Related papers: Quantum nonlinear lattices and coherent state vect…
We present a new method for solving the Schrodinger equation using the Lossless Transmission Line Model (LTL). The LTL model although extensively used in fiber optics and optical fiber design, it has not yet found application in solid state…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
By using the dual vortex method (DVM), we develop systematically a simple and effective scheme to use the vortex degree of freedoms on dual lattices to characterize the symmetry breaking patterns of the boson insulating states in the direct…
The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…
We study a model in which a Hubbard Hamiltonian is coupled to the dispersive phonons in a classical nonlinear lattice. Our calculations are restricted to the case where we have only two quasi-particles of opposite spins, and we investigate…
Dynamical spin structure factors of quantum spin nematic states are calculated in a spin-1/2 square-lattice J1-J2 model with ferromagnetic J1 and competing antiferromagnetic J2 interactions. To this end, we use a fermion representation,…
This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such…
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 derive a class of discrete nonlinear Schr{\"o}dinger (DNLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic problem. It is demonstrated that the derived class of…
In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
The interaction between two co-propagating electrostatic wavepackets characterized by arbitrary carrier wavenumber is considered. A one-dimensional (1D) non-magnetized plasma model is adopted, consisting of a cold inertial ion fluid…
We examine the linear and nonlinear modes of a one-dimensional nonlinear electrical lattice, where the usual discrete Laplacian is replaced by a fractional discrete Laplacian. This induces a long-range intersite coupling that, at long…
Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…
Discrete nonlinear Schr\"oginger equation (DNLS) of the form, $i \frac{dC_n} {dt}$ = $C_{n+1}$ + $C_{n-1}$ - $ \chi_n [|C_{n+1}|^2 + |C_{n-1}|^2 - 2 |C_n|^2] C_n$ is used to study the formation of stationary localized states in one…
We propose a quantum algorithm to tackle the quadratic nonlinearity in the Lattice Boltzmann (LB) collision operator. The key idea is to build the quantum gates based on the particle distribution functions (PDF) within the coherence time…
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…
Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant…
The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is…