We consider space-time correlations in driven diffusive systems which undergo a fluctuation into a regime with an atypically large current or dynamical activity. For a single conserved mass we show ...that the spatiotemporal density correlations in one space dimension are fully determined by conformal field theory with central charge c=1, corresponding to a ballistic universality class with dynamical exponent z=1. The full phase diagram for general atypical behavior exhibits the conformally invariant regime and, for atypically low current or activity, a region of phase separation. The phase transition line between these two regimes corresponds to typical behavior and the dynamics belongs to the Kardar-Parisi-Zhang universality class with dynamical exponent z=3/2, except for a diffusive point with z=2. The exact universal dynamical structure function is obtained in explicit form from the one-dimensional asymmetric simple exclusion process with periodic and open boundaries in the limit of maximal current.
A reverse duality between the asymmetric simple exclusion process (ASEP) with open boundary conditions and a biased random walk of a single particle is proved for a special manifold of boundary ...parameters of the ASEP. The duality function is given by the configuration probabilities of a family of Bernoulli shock measures with a microscopic shock at site
x
of the lattice. The boundary conditions of the dual random walk, which can be reflecting or absorbing, depend on the choice of the duality function. As a consequence of this duality, the full time-dependent distribution of the open ASEP starting from a fixed shock measure at
x
is given for any time
t
>
0
by a convex combination of shock measures with shock at position
y
. The coefficients are the transition probabilities
P
(
x
,
t
|
y
, 0) at time
t
of the random walk starting at site
y
. It is also shown that this family of shock measures arises from a similarity transformation of the two-dimensional representation of the matrix algebra for the stationary matrix product measure of the open ASEP. This implies a further duality between random walks with different boundary conditions.
Abstract
The discovery of two-dimensional magnets has initiated a new field of research, exploring both fundamental low-dimensional magnetism, and prospective spintronic applications. Recently, ...observations of magnetic skyrmions in the 2D ferromagnet Fe
3
GeTe
2
(FGT) have been reported, introducing further application possibilities. However, controlling the exhibited magnetic state requires systematic knowledge of the history-dependence of the spin textures, which remains largely unexplored in 2D magnets. In this work, we utilise real-space imaging, and complementary simulations, to determine and explain the thickness-dependent magnetic phase diagrams of an exfoliated FGT flake, revealing a complex, history-dependent emergence of the uniformly magnetised, stripe domain and skyrmion states. The results show that the interplay of the dominant dipolar interaction and strongly temperature dependent out-of-plane anisotropy energy terms enables the selective stabilisation of all three states at zero field, and at a single temperature, while the Dzyaloshinksii-Moriya interaction must be present to realise the observed Néel-type domain walls. The findings open perspectives for 2D devices incorporating topological spin textures.
Magnetic skyrmions are topologically nontrivial particles with a potential application as information elements in future spintronic device architectures. While they are commonly portrayed as two ...dimensional objects, in reality magnetic skyrmions are thought to exist as elongated, tube-like objects extending through the thickness of the host material. The study of this skyrmion tube state (SkT) is vital for furthering the understanding of skyrmion formation and dynamics for future applications. However, direct experimental imaging of skyrmion tubes has yet to be reported. Here, we demonstrate the real-space observation of skyrmion tubes in a lamella of FeGe using resonant magnetic x-ray imaging and comparative micromagnetic simulations, confirming their extended structure. The formation of these structures at the edge of the sample highlights the importance of confinement and edge effects in the stabilisation of the SkT state, opening the door to further investigation into this unexplored dimension of the skyrmion spin texture.
We demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ...ansatz for the nonequilibrium density matrix where the matrices satisfy a quadratic algebra. This algebra turns out to be related to the quantum algebra U(q)SU(2). Coherent state techniques are introduced for the exact solution of the isotropic Heisenberg chain with and without quantum boundary fields and Lindblad terms that correspond to two different completely polarized boundary states. We show that this boundary twist leads to nonvanishing stationary currents of all spin components. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms.
We present a three-lane exclusion process that exhibits the same universal fluctuation pattern as generic one-dimensional Hamiltonian dynamics with short-range interactions, viz., with two sound ...modes in the Kardar-Parisi-Zhang (KPZ) universality class (with dynamical exponent
z
=
3
/
2
and symmetric Prähofer-Spohn scaling function) and a superdiffusive heat mode with dynamical exponent
z
=
5
/
3
and symmetric Lévy scaling function. The lattice gas model is amenable to efficient numerical simulation. Our main findings, obtained from dynamical Monte-Carlo simulation, are: (i) The frequently observed numerical asymmetry of the sound modes is a finite time effect. (ii) The mode-coupling calculation of the scale factor for the 5/3-Lévy-mode gives at least the right order of magnitude. (iii) There are significant diffusive corrections which are non-universal.
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