Hemolytic disease of the newborn (erythroblastosis fetalis)

Thesis (M.D.)—Boston Universit

Brief Announcement: Authenticated Consensus in Synchronous Systems with Mixed Faults

Protocols solving authenticated consensus in synchronous networks with Byzantine faults have been widely researched and known to exists if and only if n > 2f for f Byzantine faults. Similarly, protocols solving authenticated consensus in partially synchronous networks are known to exist if n > 3f+2k for f Byzantine faults and k crash faults. In this work we fill a natural gap in our knowledge by presenting MixSync, an authenticated consensus protocol in synchronous networks resilient to f Byzantine faults and k crash faults if n > 2f+k. As a basic building block, we first define and then construct a publicly verifiable crusader agreement protocol with the same resilience. The protocol uses a simple double-send round to guarantee non-equivocation, a technique later used in the MixSync protocol. We then discuss how to construct a state machine replication protocol using these ideas, and how they can be used in general to make such protocols resilient to crash faults. Finally, we prove lower bounds showing that n > 2f+k is optimally resilient for consensus and state machine replication protocols

Equivalent Linear Two-Body Equations for Many-Body Systems

A method has been developed for obtaining equivalent linear two-body equations (ELTBE) for the system of many ($N$) bosons using the variational principle. The method has been applied to the one-dimensional N-body problem with pair-wise contact interactions (McGurie-Yang N-body problem) and to the dilute Bose-Einstein condensation (BEC) of atoms in anisotropic harmonic traps at zero temperature. For both cases, it is shown that the method gives excellent results for large N.Comment: 12 pages, Late

Stability of Solution of the Nonlinear Schr\"odinger Equation for the Bose-Einstein Condensation

We investigate the stability of the Bose-Einstein condensate (BEC) the case of atoms with negative scattering lengths at zero temperature using the Ginzburg-Pitaevskii-Gross (GPG) stationary theory. We have found a new exact equation for determining the upper bound of the critical numbers $N_{cr}$ of atoms for a metastable state to exist. Our calculated value of $N_{cr}$ for Bose-Einstein condensation of lithium atoms based on our new equation is in agreement with those observed in a agreement with those observed in a recent experiment.Comment: 8 pages, Late

Critical temperature and Ginzburg-Landau equation for a trapped Fermi gas

We discuss a superfluid phase transition in a trapped neutral-atom Fermi gas. We consider the case where the critical temperature greatly exceeds the spacing between the trap levels and derive the corresponding Ginzburg-Landau equation. The latter turns out to be analogous to the equation for the condensate wave function in a trapped Bose gas. The analysis of its solution provides us with the value of the critical temperature $T_{c}$ and with the spatial and temperature dependence of the order parameter in the vicinity of the phase transition point.Comment: 6 pages, 1 figure, REVTeX. The figure improved. Misprints corrected. More discussion adde

Direct observation of growth and collapse of a Bose-Einstein condensate with attractive interactions

The dynamical behavior of Bose-Einstein condensation (BEC) in a gas with attractive interactions is striking. Quantum theory predicts that BEC of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form provided that its occupation number does not exceed a limiting value. The stability limit is determined by a balance between self-attraction and a repulsion arising from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate, therefore, is punctuated by intermittent collapses, which are triggered either by macroscopic quantum tunneling or thermal fluctuation. Previous observation of growth and collapse has been hampered by the stochastic nature of these mechanisms. Here we reduce the stochasticity by controlling the initial number of condensate atoms using a two-photon transition to a diatomic molecular state. This enables us to obtain the first direct observation of the growth of a condensate with attractive interactions and its subsequent collapse.Comment: 10 PDF pages, 5 figures (2 color), 19 references, to appear in Nature Dec. 7 200

Authenticated Consensus in Synchronous Systems with Mixed Faults

Protocols solving authenticated consensus in synchronous networks with Byzantine faults have been widely researched and known to exists if and only if $n>2f$ for $f$ Byzantine faults. Similarly, protocols solving authenticated consensus in partially synchronous networks are known to exist if $n>3f+2k$ for $f$ Byzantine faults and $k$ crash faults. Currently, the only known synchronous protocol for consensus with a resilience of $n>2f+k$ is a binary consensus protocol. In this work we fill a natural gap in our knowledge by presenting MixSync, an authenticated multivalued consensus protocol in synchronous networks resilient to $f$ Byzantine faults and $k$ crash faults if $n>2f+k$. As a basic building block, we first define and then construct a publicly verifiable crusader agreement protocol with the same resilience. The protocol uses a simple double-send round to guarantee non-equivocation, a technique later used in the MixSync protocol. We then discuss how to construct a state machine replication protocol using these ideas, and how they can be used in general to make such protocols resilient to crash faults. Finally, we prove lower bounds showing that $n>2f+k$ is optimally resilient for consensus and state machine replication protocols

Influence of nearly resonant light on the scattering length in low-temperature atomic gases

We develop the idea of manipulating the scattering length $a$ in low-temperature atomic gases by using nearly resonant light. As found, if the incident light is close to resonance with one of the bound $p$ levels of electronically excited molecule, then virtual radiative transitions of a pair of interacting atoms to this level can significantly change the value and even reverse the sign of $a$. The decay of the gas due to photon recoil, resulting from the scattering of light by single atoms, and due to photoassociation can be minimized by selecting the frequency detuning and the Rabi frequency. Our calculations show the feasibility of optical manipulations of trapped Bose condensates through a light-induced change in the mean field interaction between atoms, which is illustrated for $^7$Li.Comment: 12 pages, 1 Postscript figur

Macroscopic Quantum Tunneling of a Bose Condensate

We study, by means of a variational method, the stability of a condensate in a magnetically trapped atomic Bose gas with a negative scattering length and find that the condensate is unstable in general. However, for temperatures sufficiently close to the critical temperature the condensate turns out to be metastable. For that case we determine in the usual WKB approximation the decay rate of the condensate due to macroscopic quantum fluctuations. When appropriate, we also calculate the decay rate due to thermal fluctuations. An important feature of our approach is that (nonsingular) phase fluctuations of the condensate are taken into account exactly.Comment: Invited paper for the Journal of Statistical Physic

Condensation and interaction range in harmonic boson traps: a variational approach

For a gas of N bosons interacting through a two-body Morse potential a variational bound of the free energy of a confined system is obtained. The calculation method is based on the Feynman-Kac functional projected on the symmetric representation. Within the harmonic approximation a variational estimate of the effect of the interaction range on the existence of many-particle bound states, and on the N-T phase diagram is obtained.Comment: 14 pages+4 figures, submitted to phys.rev.