Search results for "QUANTUM MECHANICS"
showing 10 items of 2468 documents
Temporal incoherent solitons supported by a defocusing nonlinearity with anomalous dispersion
2012
http://pra.aps.org/; International audience; We study temporal incoherent solitons in noninstantaneous response nonlinear media. Contrarily to the usual temporal soliton, which is known to require a focusing nonlinearity with anomalous dispersion, we show that a highly noninstantaneous nonlinear response leads to incoherent soliton structures which require the inverted situation: In the focusing regime (and anomalous dispersion) the incoherent wave packet experiences an unlimited spreading, whereas in the defocusing regime (still with anomalous dispersion) the incoherent wave packet exhibits a self-trapping. These counterintuitive results are explained in detail by a long-range Vlasov formu…
Quantum wire with periodic serial structure
1991
Electron wave motion in a quantum wire with periodic structure is treated by direct solution of the Schr\"odinger equation as a mode-matching problem. Our method is particularly useful for a wire consisting of several distinct units, where the total transfer matrix for wave propagation is just the product of those for its basic units. It is generally applicable to any linearly connected serial device, and it can be implemented on a small computer. The one-dimensional mesoscopic crystal recently considered by Ulloa, Casta\~no, and Kirczenow [Phys. Rev. B 41, 12 350 (1990)] is discussed with our method, and is shown to be a strictly one-dimensional problem. Electron motion in the multiple-stu…
A relativistic approach to gravitational instability in the expanding Universe: second-order Lagrangian solutions
1994
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and geometric quantities and compared with the corresponding ones in the Newtonian approximation. Specifically, we compute the density, the volume expansion scalar, the shear, the ``electric" part, or tide, and the ``magnetic" part of the Weyl tensor. The evolution of the shear and the tide beyond the linear regime strongly depends on the ratio of the characteristic size of the perturbation to the cosmological horizon distance. For perturbations on sub--horizon scal…
Relations between multi-resolution analysis and quantum mechanics
2005
We discuss a procedure to construct multiresolution analyses (MRA) of L2 (R) starting from a given seed function h (s) which should satisfy some conditions. Our method, originally related to the quantum mechanical Hamiltonian of the fractional quantum Hall effect, is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. This clarifies our previous procedure and makes much easier most of the original formulas, producing a convenient framework to produce examples of MRA. © 2005 American Institute of Physics.
A study of Wigner functions for discrete-time quantum walks
2013
We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative volume in phase space, as a function of time, for different initial states. This negativity can be used to quantify the degree of departure of the system from a classical state. We also relate this quantity to the entanglement between the coin and walker subspaces.
Magnetic exchange interaction in clusters of orbitally degenerate ions. II. Application of the irreducible tensor operator technique
2001
Abstract The irreducible tensor operator technique in R3 group is applied to the problem of kinetic exchange between transition metal ions possessing orbitally degenerate ground states in the local octahedral surrounding. Along with the effective exchange Hamiltonian, the related interactions (low-symmetry crystal field terms, Coulomb interaction between unfilled electronic shells, spin–orbit coupling and Zeeman interaction) are also taken into account within a unified computational scheme. Extension of this approach to high-nuclearity systems consisting of transition metal ions in the orbital triplet ground states is also demonstrated. As illustrative examples, the corner-shared D4h dimers…
Numerical Evidences of Polarization Switching in PMN Type Relaxor Ferroelectrics
2011
We present a conceptual and computational framework for chemically ordered Pb(Mg 1/3 Nb 2/3 O 3) (PMN) type supercells violating disorder of the host lattice. The effective Hamiltonian is specified by invariance under permutations of supercells and by the dipole-dipole interaction supporting both local nonzero and zero mean polarization of the structure. Statistics treated in canonical ensemble within the mean field approach reveals emergence of polar nanoregions as supported by interplay between the (random) initial state polarization of supercells and their interactions increased at cooling.
Internally Contracted Multireference Coupled Cluster Calculations with a Spin-Free Dirac-Coulomb Hamiltonian: Application to the Monoxides of Titaniu…
2017
We combine internally contracted multireference coupled cluster theory with a four-component treatment of scalar-relativistic effects based on the spin-free Dirac–Coulomb Hamiltonian. This strategy allows for a rigorous treatment of static and dynamic correlation as well as scalar-relativistic effects, which makes it viable to describe molecules containing heavy transition elements. The use of a spin-free formalism limits the impact of the four-component treatment on the computational cost to the non-rate-determining steps of the calculations. We apply the newly developed method to the lowest singlet and triplet states of the monoxides of titanium, zirconium, and hafnium and show how the in…
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
2007
Abstract This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion and is based on preliminary results of Epenoy et al. (1997) where the optimal trajectories of the energy minimization problem are approximated using averaging techniques. The averaged Hamiltonian system is explicitly computed. It is related to a Riemannian problem whose distance is an approximation of the value function. The extremal curves are analyzed, proving that the system remains integrable in the coplanar case. It is also checked that the metric associated with coplanar transfers towards a circular orbit is flat. Smoothness of small Riemannian spheres ensures global opti…
Conjugate and cut loci of a two-sphere of revolution with application to optimal control
2008
Abstract The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and gives global optimal results in orbital transfer and for Lindblad equations in quantum control.