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Quantum fluctuations of periodic domain-wall arrays in two-dimensional incommensurate states at zero temperature are investigated using the elastic theory in the vicinity of the commensurate-incommensurate transition point. Both stripe and…
We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase…
Using holography, we study the universal scaling laws governing the coarsening dynamics of strongly coupled domain walls. Specifically, we studied the universal dependence of the length of the domain wall interfaces on the quench rate. The…
Globally conserved phase ordering dynamics is investigated in systems with short range correlations in the initial condition. A Ginzburg-Landau equation with a global conservation law is employed as the phase field model. The conditions are…
Quantum anomalies are violations of classical scaling symmetries caused by quantum fluctuations. Although they appear prominently in quantum field theory to regularize divergent physical quantities, their influence on experimental…
Diffusion of a tagged particle near a constraining biological surface is examined numerically by modeling the surface-water interaction by an effective potential. The effective potential is assumed to be given by an asymmetric double well…
Position distributions of constituent particles of the perfect Bose-gas trapped in exponentially and polynomially anisotropic boxes are investigated by means of the boson random point fields (processes) and by the spatial random…
Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although, recent years have seen the extension of traditional stochastic partial differential equations…
The hypersphere model is a simple one-parameter model of the potential energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in $\mathbb{R}^{3N}$ in which $N$ is the…
In this paper, we study the phase field models with fractional-order in time. The phase field models have been widely used to study coarsening dynamics of material systems with microstructures. It is known that phase field models are…
We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean…
We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal $-5/3$ scaling law in the turbulent energy spectrum is intimately connected…
Coarsening of an isolated far-from-equilibrium quantum system is a paradigmatic many-body phenomenon, relevant from subnuclear to cosmological lengthscales, and predicted to feature universal dynamic scaling. Here, we observe universal…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
In delocalized systems, particle number fluctuations, also known as quantum surface roughness, and the mean-square displacement exhibit a temporal power-law growth followed by a saturation to a system-size-dependent value. We use simple…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
Under suitable forcing a fluid exhibits turbulence, with characteristics strongly affected by the fluid's confining geometry. Here we study two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate in an annular trap.…
The non-equilibrium dynamics of domain wall initial states in a classical anisotropic Heisenberg chain exhibits a striking coexistence of apparently linear and non-linear behaviours: the propagation and spreading of the domain wall can be…
Many fluid-dynamical systems met in nature are quasi-two-dimensional: they are constrained to evolve in approximately two dimensions with little or no variation along the third direction. This has a drastic effect in the flow evolution…
When a liquid is cooled below its melting temperature, if crystallization is avoided, it forms a glass. This phenomenon, called glass transition, is characterized by a marked increase of viscosity, about 14 orders of magnitude, in a narrow…