Entanglement Entropy and Mutual Information in Bose-Einstein Condensates

In this paper we study the entanglement properties of free {\em non-relativistic} Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system, and find it diverges logarithmically with the particle number in the subsystem. For finite temperatures, we study the mutual information between the two blocks. We first analytically study an infinite-range hopping model, then numerically study a set of long-range hopping models in one-deimension that exhibit Bose-Einstein condensation. In both cases we find that a Bose-Einstein condensate, if present, makes a divergent contribution to the mutual information which is proportional to the logarithm of the number of particles in the condensate in the subsystem. The prefactor of the logarithmic divergent term is model dependent.Comment: 12 pages, 6 figure

What kinds of coordinate can keep the Hawking temperature invariant for the static spherically symmetric black hole?

By studying the Hawking radiation of the most general static spherically symmetric black hole arising from scalar and Dirac particles tunnelling, we find the Hawking temperature is invariant in the general coordinate representation (\ref{arbitrary1}), which satisfies two conditions: a) its radial coordinate transformation is regular at the event horizon; and b) there is a time-like Killing vector.Comment: 10 page

Evolution of the Fermi surface with carrier concentration in Bi_2Sr_2CaCu_2O_{8+\delta}

We show, by use of angle-resolved photoemission spectroscopy, that underdoped Bi_2Sr_2CaCu_2O_{8+\delta} appears to have a large Fermi surface centered at (\pi,\pi), even for samples with a T_c as low as 15 K. No clear evidence of a Fermi surface pocket around (\pi/2,\pi/2) has been found. These conclusions are based on a determination of the minimum gap locus in the pseudogap regime T_c < T < T^*, which is found to coincide with the locus of gapless excitations in momentum space (Fermi surface) determined above T^*. These results suggest that the pseudogap is more likely of precursor pairing rather than magnetic origin.Comment: 4 pages, revtex, 4 postscript color figure

Extraction of the Electron Self-Energy from Angle Resolved Photoemission Data: Application to Bi2212

The self-energy $\Sigma({\bf k},\omega)$, the fundamental function which describes the effects of many-body interactions on an electron in a solid, is usually difficult to obtain directly from experimental data. In this paper, we show that by making certain reasonable assumptions, the self-energy can be directly determined from angle resolved photoemission data. We demonstrate this method on data for the high temperature superconductor $Bi_2Sr_2CaCu_2O_{8+x}$ (Bi2212) in the normal, superconducting, and pseudogap phases.Comment: expanded version (6 pages), to be published, Phys Rev B (1 Sept 99

Possible Molecular States of Ds∗Dˉs∗D^{*}_s\bar{D}^{*}_s System and Y(4140)

The interpretation of Y(4140) as a $D^{*}_s\bar{D}^{*}_s$ molecule is studied dynamically in the one boson exchange approach, where $\sigma$, $\eta$ and $\phi$ exchange are included. Ten allowed $D^{*}_s\bar{D}^{*}_s$ states with low spin parity are considered, we find that the $J^{PC}=0^{++}$, $1^{+-}$, $0^{-+}$, $2^{++}$ and $1^{--}$ $D^{*}_s\bar{D}^{*}_s$ configurations are most tightly bound. We suggest the most favorable quantum numbers are $J^{PC}=0^{++}$ for Y(4140) as a $D^{*}_s\bar{D}^{*}_s$ molecule, however, $J^{PC}=0^{-+}$ and $2^{++}$ can not be excluded. We propose to search for the $1^{+-}$ and $1^{--}$ partners in the $J/\psi\eta$ and $J/\psi\eta'$ final states, which is an important test of the molecular hypothesis of Y(4140) and the reasonability of our model. The $0^{++}$ $B^{*}_s\bar{B}^{*}_s$ molecule is deeply bound, experimental search in the $\Upsilon(1S)\phi$ channel at Tevatron and LHC is suggested.Comment: 13 pages,2 figure

Probing Nonlocal Spatial Correlations in Quantum Gases with Ultra-long-range Rydberg Molecules

We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the order of the thermal de Broglie wavelength for temperatures around 1 $\mu$K. We observe bunching for a single-component Bose gas of $^{84}$Sr and anti-bunching due to Pauli exclusion at short distances for a polarized Fermi gas of $^{87}$Sr, revealing the effects of quantum statistics.Comment: 6 pages, 5 figure

Extended phase diagram of the Lorenz model

The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-B\'enard flow is studied. Its bifurcation structure has commonly been investigated as a function of r, the normalized Rayleigh number, at fixed Prandtl number \sigma. The present work extends the analysis to the entire (r,\sigma) parameter plane. An onion like periodic pattern is found which is due to the alternating stability of symmetric and non-symmetric periodic orbits. This periodic pattern is explained by considering non-trivial limits of large r and \sigma. In addition to the limit which was previously analyzed by Sparrow, we identify two more distinct asymptotic regimes in which either \sigma/r or \sigma^2/r is constant. In both limits the dynamics is approximately described by Airy functions whence the periodicity in parameter space can be calculated analytically. Furthermore, some observations about sequences of bifurcations and coexistence of attractors, periodic as well as chaotic, are reported.Comment: 36 pages, 20 figure

The geometric sense of R. Sasaki connection

For the Riemannian manifold $M^{n}$ two special connections on the sum of the tangent bundle $TM^{n}$ and the trivial one-dimensional bundle are constructed. These connections are flat if and only if the space $M^{n}$ has a constant sectional curvature $\pm 1$. The geometric explanation of this property is given. This construction gives a coordinate free many-dimensional generalization of the connection from the paper: R. Sasaki 1979 Soliton equations and pseudospherical surfaces, Nuclear Phys., {\bf 154 B}, pp. 343-357. It is shown that these connections are in close relation with the imbedding of $M^{n}$ into Euclidean or pseudoeuclidean $(n+1)$-dimension spaces.Comment: 7 pages, the key reference to the paper of Min-Oo is included in the second versio