Related papers: Dynamics of Influence on Hierarchical Structures
We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the meanfield limit of these models manifests multistable parameter regions of coexisting steady states…
One of the most central questions in network science is: which nodes are most important? Often this question is answered using structural properties such as high connectedness or centrality in the network. However, static structural…
A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as…
In this thesis, we consider some spin effects in QCD and recurrence lattices with multi-site exchanges. Main topic of our manuscript are critical phenomena in spin systems defined on the recurrence lattices. Main tool of our approach is the…
The antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling $J$ of the Heisenberg…
It is widely recognized that entanglement generation and dynamical chaos are intimately related in semiclassical models via the process of decoherence. In this work, we propose a unifying framework which directly connects the bipartite and…
We investigate the question of whether chaotic size dependence occurs on hierarichical lattices and demonstrate that it is not present in these systems. Our results show that the metastate for spin glasses on hierarchical lattices is…
We classify four-state spin models with interactions along the edges according to their behavior under a specific group of symmetry transformations. This analysis uses the measure of complexity of the action of the symmetries, in the spirit…
Special arrangements of atoms with more than one atom per unit cell, including honeycomb or kagome (woven bamboo mat) lattices, can host propagating excitations with non-trivial topology as defined by their evolution along closed paths in…
We study the role of fluctuations on the thermodynamic glassy properties of plaquette spin models, more specifically on the transition involving an overlap order parameter in the presence of an attractive coupling between different replicas…
We derive a criterion under which splitting of all eigenstates of an open $\XYZ$ Hamiltonian with boundary fields into two invariant subspaces, spanned by chiral shock states, occurs. The splitting is governed by an integer number, which…
In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…
The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…
Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, $k$-dimensional "simplices") and how they are influenced through…
Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should it be given by a limiting value on one…
Many of the essential features of the evolution of scientific research are imprinted in the structure of citation networks. Connections in these networks imply information about the transfer of knowledge among papers, or in other words,…
Motivated by the idea that some characteristics are specific to the relations between individuals and not of the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of…
A variational technique is used to study sublattice symmetry breaking by strong on-site and nearest neighbor interactions in graphene. When interactions are strong enough to break sublattice symmetry, and with relative strengths…
The quantum Heisenberg model is studied in the geometrically frustrated body-centered tetragonal lattice(BCT lattice) with antiferromagnetic interlayer coupling J1 and intralayer first and second neighbor coupling J2 and J3. We introduce a…
We investigate the relation between integrability and decoherence in central spin models with more than one central spin. We show that there is a transition between integrability ensured by the Bethe ansatz and integrability ensured by…