Related papers: Interface Fluctuations on a Hierarchical Lattice
The interface between two materials described by spectrally gapped Hamiltonians is expected to host an in-gap interface mode, whenever a certain topological invariant changes across the interface. We provide a precise statement of this…
We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…
The nuclear collective response is investigated in the framework of a doorway picture in which the spreading width of the collective motion is described as a coupling to more and more complex configurations. It is shown that this coupling…
The flux line lattice of superconductors has been investigated when there exists a periodicity in the underlying system, such as can occur in artificially layered structures. For small fields parallel to the layers the flux lines enter the…
This paper is concerned with the regularity theory of a transmission problem arising in composite materials. We give a new self-contained proof for the $C^{k,\alpha}$ estimates on both sides of the interface under the minimal assumptions on…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
Nonlinear dynamics of wave packets in two-dimensional parity-time-symmetric optical lattices near the phase-transition point are analytically studied. A novel fourth-order equation is derived for the envelope of these wave packets. A…
We consider how membrane fluctuations can modify the miscibility of lipid mixtures, that is to say how the phase diagram of a boundary-constrained membrane is modified when the membrane is allowed to fluctuate freely in the case of zero…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity and bias. Depending on the position of the interface, there exist two exclusive ways to model the…
The Rayleigh capillary instability of a cylindrical interface between two immiscible fluids is one of the most fundamental in fluid dynamics. As Plateau observed from energetic considerations and Rayleigh clarified through hydrodynamics,…
We consider a model of lattice gas dynamics in the d-dimensional cubic lattice in the presence of disorder. If the particle interaction is only mutual exclusion and if the disorder field is given by i.i.d. bounded random variables, we prove…
We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a…
We consider a cloud of fermionic atoms in an optical lattice described by a Hubbard model with an additional linear potential. While homogeneous interacting systems mainly show damped Bloch oscillations and heating, a finite cloud behaves…
We propose and analyze a model for phase transitions in an inhomogeneous fluid membrane, that couples local composition with curvature nonlinearly. For asymmetric membranes, our model shows generic non-Ising behavior and the ensuing phase…
Using coarse grained models we investigate the behavior of water adjacent to an extended hydrophobic surface peppered with various fractions of hydrophilic patches of different sizes. We study the spatial dependence of the mean interface…
We consider the interplay of thermal fluctuations and shear on the surface of the domains in various systems coarsening under an imposed shear flow. These include systems with nonconserved and conserved dynamics, and a conserved order…
We present a systematic study of interface roughness and its effect on coherent dynamical processes in quantum dots. The potential due to a sharp, flat interface lifts the degeneracy of the lowest energy valleys and yields a set of valley…
Based on an attractive $U$ Hubbard model on a lattice with up to second neighbor hopping we derive an effective Hamiltonian for phase fluctuations. The superconducting gap is assumed to have s-wave symmetry. The effective Hamiltonian we…
We consider the critical behavior of two-dimensional layered Ising models where the exchange couplings between neighboring layers follow hierarchical sequences. The perturbation caused by the non-periodicity could be irrelevant, relevant or…