Related papers: Emergent behaviors of Thermodynamic Kuramoto ensem…
We propose a Kuramoto model of coupled oscillators on a time-varying graph, whose dynamics is dictated by a Markov process in the space of graphs. The simplest representative is considering a base graph and then the subgraph determined by…
We present new results for the Kondo lattice model of strongly correlated electrons, in 1-, 2-, and 3-dimensions, obtained from high-order linked-cluster series expansions. Results are given for varies ground state properties at…
We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this…
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…
A generic question in the field of ultrafast dynamics is concerned with the relaxation dynamics and the subsequent thermalization of optically excited charge carriers. Among several possible relaxation channels available in a solid-state…
We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a…
An approach for analytical description of thermal processes in harmonic lattices is presented. We cover longitudinal and transverse vibrations of chains and out-of-plane vibrations of two-dimensional lattices with interactions of an…
There has been a surge of experimental effort recently in cooling trapped fermionic atoms to quantum degeneracy. By varying an external magnetic field, interactions between atoms can be made arbitrarily strong. When the S wave scattering…
We study the thermodynamics of Ising spins on the triangular kagome lattice (TKL) using exact analytic methods as well as Monte Carlo simulations. We present the free energy, internal energy, specific heat, entropy, sublattice…
We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group $\mathrm{SO}(3)$ by identifying closed form expressions for geometric quantities such as covariant derivative and parallel transport in exponential…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…
Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramoto's results and obtain a mathematical…
The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogeneous groups of dynamical units…
Dynamics of complex systems are often driven by interactions that extend beyond pairwise links, underscoring the need to establish a correspondence between interpretable system parameters and emergent phenomena in hypergraph-based networks.…
The Kondo-lattice model, which couples a lattice of localized magnetic moments to conduction electrons, is often used to describe heavy-fermion systems. Because of the interplay between Kondo physics and magnetic order it displays very…
A two-temperature lattice gas model with repulsive nearest-neighbour interactions is studied using Monte Carlo simulations and dynamical mean-field approximation. The evolution of the two-dimensional, half-filled system is described by an…
We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-like atoms in optical lattices that can be effectively described by the two-band spin-$1/2$ Hubbard model including the Hund's exchange coupling…
We present an application of high-order series expansion in the coupling constants for the ground state properties of correlated lattice fermion systems. Expansions have been generated up to order $(t/J)^{14}$ for $d=1$ and $(t/J)^8$ for…
We simulate a four dimensional self-interacting scalar field theory on the lattice at finite temperature. By varying temperature, the system undergoes a phase transition from broken phase to symmetric phase. Our data show that the…
The Kuramoto model captures various synchronization phenomena in biological and man-made systems of coupled oscillators. It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from…