Instantaneous measurement of non-local variables

It is shown, under the assumption of possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously, except for a finite time required for bringing to one location the classical records from these sites which yield the result of the measurement. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.Comment: 4 pages, revised version, to be published in PR

A unified mechanistic model of niche, neutrality and violation of the competitive exclusion principle

The origin of species richness is one of the most widely discussed questions in ecology. The absence of unified mechanistic model of competition makes difficult our deep understanding of this subject. Here we show such a two-species competition model that unifies (i) a mechanistic niche model, (ii) a mechanistic neutral (null) model and (iii) a mechanistic violation of the competitive exclusion principle. Our model is an individual-based cellular automaton. We demonstrate how two trophically identical and aggressively propagating species can stably coexist in one stable homogeneous habitat without any trade-offs in spite of their 10% difference in fitness. Competitive exclusion occurs if the fitness difference is significant (approximately more than 30%). If the species have one and the same fitness they stably coexist and have similar numbers. We conclude that this model shows diffusion-like and half-soliton-like mechanisms of interactions of colliding population waves. The revealed mechanisms eliminate the existing contradictions between ideas of niche, neutrality and cases of violation of the competitive exclusion principle

Strong and weak competitors can coexist in the same niche

The competitive exclusion principle postulates that two trophically identical but fitness different species can not stably coexist in the same niche. However, this principle contradicts the observed nature's species richness. This fact is known as the biodiversity paradox. Here, using a simple cellular automaton model, we mechanistically show how two trophically identical, but fitness different species may stably coexist in the same niche. As environment is stable and any trade-offs are absent in this model, it strongly violates the competitive exclusion principle

Strong violation of the competitive exclusion principle

Bacteria and plants are able to form population waves as a result of their consumer behaviour and propagation. A soliton-like interpenetration of colliding population waves was assumed but not proved earlier. Here we show how and why colliding population waves of trophically identical but fitness different species can interpenetrate through each other without delay. We have hypothesized and revealed here that the last mechanism provides a stable coexistence of two, three and four species, competing for the same limiting resource in the small homogeneous habitat under constant conditions and without any fitness trade-offs. We have explained the mystery of biodiversity mechanistically because (i) our models are bottom-up mechanistic, (ii) the revealed interpenetration mechanism provides strong violation of the competitive exclusion principle and (iii) we have shown that the increase in the number of competing species increases the number of cases of coexistence. Thus the principled assumptions of fitness neutrality (equivalence), competitive trade-offs and competitive niches are redundant for fundamental explanation of species richness

A long-lived spin-orbit-coupled degenerate dipolar Fermi gas

We describe the creation of a long-lived spin-orbit-coupled gas of quantum degenerate atoms using the most magnetic fermionic element, dysprosium. Spin-orbit-coupling arises from a synthetic gauge field created by the adiabatic following of degenerate dressed states comprised of optically coupled components of an atomic spin. Because of dysprosium's large electronic orbital angular momentum and large magnetic moment, the lifetime of the gas is limited not by spontaneous emission from the light-matter coupling, as for gases of alkali-metal atoms, but by dipolar relaxation of the spin. This relaxation is suppressed at large magnetic fields due to Fermi statistics. We observe lifetimes up to 400 ms, which exceeds that of spin-orbit-coupled fermionic alkali atoms by a factor of 10-100, and is close to the value obtained from a theoretical model. Elastic dipolar interactions are also observed to influence the Rabi evolution of the spin, revealing an interacting fermionic system. The long lifetime of this weakly interacting spin-orbit-coupled degenerate Fermi gas will facilitate the study of quantum many-body phenomena manifest at longer timescales, with exciting implications for the exploration of exotic topological quantum liquids.Comment: 11 pages, 8 figures, one appendi

Trapping ultracold dysprosium: a highly magnetic gas for dipolar physics

Ultracold dysprosium gases, with a magnetic moment ten times that of alkali atoms and equal only to terbium as the most magnetic atom, are expected to exhibit a multitude of fascinating collisional dynamics and quantum dipolar phases, including quantum liquid crystal physics. We report the first laser cooling and trapping of half a billion Dy atoms using a repumper-free magneto-optical trap (MOT) and continuously loaded magnetic confinement, and we characterize the trap recycling dynamics for bosonic and fermionic isotopes. The first inelastic collision measurements in the few partial wave, 100 uK to 1 mK, regime are made in a system possessing a submerged open electronic f-shell. In addition, we observe unusual stripes of intra-MOT <10 uK sub-Doppler cooled atoms.Comment: 4+ pages, 4 figures; minor edits in V

The fundamental limit on the rate of quantum dynamics: the unified bound is tight

The question of how fast a quantum state can evolve has attracted a considerable attention in connection with quantum measurement, metrology, and information processing. Since only orthogonal states can be unambiguously distinguished, a transition from a state to an orthogonal one can be taken as the elementary step of a computational process. Therefore, such a transition can be interpreted as the operation of "flipping a qubit", and the number of orthogonal states visited by the system per unit time can be viewed as the maximum rate of operation. A lower bound on the orthogonalization time, based on the energy spread DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average energy E, was established by Margolus and Levitin. The bounds coincide, and can be exactly attained by certain initial states if DeltaE=E; however, the problem remained open of what the situation is otherwise. Here we consider the unified bound that takes into account both DeltaE and E. We prove that there exist no initial states that saturate the bound if DeltaE is not equal to E. However, the bound remains tight: for any given values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit value. The relation between the largest energy level, the average energy, and the orthogonalization time is also discussed. These results establish the fundamental quantum limit on the rate of operation of any information-processing system.Comment: 4 pages 1 PS figure Late

On the Low and High Frequency Correlation in Quasi-Periodic Oscillations Among White Dwarfs, Neutron Star and Black Hole Binaries

We interpret the correlation over five orders of magnitude between high frequency and low frequency in a quasi-periodic oscillations (QPO) found by Psaltis, Belloni & van der Klis (1999) for black hole (BH), neutron star (NS) systems and then extended by Mauche (2002) to white dwarf (WD) binaries. We argue that the observed correlation is a natural consequence of the Keplerian disk flow adjustment to the innermost sub-Keplerian boundary conditions near the central object. In the framework of the transition layer model the high frequency is related to the Keplerian frequency at the outer (adjustment) radius and the low frequency is related to the magnetoacoustic oscillation (MA) frequency. Using a relation between the MA frequency the magnetic and gas pressure and the density and the hydrostatic equilibrium condition in the disk we infer a linear correlation the Keplerian frequency and the MA frequency. We estimate the magnetic field strength near the TL outer radius for BHs NSs and WDs. The fact that the observed high-low frequency correlation over five orders of magnitude is valid for BHs, NSs, and down to WDs strongly rules out relativistic models for QPO phenomena. We come to the conclusion that the QPOs observations indicate the adjustment of the geometrically thin disk to sub-Keplerian motion near the central object. This effect is a common feature for a wide class of systems, starting from white dwarf binaries up to black hole binaries.Comment: 8 pages, 1 figure, accepted for publication in the ApJ. Letters 2002 August