Related papers: Quantum Lattice Solitons
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
To avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not…
We suggest a Hamiltonian formulation on a momentum lattice using a physically motivated regularization using the Breit-frame which links the maximal parton number to the lattice size. This scheme restricts parton momenta to positive values…
We introduce a new type of boundary conditions, {\it smooth boundary conditions}, for numerical studies of quantum lattice systems. In a number of circumstances, these boundary conditions have substantially smaller finite-size effects than…
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…
We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices, and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance…
We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by…
In this article, associated with each lattice $T\subseteq \mathbb{Z}^n$ the concept of a harmonic-counting measure $\nu_T$ on a sphere $S^{n-1}$ is introduced and it is applied to determine the asymptotic behavior of the eigenfunctions of…
The sharp pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones (LJ) anharmonic lattices. Numerical simulations reveal the presence of high energy strongly localized ``discrete'' kink-solitons (DK), which move with supersonic…
We consider the spectrum of the totally asymmetric simple exclusion process on a periodic lattice of $L$ sites. The first eigenstates have an eigenvalue with real part scaling as $L^{-3/2}$ for large $L$ with finite density of particles.…
In this work we introduce a worldline based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our…
We study a quantum particle in a tilted honeycomb lattice in the tight-binding approximation. First we discuss the particle eigenstates, i.e., the stationary Wannier-Stark states. These states are proved to be extended states for the…
A model is investigated where a monochromatic, spatially homogeneous laser field interacts with an electron in a one-dimensional periodic lattice. The classical Hamiltonian is presented and the technique of stroboscopic maps is used to…
Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged…
We explore the potential application of quantum computers to the examination of lattice holography, which extends to the strongly-coupled bulk theory regime. With adiabatic evolution, we compute the ground state of a spin system on a…
In this paper we study the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan. This system with position-dependent mass allows a natural quantization procedure and is shown to display shape invariance. Its energy…
We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest…
Quantised sound waves -- phonons -- govern the elastic response of crystalline materials, and also play an integral part in determining their thermodynamic properties and electrical response (e.g., by binding electrons into superconducting…
In this work, we exactly solve a Kondo lattice model in the thermodynamic limit. The system consists of an electronic conduction band described by unconstrained hopping matrix elements between the lattice sites. The conducting electrons…
Periodic potentials with flat bands in their spectra support strongly localized nonlinear excitations. Although a perfectly flat band cannot exist in a continuous system, a spin-orbit-coupled Bose-Einstein condensate loaded in a Zeeman…