Fermions on one or fewer Kinks

We find the full spectrum of fermion bound states on a Z_2 kink. In addition to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the fermion and m_s the scalar mass. We also study fermion modes on the background of a well-separated kink-antikink pair. Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, 2L, and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, we find some of the low lying bound states explicitly.Comment: 7 pages, 4 figure

Collaboration in museums and health research

This study reflects on the range of collaborations in two distinct but thematically linked UCL research projects which consider the role of culture in health promotion: Museums on Prescription (2014–2017), in partnership with Canterbury Christ Church University, explores the value of heritage encounters in social prescribing for lonely older adults at risk of social isolation; and Not So Grim Up North (2016–2018), in conjunction with Whitworth Art Gallery, University of Manchester and Tyne & Wear Archives & Museums, investigates the health and wellbeing impacts of museum activities for stroke survivors; older adults with dementia; and mental health and addiction recovery service-users. Both projects employ a mixed-methods approach using quantitative and qualitative data. The research projects have been developed and delivered through collaborations between interdisciplinary university researchers, museum practitioners, health and social care professionals and end-users. Collaboration has taken different forms including co-developing evaluation methods, co-disseminating outputs, and through advisory boards. This study reflects on the opportunities and challenges of collaboration, noting the language and practice dissonance across different fields and the importance of finding common ground. It also highlights the considerable amount of time that is required to build genuine collaborative relationships, which is not often acknowledged in research outputs

Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with one-dimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neighborhood of the origin at least once. In contrast to other works addressing convergence issues in unstable systems, our results require neither input-output characterizations for the stable part nor estimates of convergence rates. The results are illustrated with examples, including the analysis of phase synchronization of neural oscillators with heterogenous coupling

Transport coefficients for electrolytes in arbitrarily shaped nano and micro-fluidic channels

We consider laminar flow of incompressible electrolytes in long, straight channels driven by pressure and electro-osmosis. We use a Hilbert space eigenfunction expansion to address the general problem of an arbitrary cross section and obtain general results in linear-response theory for the hydraulic and electrical transport coefficients which satisfy Onsager relations. In the limit of non-overlapping Debye layers the transport coefficients are simply expressed in terms of parameters of the electrolyte as well as the geometrical correction factor for the Hagen-Poiseuille part of the problem. In particular, we consider the limits of thin non-overlapping as well as strongly overlapping Debye layers, respectively, and calculate the corrections to the hydraulic resistance due to electro-hydrodynamic interactions.Comment: 13 pages including 4 figures and 1 table. Typos corrected. Accepted for NJ

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

Thermodynamic Casimir effects involving interacting field theories with zero modes

Systems with an O(n) symmetrical Hamiltonian are considered in a $d$-dimensional slab geometry of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$. The effective forces induced by thermal fluctuations at and above the bulk critical temperature $T_{c,\infty}$ (thermodynamic Casimir effect) are investigated below the upper critical dimension $d^*=4$ by means of field-theoretic renormalization group methods for the case of periodic and special-special boundary conditions, where the latter correspond to the critical enhancement of the surface interactions on both boundary planes. As shown previously [\textit{Europhys. Lett.} \textbf{75}, 241 (2006)], the zero modes that are present in Landau theory at $T_{c,\infty}$ make conventional RG-improved perturbation theory in $4-\epsilon$ dimensions ill-defined. The revised expansion introduced there is utilized to compute the scaling functions of the excess free energy and the Casimir force for temperatures T\geqT_{c,\infty} as functions of $\mathsf{L}\equiv L/\xi_\infty$, where $\xi_\infty$ is the bulk correlation length. Scaling functions of the $L$-dependent residual free energy per area are obtained whose $\mathsf{L}\to0$ limits are in conformity with previous results for the Casimir amplitudes $\Delta_C$ to $O(\epsilon^{3/2})$ and display a more reasonable small-$\mathsf{L}$ behavior inasmuch as they approach the critical value $\Delta_C$ monotonically as $\mathsf{L}\to 0$.Comment: 23 pages, 10 figure

Comparative study of semiclassical approaches to quantum dynamics

Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator.Comment: 32 pages, 8 figures, corrected typos and added references; version as publishe

On the field dependence of the vortex core size

We argue that in clean high-$\kappa$ type II superconductors, the low temperature vortex core size (defined as the coherence length $\xi$) in high fields should decrease with increasing applied field in qualitative agreement with experimental data. Calculations are done for the Fermi sphere and cylinder (with the field parallel to the cylinder axis). The results for clean materials at T=0 can be represented as $\xi(H)/\xi(H_{c2}) = U (H/H_{c2})$ with $U$ being an universal function.Comment: 8 pages, 2 figure

Vortex-induced dissipation in narrow current-biased thin-film superconducting strips

A vortex crossing a thin-film superconducting strip from one edge to the other, perpendicular to the bias current, is the dominant mechanism of dissipation for films of thickness d on the order of the coherence length XI; and of width w much narrower than the Pearl length LAMBDA >> w >> XI. At high bias currents, I* < I < Ic, the heat released by the crossing of a single vortex suffices to create a belt-like normal-state region across the strip, resulting in a detectable voltage pulse. Here Ic is the critical current at which the energy barrier vanishes for a single vortex crossing. The belt forms along the vortex path and causes a transition of the entire strip into the normal state. We estimate I* to be roughly Ic/3. Further, we argue that such "hot" vortex crossings are the origin of dark counts in photon detectors, which operate in the regime of metastable superconductivity at currents between I* and Ic. We estimate the rate of vortex crossings and compare it with recent experimental data for dark counts. For currents below I*, i.e., in the stable superconducting but resistive regime, we estimate the amplitude and duration of voltage pulses induced by a single vortex crossing.Comment: 9 pages, 3 figure