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Register a new userThe correlations and anticorrelations in QPO data
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Double peak kHz QPO frequencies in neutron star sources varies in time by a factor of hundreds Hz while in microquasar sources the frequencies are fixed and located at the line u_2 = 1.5 u_1 in the frequency-frequency plot. The crucial question in the theory of twin HFQPOs is whether or not those observed in neutron-star systems are essentially different from those observed in black holes. In black hole systems the twin HFQPOs are known to be in a 3:2 ratio for each source. At first sight, this seems not to be the case for neutron stars. For each individual neutron star, the upper and lower kHz QPO frequencies, u_2 and u_1, are linearly correlated, u_2=A u_1 + B, with the slope A < 1.5, i.e., the frequencies definitely are not in a 1.5 ratio. In this contribution we show that when considered jointly on a frequency-frequency plot, the data for the twin kHz QPO frequencies in several (as opposed to one) neutron stars uniquely pick out a certain preferred frequency ratio that is equal to 1.5 for the six sources examined so far.
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We analyse archival CGRO-BATSE X-ray flux and spin frequency measurements of GX 1+4 over a time span of 3000 days. We systematically search for time dependent variations of torque luminosity correlation. Our preliminary results indicate that the correlation shifts from being positive to negative on time scales of few 100 days.
We analyzed the recently published kHz QPO data in the neutron star low-mass X-ray binaries (LMXBs), in order to investigate the different correlations of the twin peak kilohertz quasi-eriodic oscillations (kHz QPOs) in bright Z sources and in the less luminous Atoll sources. We find that a power-law relation $ osim t^{b}$ between the upper and the lower kHz QPOs with different indices: $bsimeq$1.5 for the Atoll source 4U 1728-34 and $bsimeq$1.9 for the Z source Sco X-1. The implications of our results for the theoretical models for kHz QPOs are discussed.
For an even qudit dimension $dgeq 2,$ we introduce a class of two-qudit states exhibiting perfect correlations/anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value $3/2$ - the upper bound attained on some two-qubit states. We show that the two-qudit Greenberger-Horne-Zeilinger (GHZ) state with an arbitrary even $dgeq 2$ exhibits perfect correlations/anticorrelations and belongs to the introduced two-qudit state class. These new results are important steps towards proving in general the $frac{3}{2}$ upper bound on quantum violation of the original Bell inequality. The latter would imply that similarly as the Tsirelson upper bound $2sqrt{2}$ specifies the quantum analog of the CHSH inequality for all bipartite quantum states, the upper bound $frac{3}{2}$ specifies the quantum analog of the original Bell inequality for all bipartite quantum states with perfect correlations/ anticorrelations. Possible consequences for the experimental tests on violation of the original Bell inequality are briefly discussed.
We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by 3/2 and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound 3/2 for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study.
It is found that there exists an empirical linear relation between the high frequency $ high$ and low frequency $ low$ of quasi-periodic oscillations (QPOs) for black hole candidate (BHC), neutron star (NS) and white dwarf (WD) in the binary systems, which spans five orders of magnitude in frequency. For the NS Z (Atoll) sources, $ u_{high}$ and $ u_{low}$ are identified as the lower kHz QPO frequency and horizontal branch oscillations (HBOs) $ h$ (broad noise components); for the black hole candidates and low-luminosity neutron stars, they are the QPOs and broad noise components at frequencies between 1 and 10 Hz; for WDs, they are the ``dwarf nova oscillations (DNOs) and QPOs of cataclysmic variables (CVs). To interpret this relation, our model ascribes $ u_{high}$ to the Alfven wave oscillation frequency at a preferred radius and $ u_{low}$ to the same mechanism at another radius. Then, we can obtain $ low = 0.08 high$ and the relation between the upper kHz QPO frequency $ t$ and HBO to be $ h simeq 56 ({rm Hz}) ( t/{rm kHz})^{2}$, which are in accordance with the observed empirical relations. Furthermore, some implications of model are discussed, including why QPO frequencies of white dwarfs and neutron stars span five orders of magnitude in frequency.
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