A random number generator for continuous random variables

A FORTRAN 4 routine is given which may be used to generate random observations of a continuous real valued random variable. Normal distribution of F(x), X, E(akimas), and E(linear) is presented in tabular form

Mechanical Unfolding of a Simple Model Protein Goes Beyond the Reach of One-Dimensional Descriptions

We study the mechanical unfolding of a simple model protein. The Langevin dynamics results are analyzed using Markov-model methods which allow to describe completely the configurational space of the system. Using transition path theory we also provide a quantitative description of the unfolding pathways followed by the system. Our study shows a complex dynamical scenario. In particular, we see that the usual one-dimensional picture: free-energy vs end-to-end distance representation, gives a misleading description of the process. Unfolding can occur following different pathways and configurations which seem to play a central role in one-dimensional pictures are not the intermediate states of the unfolding dynamics.Comment: 10 pages, 6 figure

Recycling of quantum information: Multiple observations of quantum systems

Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the information obtainable by a given observer as a function of the number of copies in the ensemble, and of the number of independent observers that, one after the other, have independently measured the same ensemble of qubits before him. The optimality of the protocol is proven and extensions to other states and encodings are also studied. According to the general lore, the state after a measurement has no information about the state before the measurement. Our results manifestly show that this statement has to be taken with a grain of salt, specially in situations where the quantum states encode confidential information.Comment: 4 page

Universal field equations for metric-affine theories of gravity

We show that almost all metric--affine theories of gravity yield Einstein equations with a non--null cosmological constant $\Lambda$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field $W_\mu$ and therefore the presence of an anisotropy. The viability of these field equations is discussed in view of recent astrophysical observations.Comment: 13 pages. This is a copy of the published paper. We are posting it here because of the increasing interest in f(R) theories of gravit

On the geometry of four qubit invariants

The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four-qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six lines and four planes in complex projective space ${\bf CP}^3$. For the generic entanglement class of stochastic local operations and classical communication they take a very simple form related to the elementary symmetric polynomials in four complex variables. Moreover, their magnitudes are entanglement monotones that fit nicely into the geometric set of $n$-qubit ones related to Grassmannians of $l$-planes found recently. We also show that in terms of these invariants the hyperdeterminant of order 24 in the four-qubit amplitudes takes a more instructive form than the previously published expressions available in the literature. Finally in order to understand two, three and four-qubit entanglement in geometric terms we propose a unified setting based on ${\bf CP}^3$ furnished with a fixed quadric.Comment: 19 page

Canonical formulation of the embedded theory of gravity equivalent to Einstein's General Relativity

We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form, which requires imposing additional constraints, which are a part of Einstein's equations. As a result, we obtain a theory with an eight-parameter gauge symmetry. This theory becomes equivalent to Einstein's general relativity either after partial gauge fixing or after rewriting the metric in the form that is invariant under the additional gauge transformations. We write the action for such a theory.Comment: LaTeX, 17 page

Constraint algebra for Regge-Teitelboim formulation of gravity

We consider the formulation of the gravity theory first suggested by Regge and Teitelboim where the space-time is a four-dimensional surface in a flat ten-dimensional space. We investigate a canonical formalism for this theory following the approach suggested by Regge and Teitelboim. Under constructing the canonical formalism we impose additional constraints agreed with the equations of motion. We obtain the exact form of the first-class constraint algebra. We show that this algebra contains four constraints which form a subalgebra (the ideal), and if these constraints are fulfilled, the algebra becomes the constraint algebra of the Arnowitt-Deser-Misner formalism of Einstein's gravity. The reasons for the existence of additional first-class constraints in the canonical formalism are discussed.Comment: LaTeX, 12 pages; in this version the misprints in eq. (37) and (41) was correcte

Three Bosons in One Dimension with Short Range Interactions I: Zero Range Potentials

We consider the three-boson problem with $\delta$-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the scattering of one free particle a off of a bound pair. We first follow a procedure outlined by McGuire in order to obtain an analytic expression for the desired S-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on some of the important features in the scattering and bound-state sectors. In particular, we find that the 1+2 scattering length is divergent, marking the presence of a zero-energy resonance which appears as a feature when the pair-wise interactions are short-range. Finally, we consider the introduction of a three-body interaction, and comment on the cutoff dependence of the coupling.Comment: 9 figures, 2 table

Discovery of New Milky Way Star Cluster Candidates in the 2MASS Point Source Catalog II. Physical Properties of the Star Cluster CC01

Three new obscured Milky Way clusters were detected as surface density peaks in the 2MASS point source catalog during our on-going search for hidden globular clusters and massive Arches-like star clusters. One more cluster was discovered serendipitously during a visual inspection of the candidates. The first deep J, H, and Ks imaging of the cluster [IBP2002] CC01 is presented. We estimated a cluster age of ~1-3 Myr, distance modulus of (m-M)0=12.56+-0.08 mag (D=3.5 Kpc), and extinction of AV~7.7 mag. We also derived the initial mass function slope for the cluster: Gamma=-2.23+-0.16. The integration over the initial mass function yielded a total cluster mass M_{total}<=1800+-200Msol. CC01 appears to be a regular, not very massive star cluster, whose formation has probably been induced by the shock front from the nearby HII region Sh2-228.Comment: 8 pages, 9 figures, accepted in A&