Développements asymptotiques dans l'approximation de Born-Oppenheimer
Développements asymptotiques des perturbations lentes de l'opérateur de Schrödinger périodique
Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique
Diamagnetic behavior of sums Dirichlet eigenvalues
The Li-Yau semiclassical lower bound for the sum of the first eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.
Differential representations of dynamical oscillator symmetries in discrete Hilbert space.
Diffusion Monte Carlo method: Numerical Analysis in a Simple Case
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove...
Dirac equations with moving nuclei
Discrete spectrum of operator valued Friedrichs models
Discretized representations of harmonic variables by bilateral Jacobi operators.
Dispersive waves and caustics.
Distribution of matrix elements and level spacings for classically chaotic systems
Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
Do nonsingular globally bounded positon solutions exist?
Double and triple summation expressions obtained using perturbation theory.
Dynamical entropy of a non-commutative version of the phase doubling
A quantum dynamical system, mimicking the classical phase doubling map on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.
Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator
We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic...
Dynamical symmetries in supersymmetric matrix models.
Dynamics of entanglement between a quantum dot spin qubit and a photon qubit inside a semiconductor high-Q nanocavity.
Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model
Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [8], is a random process which takes values in the vertex set of a graph and is more likely to cross edges it has visited before. We show that it can be represented in terms of a vertex-reinforced jump process (VRJP) with independent gamma conductances; the VRJP was conceived by Werner and first studied by Davis and Volkov [10, 11], and is a continuous-time process favouring sites with more local time. We calculate,...
Effective Hamiltonians and Quantum States
We recount here some preliminary attempts to devise quantum analogues of certain aspects of Mather’s theory of minimizing measures [M1-2, M-F], augmented by the PDE theory from Fathi [F1,2] and from [E-G1]. This earlier work provides us with a Lipschitz continuous function solving the eikonal equation aėȧnd a probability measure solving a related transport equation.We present some elementary formal identities relating certain quantum states and . We show also how to build out of an approximate...