相关论文: Continuous vs. discrete models for the quantum har…

For the symmetric harmonic oscillator and the symmetric bouncer defined in 2-D, two different Hamiltonian are given describing the same classical dynamics; however, their quantum dynamics behavior are different.

Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…

We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the…

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…

We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…

We study a new family of q-Meixner multiple orthogonal polynomials of the first kind. The discrete orthogonality conditions are considered over a non-uniform lattice with respect to different q-analogues of Pascal distributions. We address…

We describe recent developments in the hybrid atomistic/continuum modelling of dense fluids. We discuss the general implementation of mass, momentum and energy transfers between a region described by molecular dynamics and the neighbouring…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

In this contribution, we briefly discuss the results for charmonium and bottomonium spectra with self-energy corrections in the unquenched quark model, due to the coupling to the meson-meson continuum. The UQM formalism can be extended to…

Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…

We derive discrete and oscillatory Chern-Simons matrix models. The method is based on fundamental properties of the associated orthogonal polynomials. As an application, we show that the discrete model allows to prove and extend the…

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…

Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that…

We provide in this paper the discrete equations of motion for the newtonian $n$-body problem deduced from the quantum calculus of variations (Q.C.V.) developed in \cite{Cre,CFT,RS1,RS2}. These equations are brought into the usual lagrangian…

We present two semidiscretizations of the Camassa-Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an existing conservative multipeakon method on the real line,…

We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…

Real atomic systems, like the hydrogen atom in a magnetic field or the helium atom, whose classical dynamics are chaotic, generally present both discrete and continuous symmetries. In this letter, we explain how these properties must be…

Exact solvability of two typical examples of the discrete quantum mechanics, i.e. the dynamics of the Meixner-Pollaczek and the continuous Hahn polynomials with full parameters, is newly demonstrated both at the Schroedinger and Heisenberg…

We explore a new type of discretizations of lattice dynamical models of the Klein-Gordon type relevant to the existence and long-term mobility of nonlinear waves. The discretization is based on non-holonomic constraints and is shown to…

For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for…