Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory

We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem and the problem of time in reparametrization invariant theories as for example in canonical quantum gravity. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem.Comment: 23 pages, Few changes and added references in v

Consistent histories, the quantum Zeno effect, and time of arrival

We present a decomposition of the general quantum mechanical evolution operator, that corresponds to the path decomposition expansion, and interpret its constituents in terms of the quantum Zeno effect (QZE). This decomposition is applied to a finite dimensional example and to the case of a free particle in the real line, where the possibility of boundary conditions more general than those hitherto considered in the literature is shown. We reinterpret the assignment of consistent probabilities to different regions of spacetime in terms of the QZE. The comparison of the approach of consistent histories to the problem of time of arrival with the solution provided by the probability distribution of Kijowski shows the strength of the latter point of view

Relativistic quantum measurement

Does the measurement of a quantum system necessarily break Lorentz invariance? We present a simple model of a detector that measures the spacetime localization of a relativistic particle in a Lorentz invariant manner. The detector does not select a preferred Lorentz frame as a Newton-Wigner measurement would do. The result indicates that there exists a Lorentz invariant notion of quantum measurement and sheds light on the issue of the localization of a relativistic particle. The framework considered is that of single-particle mechanics as opposed to field theory. The result may be taken as support for the interpretation postulate of the spacetime-states formulation of single-particle quantum theory.Comment: 9 pages, no figures: Revision: references adde

Electronic structures of B-2p and C-2p of boron-doped diamond film by soft X-ray absorption and emission spectroscopy

X-ray absorption (XAS) and emission (XES) spectroscopy near B-K and C-K edges have been performed on metallic (~1at%B, B-diamond) and semiconducting (~0.1at%B and N, BN-diamond) doped-diamond films. Both B-K XAS and XES spectra shows metallic partial density of state (PDOS) with the Fermi energy of 185.3 eV, and there is no apparent boron-concentration dependence in contrast to the different electric property. In C-K XAS spectrum of B-diamond, the impurity state ascribed to boron is clearly observed near the Fermi level. The Fermi energy is found to be almost same with the top of the valence band of non-doped diamond, E_V, 283.9 eV. C-K XAS of BN-diamond shows both the B-induced shallow level and N-induced deep-and-broad levels as the in-gap states, in which the shallow level is in good agreement with the activation energy (E_a=0.37 eV) estimated from the temperature dependence of the conductivity, namely the change in C-2p PDOS of impurity-induced metallization is directly observed. The electric property of this diamond is mainly ascribed to the electronic structure of C-2p near the Fermi level. The observed XES spectra are compared with the DVX-alpha cluster calculation. The DVX-alpha result supports the strong hybridization between B-2p and C-2p observed in XAS and XES spectra, and suggests that the small amount of borons (<1at%) in diamond occupy the substitutional site rather than interstitial site.Comment: submitted to Phys. Rev. B, 5 pages and 5 figure

Heavy flavor diffusion in weakly coupled N=4 Super Yang-Mills theory

We use perturbation theory to compute the diffusion coefficient of a heavy quark or scalar moving in N=4 SU(N_c) Super Yang-Mills plasma to leading order in the coupling and the ratio T/M<<1. The result is compared both to recent strong coupling calculations in the same theory and to the corresponding weak coupling result in QCD. Finally, we present a compact and simple formulation of the Lagrangian of our theory, N=4 SYM coupled to a massive fundamental N=2 hypermultiplet, which is well-suited for weak coupling expansions.Comment: 22 pages, 4 figures; v3: error corrected in calculations, figures and discussion modified accordingl

Quantum Arrival Time Formula from Decoherent Histories

In the arrival time problem in quantum mechanics, a standard formula that frequently emerges as the probability for crossing the origin during a given time interval is the current integrated over that time interval. This is semiclassically correct but can be negative due to backflow. Here, we show that this formula naturally arises in a decoherent histories analysis of the arrival time problem. For a variety of initial states, we show that histories crossing during different time intervals are approximately decoherent. Probabilities may therefore be assigned and coincide with the standard formula (in a semiclassical approximation), which is therefore positive for these states. However, for initial states for which there is backflow, we show that there cannot be decoherence of histories, so probabilities may not be assigned.Comment: 11 page

Soft x-ray spectroscopy experiments on the near K-edge of B in MB2 (M=Mg, Al, Ta, and Nb)

Soft X-ray absorption and emission measurements are performed for the K- edge of B in MB$_2$ (M=Mg, Al, Ta and Nb). Unique feature of MgB$_2$ with a high density of B 2$p_{xy}(\sigma)$-state below and above the Fermi edge, which extends to 1 eV above the edge, is confirmed. In contrast, the B 2$p$ density of states in AlB$_2$ and TaB$_2$, both of occupied and unoccupied states, decreased linearly towards the Fermi energy and showed a dip at the Fermi energy. Furthermore, there is a broadening of the peaks with $p\sigma$-character in XES and XAS of AlB$_2$, which is due to the increase of three dimensionality in the $p\sigma$-band in AlB$_2$. The DOS of NbB$_2$ has a dip just below the Fermi energy. The present results indicate that the large DOS of B-2$p\sigma$ states near the Fermi energy are crucial for the superconductivity of MgB$_2$.Comment: 3 pages text and 4 pages figures. accepted for publication to Phys. Rev.

Semiclassical approach to the thermodynamics of spin chains

Using the PQSCHA semiclassical method, we evaluate thermodynamic quantities of one-dimensional Heisenberg ferro- and antiferromagnets. Since the PQSCHA reduces their evaluation to classical-like calculations, we take advantage of Fisher's exact solution to get all results in an almost fully analytical way. Explicitly considered here are the specific heat, the correlations length and susceptibility. Good agreement with Monte Carlo simulations is found for S>1 antiferromagnets, showing that the relevance of the topological terms and of the Haldane gap is significant only for the lowest spin values and temperatures.Comment: 4 pages, 7 figure

Nuclear Alpha-Particle Condensates

The $\alpha$-particle condensate in nuclei is a novel state described by a product state of $\alpha$'s, all with their c.o.m. in the lowest 0S orbit. We demonstrate that a typical $\alpha$-particle condensate is the Hoyle state ($E_{x}=7.65$ MeV, $0^+_2$ state in $^{12}$C), which plays a crucial role for the synthesis of $^{12}$C in the universe. The influence of antisymmentrization in the Hoyle state on the bosonic character of the $\alpha$ particle is discussed in detail. It is shown to be weak. The bosonic aspects in the Hoyle state, therefore, are predominant. It is conjectured that $\alpha$-particle condensate states also exist in heavier $n\alpha$ nuclei, like $^{16}$O, $^{20}$Ne, etc. For instance the $0^+_6$ state of $^{16}$O at $E_{x}=15.1$ MeV is identified from a theoretical analysis as being a strong candidate of a $4\alpha$ condensate. The calculated small width (34 keV) of $0^+_6$, consistent with data, lends credit to the existence of heavier Hoyle-analogue states. In non-self-conjugated nuclei such as $^{11}$B and $^{13}$C, we discuss candidates for the product states of clusters, composed of $\alpha$'s, triton's, and neutrons etc. The relationship of $\alpha$-particle condensation in finite nuclei to quartetting in symmetric nuclear matter is investigated with the help of an in-medium modified four-nucleon equation. A nonlinear order parameter equation for quartet condensation is derived and solved for $\alpha$ particle condensation in infinite nuclear matter. The strong qualitative difference with the pairing case is pointed out.Comment: 71 pages, 41 figures, review article, to be published in "Cluster in Nuclei (Lecture Notes in Physics) - Vol.2 -", ed. by C. Beck, (Springer-Verlag, Berlin, 2011

Cu Nuclear Quadrupole Resonance Study of Site-Disorder and Chemical Pressure Effects on Y(Ba1-xSrx)2Cu4O8

We report a zero-field Cu nuclear quadrupole resonance (NQR) study on the effects of nonmagnetic Sr substitution for high-Tc superconductors, Y(Ba1-xSrx)2Cu4O8 (Tc=82-80 K for x=0-0.4), using a spin-echo technique. The site-disordering and chemical pressure effects associated with doping Sr were observed in the broadened, shifted Cu NQR spectra. Nevertheless, the site disorder did not significantly affect the homogeneity of Cu electron spin dynamics, in contrast to the in-plane impurity. The peak shift of Cu NQR spectrum due to Sr was different between the chain- and the plane-Cu sites, more remarkably than those under a hydrostatic physical pressure, suggesting anisotropic or nonuniform local structural strains. The small decrease of Tc due to Sr can be traced back to either a cancellation effect on Tc between the disorder and the pressure, or an anisotropic or nonuniform chemical pressure effect on Tc.Comment: 4 pages, 5 figure