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

Time-minimal control of dissipative two-level quantum systems: The Integrable case

The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus our analysis on the case where the extremal Hamiltonian is integrable.Comment: 24 pages, 6 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

Controllability properties for finite dimensional quantum Markovian master equations

Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail.Comment: 15 page

Time-Minimal Control of Dissipative Two-level Quantum Systems: the Generic Case

The objective of this article is to complete preliminary results concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by Lindblad equations. The extremal system is described by a 3D-Hamiltonian depending upon three parameters. We combine geometric techniques with numerical simulations to deduce the optimal solutions.Comment: 24 pages, 16 figures. submitted to IEEE transactions on automatic contro

The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry

We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Riemannian geometry. We compute estimations of the exponential map which allow us to describe the conjugate locus and the cut locus at a tangency point. We prove that this last one generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set