Related papers: Dynamics of one-dimensional spin models under the …
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…
Networks are widely used to model the interaction between individual dynamical systems. In many instances, the total number of units as well as the interaction coupling are not fixed in time, but rather constantly evolve. In terms of…
This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…
The dynamics of a single chain tethered to an interface and in contact with a cross-linked network is examined numerically. When the network is put in contact with the tethered chain, the chain moves with dynamics that are highly…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
We develop an analytic approach which allows us to study the behaviour of spin models with competing interactions and $p$-fold spin anisotropy, $D$, in the limit where the pinning potential which results from $D$ is large. This is an…
We establish the conditions under which scalable spin squeezing can be achieved in interacting spin ensembles embedded in arbitrary, inhomogeneous graph geometries. We identify two different forms of squeezing: OAT-like scalable squeezing…
The inverse statistical problem of finding direct interactions in complex networks is difficult. In the natural sciences, well-controlled perturbation experiments are widely used to probe the structure of complex networks. However, our…
When two molecular species with mutual affinity are mixed together, various self-assembled phases can arise at low temperature, depending on the shape of like and unlike interactions. Among them, stripes -- where layers of one type are…
We propose a model describing $N$ spin-1/2 systems coupled through $N$-order homogeneous interaction terms, in presence of local time-dependent magnetic fields. This model can be experimentally implemented with current technologies in…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
We demonstrate that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for $N$ spins at time $T$ is related to one of a non-unitary evolution operator for $T$ spins at time…
We study the unitary relaxation dynamics of disordered spin chains following a sudden quench of the Hamiltonian. We give analytical arguments, corroborated by specific numerical examples, to show that the existence of a stationary state…
A parametrized spin model was recently introduced and intended for one-dimensional ferromagnets with a deformable Zeeman energy. This model is revisited and given more realistic interpretation in terms of a model for ferromagnetic systems…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
We study the low temperature out of equilibrium Monte Carlo dynamics of the disordered Ising $p$-spin Model with $p=3$ and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips…
One-dimensional atomic mixtures of fermions can effectively realize spin chains and thus constitute a clean and controllable platform to study quantum magnetism. Such strongly correlated quantum systems are also of sustained interest to…
We study the dynamics of a spin facilitated Ising model with long range kinetic constraints. To formulate those restrictions within an analytical approach we introduce the size of a kinetic active environment of a given spin. Based on a…
To identify emerging microscopic structures in low temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of…
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…