Constrained-Path Quantum Monte-Carlo Approach for Non-Yrast States Within the Shell Model

The present paper intends to present an extension of the constrained-path quantum Monte-Carlo approach allowing to reconstruct non-yrast states in order to reach the complete spectroscopy of nuclei within the interacting shell model. As in the yrast case studied in a previous work, the formalism involves a variational symmetry-restored wave function assuming two central roles. First, it guides the underlying Brownian motion to improve the efficiency of the sampling. Second, it constrains the stochastic paths according to the phaseless approximation to control sign or phase problems that usually plague fermionic QMC simulations. Proof-of-principle results in the $sd$ valence space are reported. They prove the ability of the scheme to offer remarkably accurate binding energies for both even- and odd-mass nuclei irrespective of the considered interaction.Comment: 11 pages, 4 figure

Radii in the sdsd shell and the s1/2s_{1/2} "halo" orbit: A game changer

Proton radii of nuclei in the $sd$ shell depart appreciably from the asymptotic law, $\rho_{\pi}=\rho_0A^{1/3}$. The departure exhibits systematic trends fairly well described by a single phenomenological term in the Duflo-Zuker formulation, which also happens to explain the sudden increase in slope in the isotope shifts of several chains at neutron number $N=28$. It was recently shown that this term is associated with the abnormally large size of the $s_{1/2}$ and $p$ orbits in the $sd$ and $pf$ shells respectively. Further to explore the problem, we propose to calculate microscopically radii in the former. Since the (square) radius is basically a one body operator, its evolution is dictated by single particle occupancies determined by shell model calculations. Assuming that the departure from the asymptotic form is entirely due to the $s_{1/2}$ orbit, the expectation value $\langle s_{1/2}|r^2|s_{1/2}\rangle$ is determined by demanding that its evolution be such as to describe well nuclear radii. It does, for an orbit that remains very large (about 1.6 fm bigger than its $d$ counterparts) up to $N,\,Z=14$ then drops abruptly but remains some 0.6 fm larger than the $d$ orbits. An unexpected behavior bound to challenge our understanding of shell formation.Comment: 4 pages 6(7) figure

A constrained-path quantum Monte-Carlo approach for the nuclear shell model

International audienceA new QMC approach for the shell model yielding nearly exact spectroscopy of nuclei is presented. The originality of the formalism lies in the use of a variational symmetry-restored wave function to ‘steer’ the Brownian motion, and to control the sign/phase problem that generally makes the traditional QMC samplings totally ineffective by causing a prohibitive growth of the statistical errors. Tests of convergence and proof-of-principle results are reported

Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance

The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.Comment: 30 pages, 13 figur

Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity

We analytically determine the minimal time and the optimal control laws required for the realization, up to an assigned fidelity and with a fixed energy available, of entangling quantum gates ($\mathrm{CNOT}$) between indirectly coupled qubits of a trilinear Ising chain. The control is coherent and open loop, and it is represented by a local and continuous magnetic field acting on the intermediate qubit. The time cost of this local quantum operation is not restricted to be zero. When the matching with the target gate is perfect (fidelity equal to one) we provide exact solutions for the case of equal Ising coupling. For the more general case when some error is tolerated (fidelity smaller than one) we give perturbative solutions for unequal couplings. Comparison with previous numerical solutions for the minimal time to generate the same gates with the same Ising Hamiltonian but with instantaneous local controls shows that the latter are not time-optimal.Comment: 11 pages, no figure

Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field

We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using band-pass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.Comment: 16 pages, 4 figures. To appear in Physical Review

Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.Comment: 33 page

Absorption foliaire des métaux présents dans des particules atmosphériques issues d'une usine de recyclage de batteries : biotest laitue

National audienceLes flux de polluants émis dans l'environnement ont été considérablement réduits en particulier par la mise en place par les industriels de système de filtres performants. Cependant les particules très fines et particulièrement réactives sont toujours émises dans l'environnement. De nombreuses études décrivent le transfert sol-plante des métaux mais très peu concernent la voie de transfert atmosphère plante. Pourtant, selon le rapport parlementaire de Miquel (2001), l'enrichissement actuel des sols en plomb provient pour 68% des retombées atmosphériques qui sont aussi interceptées par les plantes. Le transfert foliaire direct via des aérosols particulaires a été démontré pour des radionucléides (137Cs, 85Sr, 133Ba et 123mTe) par Madoz-Escande et al. (2004). Or les voies de transport des radionucléides et métaux sont aussi celles des "oligoélements" (Zn, Co, Mo, Cu) dans les plantes. C'est pourquoi il paraît pertinent de s'intéresser au transfert foliaire des métaux. De nombreuses questions scientifiques se posent en effet concernant le transfert foliaire des métaux. Est-il possible? Si oui sous quelle forme sont les métaux? Quels sont les mécanismes physico chimiques et biologiques impliqués? Quelle est l'importance de cette voie vis-à-vis du transfert sol plante ? Pour répondre à ces questions, le transfert du plomb et du cadmium vers les parties aériennes des plantes via le dépôt atmosphérique de particules industrielles riches en métaux a été expérimenté et modélisé

Saturation of a spin 1/2 particle by generalized Local control

We show how to apply a generalization of Local control design to the problem of saturation of a spin 1/2 particle by magnetic fields in Nuclear Magnetic Resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with respect to the time-optimal solution which has been recently derived using geometric methods.Comment: 12 pages, 4 figures, submitted to new journal of physics (2011