相关论文: Some Integrable Quantum Systems on the Lattice
Lattice calculations for hadrons are now entering the domain of resonances and scattering, necessitating a better understanding of the observed discrete energy spectrum. This is a reviewing survey about recent lattice QCD results, with some…
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…
We construct a W^*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb-Robinson bounds for such systems on finite…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in the hierarchy is an N-component system defined on an…
Lattice calculations of heavy quark systems provide very good measures of the lattice spacing, a key element in recent determinations of the strong coupling constant using lattice methods. They also provide excellent testing grounds for…
The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations,…
A general scheme of construction and analysis of physical fields on the various homogeneous spaces of the Poincar\'{e} group is presented. Different parametrizations of the field functions and harmonic analysis on the homogeneous spaces are…
All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular…
Introducing a new and universally applicable discretizing technique, I construct a class of local and unitary lattice theories of Weyl neutrinos; this solves a longstanding and allegedly unsolvable problem in quantum field theory. En route,…
The one dimensional Coulomb lattice fluid in a capacitor configuration is studied. The model is formally exactly soluble via a transfer operator method within a field theoretic representation of the model. The only interactions present in…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…