inside Skyrmions is briefly discussed.Comment: 26 pages, 5 figure

Not all waits are equal: An investigation of emergency care patient pathway.

Abstract Background: Increasing pressure in the United Kingdom (UK) urgent care system has led to Emergency Departments (EDs) failing to meet the national requirement that 95% of patients are admitted, discharged or transferred within 4-h of arrival. Despite the target being the same for all acute hospitals, individual Trusts organise their services in different ways. The impact of this variation on patient journey time and waiting is unknown. Our study aimed to apply the Lean technique of Value Stream Mapping (VSM) to investigate care processes and delays in patient journeys at four contrasting hospitals. Methods: VSM timing data were collected for patients accessing acute care at four hospitals in South West England. Data were categorised according to waits and activities, which were compared across sites to identify variations in practice from the patient viewpoint. We included Public and Patient Involvement (PPI) to fully interpret our findings; observations and initial findings were considered in a PPI workshop. Results: One hundred eight patients were recruited, comprising 25,432 min of patient time containing 4098 episodes of care or waiting. The median patient journey was 223 min (3 h, 43 min); just within the 4-h target. Although total patient journey times were similar between sites, the stage where the greatest proportion of waiting occurred varied. Reasons for waiting were dominated by waits for beds, investigations or results to be available. From our sample we observed that EDs without a discharge/clinical decision area exhibited a greater proportion of waiting time following an admission or discharge decision. PPI interpretation indicated that patients who experience waits at the beginning of their journey feel more anxious because they are ‘not in the system yet’. Conclusions: The novel application of VSM analysis across different hospitals, coupled with PPI interpretation, provides important insight into the impact of care provision on patient experience. Measures that could reduce patient waiting include automatic notification of test results, and the option of discharge/clinical decision areas for patients awaiting results or departure. To enhance patient experience, good communication with patients and relatives about reasons for waits is essential. Keywords: Health service research, Acute care, Emergency admissions, Patient care, Value stream mapping, Emergency department, Patient public involvemen