Magnonic Goos–Hänchen Effect Induced by 1D Solitons

The spin wave spectral problem is solved in terms of the spectrum of a diagonalizable operator for a class of magnetic states that includes several types of domain walls and the chiral solitons of monoaxial helimagnets. Focusing on these latter solitons, it is shown that the spin waves reflected and transmitted by them suffer a lateral displacement analogous to the Goos-Hänchen effect of optics. The displacement is a fraction of the wavelength, but can be greatly enhanced by using an array of well separated solitons. Contrarily to the Goos–Hänchen effect recently studied in some magnetic systems, which takes place at the interfaces between different magnetic systems, the effect predicted here takes place at the soliton position, which is interesting for applications since solitons can be created at different places and moved across the material by suitable means. Moreover, the effect predicted here is not particular to monoaxial helimagnets, but it is generic of 1D solitons, although it is accidentally absent in the domain walls of ferromagnets with uniaxial anisotropy. Even though in this work the dipolar interaction is ignored for simplicity, we argue that the Goos–Hänchen shift is also present when it is taken into account. © 2021 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH

Stability of spinor Fermi gases in tight waveguides

The two and three-body correlation functions of the ground state of an optically trapped ultracold spin-1/2 Fermi gas (SFG) in a tight waveguide (1D regime) are calculated in the plane of even and odd-wave coupling constants, assuming a 1D attractive zero-range odd-wave interaction induced by a 3D p-wave Feshbach resonance, as well as the usual repulsive zero-range even-wave interaction stemming from 3D s-wave scattering. The calculations are based on the exact mapping from the SFG to a ``Lieb-Liniger-Heisenberg'' model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, and indicate that the SFG should be stable against three-body recombination in a large region of the coupling constant plane encompassing parts of both the ferromagnetic and antiferromagnetic phases. However, the limiting case of the fermionic Tonks-Girardeau gas (FTG), a spin-aligned 1D Fermi gas with infinitely attractive p-wave interactions, is unstable in this sense. Effects due to the dipolar interaction and a Zeeman term due to a resonance-generating magnetic field do not lead to shrinkage of the region of stability of the SFG.Comment: 5 pages, 6 figure

A Unified Framework for the Study of Anti-Windup Designs

We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: "Design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance". The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. It is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model. The actual analysis of stability and performance, and robustness issues are problems in their own right and hence not detailed here. The main result is the unification of existing schemes for AWBT compensation under a general framework

On the heterochromatic number of hypergraphs associated to geometric graphs and to matroids

The heterochromatic number hc(H) of a non-empty hypergraph H is the smallest integer k such that for every colouring of the vertices of H with exactly k colours, there is a hyperedge of H all of whose vertices have different colours. We denote by nu(H) the number of vertices of H and by tau(H) the size of the smallest set containing at least two vertices of each hyperedge of H. For a complete geometric graph G with n > 2 vertices let H = H(G) be the hypergraph whose vertices are the edges of G and whose hyperedges are the edge sets of plane spanning trees of G. We prove that if G has at most one interior vertex, then hc(H) = nu(H) - tau(H) + 2. We also show that hc(H) = nu(H) - tau(H) + 2 whenever H is a hypergraph with vertex set and hyperedge set given by the ground set and the bases of a matroid, respectively

Surprises in the suddenly-expanded infinite well

I study the time-evolution of a particle prepared in the ground state of an infinite well after the latter is suddenly expanded. It turns out that the probability density $|\Psi(x, t)|^{2}$ shows up quite a surprising behaviour: for definite times, {\it plateaux} appear for which $|\Psi(x, t)|^{2}$ is constant on finite intervals for $x$. Elements of theoretical explanation are given by analyzing the singular component of the second derivative $\partial_{xx}\Psi(x, t)$. Analytical closed expressions are obtained for some specific times, which easily allow to show that, at these times, the density organizes itself into regular patterns provided the size of the box in large enough; more, above some critical time-dependent size, the density patterns are independent of the expansion parameter. It is seen how the density at these times simply results from a construction game with definite rules acting on the pieces of the initial density.Comment: 24 pages, 14 figure

Quantum Dynamics in a Time-dependent Hard-Wall Spherical Trap

Exact solution of the Schr\"{o}dinger equation is given for a particle inside a hard sphere whose wall is moving with a constant velocity. Numerical computations are presented for both contracting and expanding spheres. The propagator is constructed and compared with the propagator of a particle in an infinite square well with one wall in uniform motion.Comment: 6 pages, 4 figures, Accepted by Europhys. Let

Exact propagators for atom-laser interactions

A class of exact propagators describing the interaction of an $N$-level atom with a set of on-resonance $\delta$-lasers is obtained by means of the Laplace transform method. State-selective mirrors are described in the limit of strong lasers. The ladder, V and $\Lambda$ configurations for a three-level atom are discussed. For the two level case, the transient effects arising as result of the interaction between both a semi-infinite beam and a wavepacket with the on-resonance laser are examined.Comment: 13 pages, 6 figure

False vacuum decay in a brane world cosmological model

The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein's theory of relativity.Comment: minor changes done, references added, version to appear in GR

Chiral helimagnetism and stability of magnetic textures in MnNb3S6

We analyze the nature of the modulated magnetic states in a micromagnetic model for the monoaxial chiral magnet MnNb3S6, for which the Dzyaloshinskii-Moriya interaction and the dipolar interaction compete evenly. We show that the interplay between these interactions lead to a complex phase diagram including ferromagnetic states, fanlike states, in-plane stripes patterns, and chiral soliton lattices. In particular, stripe patterns and chiral soliton lattices comprise nontrivial topological states with fixed chirality. The obtained phase diagram exhibits a strong dependency on the thickness and on the strength of the Dzyaloshinskii-Moriya interaction. Our results can help to understand the magnetic properties of systems such as MnNb3S6