Non-self-adjoint resolutions of the identity and associated operators

Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity \{X(\lambda)\}_{\lambda\in {\mb R}}, whose adjoints constitute also a resolution of the identity, are studied . In particular, it is shown that a closed operator $B$ has a spectral representation analogous to the familiar one for self-adjoint operators if and only if $B=TAT^{-1}$ where $A$ is self-adjoint and $T$ is a bounded operator with bounded inverse

Pattern-recalling processes in quantum Hopfield networks far from saturation

As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the input-output relation. To model the situation artificially, a kind of 'heat bath' that surrounds neurons is introduced. The heat bath, which is a source of noise, is specified by the 'temperature'. Several studies concerning the pattern-recalling processes of the Hopfield model governed by the Glauber-dynamics at finite temperature were already reported. However, we might extend the 'thermal noise' to the quantum-mechanical variant. In this paper, in terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as 'overlap' in a quantum-mechanical variant of the Hopfield neural networks (let us call "quantum Hopfield model" or "quantum Hopfield networks"). For the case in which non-extensive number $p$ of patterns are embedded via asymmetric Hebbian connections, namely, $p/N \to 0$ for the number of neuron $N \to \infty$ ('far from saturation'), we evaluate the recalling processes for one of the built-in patterns under the influence of quantum-mechanical noise.Comment: 10 pages, 3 figures, using jpconf.cls, Proc. of Statphys-Kolkata VI

Neutrino emission from BL Lac objects: the role of radiatively inefficient accretion flows

The origin of the astrophysical high-energy neutrinos discovered by IceCube is currently a major mystery. The recent detection of IceCube-170922A, a $\sim$300 TeV neutrino potentially correlated with the flaring $\gamma$-ray source TXS 0506+056, directs attention toward BL Lac objects (BL Lacs), the subclass of blazars with weak emission lines. While high-energy neutrinos can be produced via photohadronic interactions between protons accelerated in their jets and ambient low-energy photons, the density of the latter in such objects had generally been thought to be too low for efficient neutrino emission. Here we consider the role of radiatively inefficient accretion flows (RIAFs), which can plausibly exist in the nuclei of BL Lacs, as the source of target photons for neutrino production. Based on simple model prescriptions for the spectra of RIAFs at different accretion rates, we find that they can be sufficienly intense to allow appreciable neutrino emission for the class of low-synchrotron-peak BL Lacs such as TXS 0506+056. In constrast, for high-synchrotron-peak BL Lacs including Mkn 421 and Mkn 501, the contribution of RIAFs is subdominant and their neutrino production efficiency can remain low, consistent with their non-detection by IceCube to date.Comment: 5 pages, 4 figures, accepted to MNRAS as Lette

Quantum secret sharing based on modulated high-dimensional time-bin entanglement

We propose a new scheme for quantum secret sharing (QSS) that uses a modulated high-dimensional time-bin entanglement. By modulating the relative phase randomly by {0,pi}, a sender with the entanglement source can randomly change the sign of the correlation of the measurement outcomes obtained by two distant recipients. The two recipients must cooperate if they are to obtain the sign of the correlation, which is used as a secret key. We show that our scheme is secure against intercept-and-resend (I-R) and beam splitting attacks by an outside eavesdropper thanks to the non-orthogonality of high-dimensional time-bin entangled states. We also show that a cheating attempt based on an I-R attack by one of the recipients can be detected by changing the dimension of the time bin entanglement randomly and inserting two "vacant" slots between the packets. Then, cheating attempts can be detected by monitoring the count rate in the vacant slots. The proposed scheme has better experimental feasibility than previously proposed entanglement-based QSS schemes.Comment: To appear in Phys. Rev.

Doubly magic nuclei from Lattice QCD forces at MPS=M_{PS}=469 MeV/c2^2

We perform ab initio self-consistent Green's function calculations of the closed shell nuclei $^{\rm 4}$He, $^{\rm 16}$O and $^{\rm 40}$Ca, based on two-nucleon potentials derived from Lattice QCD simulations, in the flavor SU(3) limit and at the pseudo-scalar meson mass of 469~MeV/c$^{\rm 2}$. The nucleon-nucleon interaction is obtained using the HAL QCD method and its short-distance repulsion is treated by means of ladder resummations outside the model space. Our results show that this approach diagonalises ultraviolet degrees of freedom correctly. Therefore, ground state energies can be obtained from infrared extrapolations even for the relatively hard potentials of HAL QCD. Comparing to previous Brueckner Hartree-Fock calculations, the total binding energies are sensibly improved by the full account of many-body correlations. The results suggest an interesting possible behaviour in which nuclei are unbound at very large pion masses and islands of stability appear at first around the traditional doubly-magic numbers when the pion mass is lowered toward its physical value. The calculated one-nucleon spectral distributions are qualitatively close to those of real nuclei even for the pseudo-scalar meson mass considered here.Comment: 7 pages, 4 figures, RIKEN-QHP-286, RIKEN-iTHEMS-Report-1

Variation of the broad X-ray iron line in MCG-6-30-15 during a flare

We report results on the broad iron emission line of the Seyfert galaxy MCG-6-30-15, obtained from the second long ASCA observation in 1997. The time-averaged profile of the broad line is very similar to that seen with ASCA in 1994, so confirming the detailed model fit then obtained. A bright flare is seen in the light curve, during which the continuum was soft. At that time the emission line peaks around 5 keV and most of its emission is shifted below 6 keV with no component detected at 6.4 keV (EW<60 eV). This can be interpreted as the result of an extraordinarily large gravitational redshift due to a dominant flare occurring very close to the black hole at a radius of <5m.Comment: 5 pages, accepted or publication in MNRAS Letter

Charmless B→PV,VVB \to PV, VV decays and new physics effects in the mSUGRA model

By employing the QCD factorization approach, we calculate the new physics contributions to the branching radios of the two-body charmless $B \to PV$ and $B \to VV$ decays in the framework of the minimal supergravity (mSUGRA) model. we choose three typical sets of the mSUGRA input parameters in which the Wilson coefficient $C_{7\gamma}(m_b)$ can be either SM-like (the case A and C) or has a flipped-sign (the case B). We found numerically that (a) the SUSY contributions are always very small for both case A and C; (b) for those tree-dominated decays, the SUSY contributions in case B are also very small; (c) for those QCD penguin-dominated decay modes, the SUSY contributions in case B can be significant, and can provide an enhancement about $30$ to the branching ratios of $B \to K^*(\pi,\phi,\rho)$ and $K \phi$ decays, but a reduction about $30$ to $B\to K(\rho, \omega)$ decays; and (d) the large SUSY contributions in the case B may be masked by the large theoretical errors dominated by the uncertainty from our ignorance of calculating the annihilation contributions in the QCD factorization approach.Comment: 34 pages, 8 PS figures, this is the correct version