Holon-pair boson theory based on the U(1) and SU(2) slave-boson approaches to the t-J Hamiltonian

To supplement our recent brief report on the theory of holon-pair boson approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B {\bf 64}, 052501(2001)], in this paper we present a full exposure to the theory, detailed physical implications and predicted various physical properties of high $T_c$ cuprates. We discuss the significance of coupling (interplay) between the spin and charge degrees of freedom in the Heisenberg interaction term of the t-J Hamiltonian. We discuss its importance in causing the arch-shaped superconducting transition temperature $T_c$ and the pseudogap (spin gap) temperature $T^*$ tangential to $T_c$ in the overdoped region in the observed phase diagram of high $T_c$ cuprates. A universal parabolic scaling behavior of $T^*/T_c$ (or $T_c/T^*$) with hole doping concentration is predicted in agreement with observations, indicating that there exists correlation between the pseudogap (spin gap) phase and the superconducting phase through antiferromagnetic fluctuations. Our proposed holon-pair boson theory is shown to be self-consistent in that it not only yields the arch (dome) shape structure of $T_c$ but also reproduces various other physical properties such as superfluid weight, bose condensation energy, spectral function, optical conductivity and spin susceptibility, including their temperature and doping dependence

Origin of the Quasiparticle Peaks of Spectral Functions in High TcT_c Cuprates

Based on the SU(2) slave-boson approach to the t-J Hamiltonian, we examine the cause of the sharp peaks('quasiparticle' peaks) in the observed spectral functions in high $T_c$ cuprates. The computed results reveal that the spectral weight of the sharp peaks increases with hole doping rate in agreement with observation. It is shown that the observed sharp peaks are attributed to the enhancement of spinon pairing(spin singlet pair formation) by the presence of holon pair bosons in the superconducting state.Comment: 4 pages, 6 figure

Snapshot projection optical tomography

We present a plenoptic microscopy configuration for 3D snapshot imaging, which is dual telecentric and can directly record true projection images corresponding with different viewing angles. It also allows blocking high-angle stray rays without sacrificing the light collection efficiency. This configuration named as snapshot projection optical tomography (SPOT) arranges an objective lens and a microlens array (MLA) in a 4-f telecentric configuration and places an aperture stop at the back focal plane of a relay lens. We develop a forward imaging model for SPOT, which can also be applied to existing light field microscopy techniques using an MLA as tube lens. Using the developed system, we demonstrate snapshot 3D imaging of various fluorescent beads and a biological cell, which confirms the capability of SPOT for imaging specimens with an extended fluorophore distribution as well as isolated fluorochromes. The transverse and vertical resolutions are measured to be 0.8 $\mu$m and 1.6 $\mu$m, respectively

Holon Pairing Instability based on the Bethe-Salpeter Equation obtained from the t-J Hamiltonians of both U(1) and SU(2) Slave-boson Symmetries

We investigate a possibility of holon pairing for bose condensation based on the Bethe-Salpeter equation obtained from the use of the t-J Hamiltonians of both t he U(1) and SU(2) slave-boson symmetries. It is shown that the vertex function contributed from ladder diagram series involving holon-holon scattering channel in the Bethe-Salpeter equation leads to a singular behavior at a critical temperature at each hole doping concentration, showing the instability of the normal state against holon pairing. We find that the holon pairing instability occurs only in a limited range of hole doping, by showing an "arch" shaped bose condensation line in agreement with observation for high $T_c$ cuprates. It is revealed that this is in agreement with a functional integral approach of the slave-boson theories.Comment: 4 pages, 5 figure

Universal scaling behavior of pseudogap with doping in high Tc cuprates; temperature and doping dependence of spectral intensity

Based on our improved SU(2) slave-boson approach (Phys. Rev. B 64, 052501(2001)) to the t-J Hamiltonian, we report a scaling behavior of pseudogap with doping and the temperature and doping dependence of spectral functions. In addition we discuss the cause of hump and quasi-particle peak in the observed spectral functions of high Tc cuprates. It is demonstrated that the sharpening of the observed quasi-particle peak below Tc is attributed to the bose condensation of holon pair. From the computed ratios of pseudogap $\Delta_0$ to both the superconducting temperature Tc and the pseudogap temperature $T^*$ as a function of hole doping concentration x, we find that there exists a universal scaling of these ratios with doping, that is, the hyperbolic scaling behavior of the former, $\frac{2 \Delta_0}{k_B T_c} \sim x^{-\alpha}$ with $\alpha \sim 2$ and near doping independence of the latter, $\frac{2 \Delta_0}{k_B T^*} \approx 4 \sim 6$ are found.Comment: 5 pages, 5 figure

Liouville-type theorems and applications to geometry on complete Riemannian manifolds

On a complete Riemannian manifold M with Ricci curvature satisfying $$\textrm{Ric}(\nabla r,\nabla r) \geq -Ar^2(\log r)^2(\log(\log r))^2...(\log^{k}r)^2$$ for $r\gg 1$, where A>0 is a constant, and r is the distance from an arbitrarily fixed point in M. we prove some Liouville-type theorems for a C^2 function $f:M\rightarrow \Bbb R$ satisfying $\Delta f\geq F(f)$ for a function $F:\Bbb R\rightarrow \Bbb R$

Finite group actions and G-monopole classes on smooth 4-manifolds

On a smooth closed oriented $4$-manifold $M$ with a smooth action by a compact Lie group $G$, we define a $G$-monopole class as an element of $H^2(M;\Bbb Z)$ which is the first Chern class of a $G$-equivariant Spin$^c$ structure which has a solution of the Seiberg-Witten equations for any $G$-invariant Riemannian metric on $M$. We find $\Bbb Z_k$-monopole classes on some $\Bbb Z_k$-manifolds such as the connected sum of $k$ copies of a 4-manifold with nontrivial mod 2 Seiberg-Witten invariant or Bauer-Furuta invariant, where the $\Bbb Z_k$-action is a cyclic permutation of $k$ summands. As an application, we produce infinitely many exotic non-free actions of $\Bbb Z_k\oplus H$ on some connected sums of finite number of $S^2\times S^2$, $\Bbb CP_2$, $\overline{\Bbb CP}_2$, and $K3$ surfaces, where $k\geq 2$, and $H$ is any nontrivial finite group acting freely on $S^3$

Doping dependence of bose condensation energy and correlations with spectral peak intensity and superfluid weight in high Tc cuprates

Based on our recent holon-pair boson theory of the t-J Hamiltonian (Phys. Rev. B 64, 052501 (2001)) we report the doping dependence of the bose condensation energy, superfluid weight and spectral peak intensity. We find a universality of doping dependence in these physical quantities, by equally showing an arch shape in the variations of their magnitudes with the hole doping concentration. We find that all of these physical quantities scale well with the positive charge carrier (hole) density x, but not with the electron density 1-x for the entire range of hole doping. It is shown that the doping dependence of the condensation energy U at T = 0 K is given by the relation, $U(0) \approx \alpha x^2 |\Delta_0|^2$ with $\Delta_0$, the pairing gap at 0 K and $\alpha$, a constant.Comment: 5 pages, 2 figure

Probing the Gauge Content of Heavy Resonances with Soft Radiation

The use of energy flow is investigated as a diagnostic tool for determining the color SU(3) representation of new resonances. It is found that the pattern of soft gluon radiation into a rapidity gap depends on color flow in the hard scattering, and reflects the gauge content of new physics. The massive soft anomalous dimension matrix for rapidity gap events is introduced for describing soft gluon emission analytically in heavy quark pair production. A gap fraction is used for quantifying the amount of soft radiation into the gap region. In general, the results illustrate that radiation is greater for a singlet resonance than for an octet. Especially, it is found that the quantitative difference is quite distinguishable for spin-1 resonances, depending on the gauge content in the new sector.Comment: 40 pages, 14 figure

Connected sums with HP^n or CaP^2 and the Yamabe invariant

Let $M$ be a smooth closed $4k$-manifold whose Yamabe invariant $Y(M)$ is nonpositive. We show that $$Y(M\sharp l \Bbb HP^k\sharp m \bar{\Bbb HP^k})=Y(M),$$ where $l,m$ are nonnegative integers, and $\Bbb HP^k$ is the quaternionic projective space. When $k=4$, we also have $$Y(M\sharp l CaP^2\sharp m \bar{CaP^2})=Y(M),$$ where $CaP^2$ is the Cayley plane