Related papers: Phase ordering percolation and an infinite domain …
We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that, at criticality, the finite third moment assumption on the…
The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will…
Recent realization of Bose-Einstein condensation of light in 2D provides a new platform for studying novel phases and phase transitions. The combination of low effective mass of the confined light and the presence of the dye molecules with…
The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
We present a numerical study of turbulence in Bose-Einstein condensates within the 3D Gross-Pitaevskii equation. We concentrate on the direct energy cascade in forced-dissipated systems. We show that behavior of the system is very sensitive…
Dynamical vortex production and quantum turbulence emerging in periodic perturbed quasi-two-dimensional (q2D) Bose-Einstein condensates are reported by considering two distinct time-dependent approaches. In both cases, dynamical simulations…
To depict the complex relationship among nodes and the evolving process of a complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based on two basic evolutionary mechanisms, growth and preference jumping, the distribution…
We investigate schemes to dynamically create many particle entangled states of a two component Bose-Einstein condensate in a very short time proportional to 1/N where $N$ is the number of condensate particles. For small $N$ we compare exact…
We propose and analyze a general mechanism of disorder-induced order in two-component Bose-Einstein condensates, analogous to corresponding effects established for XY spin models. We show that a random Raman coupling induces a relative…
Phase transitions are ubiquitous in nature, ranging from protein folding and denaturisation, to the superconductor-insulator quantum phase transition, to the decoupling of forces in the early universe. Remarkably, phase transitions can be…
Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations.…
Bose-Einstein condensates are studied in a potential of finite depth which supports both bound and quasi-bound states. This potential, which is harmonic for small radii and decays as a Gaussian for large radii, models experimentally…
We introduce higher dimensions into the problem of Bose-Einstein condensates in a double-well potential, taking into account orbital angular momentum. We completely characterize the eigenstates of this system, delineating new regimes via…
The miscibility-immiscibility phase transition in binary Bose-Einstein condensates (BECs) can be controlled by a coupling between the two components. Here we propose a new scheme that uses coupling-induced pattern formation to test the…
We consider the phase transition dynamics of a trapped Bose-Einstein condensate subject to Raman-type spin-orbit coupling (SOC). By tuning the coupling strength the condensate is taken through a second order phase transition into an…
We study the generation of two-mode entanglement in a two-component Bose-Einstein condensate trapped in a double-well potential. By applying the Holstein-Primakoff transformation, we show that the problem is exactly solvable as long as the…
In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities of Bose-Einstein condensates in one- and two-dimensional settings. In particular, we illustrate the trapping conditions that allow the…
We analyze the formation of transient patterns and spin-spin correlations in quasi-two-dimensional spin-1 homogeneous Bose-Einstein condensates subjected to parametric driving of $s$-wave scattering lengths. The dynamics for an initial…
The dynamics of Bose-Einstein condensates in the lowest energy band of a one-dimensional optical lattice is generally disturbed by the presence of transversally excited resonant states. We propose an effective one-dimensional theory which…