An approximation scheme for quasi-stationary distributions of killed diffusions

In this paper we study the asymptotic behavior of the normalized weighted empirical occupation measures of a diffusion process on a compact manifold which is killed at a smooth rate and then regenerated at a random location, distributed according to the weighted empirical occupation measure. We show that the weighted occupation measures almost surely comprise an asymptotic pseudo-trajectory for a certain deterministic measure-valued semiflow, after suitably rescaling the time, and that with probability one they converge to the quasi-stationary distribution of the killed diffusion. These results provide theoretical justification for a scalable quasi-stationary Monte Carlo method for sampling from Bayesian posterior distributions.Comment: v2: revised version, 29 pages, 1 figur

Neutron matter at zero temperature with auxiliary field diffusion Monte Carlo

The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary field Monte Carlo to separate the spin-isospin operators, quantum Monte Carlo can be used to simulate the ground state of many nucleon systems (A\alt 100). We use a path constraint to control the fermion sign problem. We have made simulations for realistic interactions, which include tensor and spin--orbit two--body potentials as well as three-nucleon forces. The Argonne $v_8'$ and $v_6'$ two nucleon potentials plus the Urbana or Illinois three-nucleon potentials have been used in our calculations. We compare with fermion hypernetted chain results. We report results of a Periodic Box--FHNC calculation, which is also used to estimate the finite size corrections to our quantum Monte Carlo simulations. Our AFDMC results for $v_6$ models of pure neutron matter are in reasonably good agreement with equivalent Correlated Basis Function (CBF) calculations, providing energies per particle which are slightly lower than the CBF ones. However, the inclusion of the spin--orbit force leads to quite different results particularly at relatively high densities. The resulting equation of state from AFDMC calculations is harder than the one from previous Fermi hypernetted chain studies commonly used to determine the neutron star structure.Comment: 15 pages, 15 tables and 5 figure

Quantum optimal control within the rotating wave approximation

We study the interplay between rotating wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time-independent under the rotating wave approximation. Thus, we show how to recast the functional minimization defined by the optimal control problem into a simpler multi-variable function minimization. We provide the analytic solution to the state-to-state transfer of the paradigmatic two-level system and to the more general star configuration of an $N$-level system. We demonstrate numerically the usefulness of this approach in the more general class of connected acyclic $N$-level systems with random spectra. Finally, we use it to design a protocol to entangle Rydberg via constant laser pulses atoms in an experimentally relevant range of parameters.Comment: 8 pages, 5 figure

Quantum selfish gene (biological evolution in terms of quantum mechanics)

I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can live relatively independently of the others, and can contain a few real creatures. Each population of living creatures we treat as the wave function on meta- genes, which module squared is the total number of creatures with the given meta-gene, and the phase is the sum of "aspirations" to change the classical states of meta- genes. Each individual life thus becomes one of possible outcomes of the virtual quantum measurement of this function. The evolution of genomes is described by the unitary operator in the space of psi-functions or by Kossovsky-Lindblad equation in the case of open biosystems. This operator contains all the information about specific conditions under which individuals are, and how "aspirations" of their meta- genes may be implemented at the biochemical level. We show the example of quantum description of the population with two parts of meta-gene: "wolves" and "deer", which can be simultaneously in the same abstract living unity. "Selfish gene" reconciled with the notion of individuality of alive beings that gives possibility to consider evolutionary scenarios and their possible physical causes from the single position.Comment: 15 pages, LATE