Conjectures for the microscopic theory of high temperature superconductivity

Based on experimental results and our previous theoretical work, a microscopic theory of high temperature superconductivity is conjectured. In this conjecture, superconducting and antiferromagnetic long-range orders are driven by interlayer coupling. Strictly in two dimensions, the microscopic Hubbard model has an (resonating valence bond) insulator-to-metal transition at $x=x_{c}$ near optimal doping for zero temperature, leading to a quantum critical point, and one of the crossover lines is given by the pseudogap temperature $T^{*}$. We argue that various singular and non-Fermi liquid properties observed near optimal doping are due to the presence of this quantum critical point. In our conjecture, the crossover line $T^{*}$ also practically divides the superconducting region into two, depending on the doping level with respect to $x_{c}$. For $x \leq x_{c}$ the superconducting state has significant antiferromagnetic correlations, while for $x > x_{c}$ it has virtually no antiferromagnetic correlations, thus justifying the conventional BCS theory based on the noninteracting electrons. Inelastic neutron scattering resonance and systematically reduced superfluid density in the superconducting state below $x_{c}$ have their natural explanations in the present scenario. The present approach supports interlayer pair tunneling model where the superconducting condensation energy comes from the lowering of the c-axis kinetic energy in the superconducting state. Comparison of the present scenario with some of the leading theories based on the Hubbard and $t-J$ models is given. The generic features of both hole-doped and electron-doped cuprates as well as heavy-fermion superconductors may be understood in the {\em unified} framework within the present picture.Comment: 12 pages, 2 figure

New interpretation of slave boson mean-field theory of the t−Jt-J model: short-range antiferromagnetic and d-wave pairing correlations

The $t-J$ Hamiltonian is studied in a mean-field approximation by taking into account antiferromagnetic and d-wave pairing correlations. Considering the presence of antiferromagnetic fluctuations, the weaknesses of a mean-field approximation and the limitation of the $t-J$ model near half-filling, we give a new interpretation to the slave boson mean-field theory of the $t-J$ model. We argue that due to phase coherence-breaking antiferromagnetic fluctuations and quantum fluctuations, superconducting long-range order does not appear strictly in two dimensions. $T_{c}$ resulting from interlayer pairing hopping can lead to a universal relation, when $T_{c}$ is scaled by $T^{max}_{c}$. Systematic reduction of superfluid density and increase of $(\Delta_{d})_{max}/K_{B}T_{c}$ ratio below and near optimal doping have their natural explanation in our picture. A crossover temperature $T^{0}$ found in some of magnetic experiments such as NMR is also easily understood in the present framework.Comment: 8 pages, 2 figure

A Kirchberg type tensor theorem for operator systems

We construct operator systems $\mathfrak C_I$ that are universal in the sense that all operator systems can be realized as their quotients. They satisfy the operator system lifting property. Without relying on the theorem by Kirchberg, we prove the Kirchberg type tensor theorem $$\mathfrak C_I \otimes_{\min} B(H) = \mathfrak C_I \otimes_{\max} B(H).$$ Combining this with a result of Kavruk, we give a new operator system theoretic proof of Kirchberg's theorem and show that Kirchberg's conjecture is equivalent to its operator system analogue $$\mathfrak C_I \otimes_{\min} \mathfrak C_I =\mathfrak C_I \otimes_{\rm c} \mathfrak C_I.$$ It is natural to ask whether the universal operator systems $\mathfrak C_I$ are projective objects in the category of operator systems. We show that an operator system from which all unital completely positive maps into operator system quotients can be lifted is necessarily one-dimensional. Moreover, a finite dimensional operator system satisfying a perturbed lifting property can be represented as the direct sum of matrix algebras. We give an operator system theoretic approach to the Effros-Haagerup lifting theorem.Comment: 27 pages, to appear in Pacific Journal of Mathematic

Master\u27s Recital

List of performers and performances

Noncommutative LpL_p-space and operator system

We show that noncommutative $L_p$-spaces satisfy the axioms of the (nonunital) operator system with a dominating constant $2^{1 \over p}$. Therefore, noncommutative $L_p$-spaces can be embedded into $B(H)$ $2^{1 \over p}$-completely isomorphically and complete order isomorphically.Comment: 10 pages, final version, to appear in PAM

Throat Finding Algorithms based on Throat Types

The three-dimensional geometry and connectivity of pore space determines the flow of single-phase incompressible flow. Herein I report on new throat finding algorithms that contribute to finding the exact flow-relevant geometrical properties of the void space, including high porosity samples of X2B images, three-dimensional synchrotron X-ray computed microtomographic images, and amounting to over 20% porosity. These new algorithms use the modified medial axis that comes from the 3DMA-Rock software package. To find accurate throats, we classify three major throat types: mostly planar and simply connected type, non-planar and simply connected type, and non-planar and non-simply connected type. For each type, we make at least one algorithm to find the throats. Here I introduce an example that has a non-planar and simply connected throat, and my solution indicated by one of my algorithms. My five algorithms each calculate the throat for each path. It selects one of them, which has the smallest inner area. New algorithms find accurate throats at least 98% among 12 high porosity samples (over 20%). Also, I introduce a new length calculation in the digitized image. The new calculation uses three mathematical concepts: i) differentiability, ii) implicit function theorem, iii) line integral. The result can convert the discrete boundary of the XMCT image to the real boundary. When the real boundary has an arc shape, the new calculation has less than 1% relative error.Comment: 23 pages, 15 figure

Effect of Nonlocal Spin-Transfer Torque on Current-Induced Magnetization Dynamics

Using the self-consistent model, we present nonlocal spin-transfer effects caused by the feedback between inhomogeneous magnetization and spin-transfer torque on the current-induced magnetization dynamics in nanomagnets. The nonlocal effects can substantially improve the coherence time of precession in nanomagnets and thus reduce the linewidth of power spectrum. This narrow linewidth results from the nonlinear damping of spin-waves due to the nonlocal spin torque which is inherent and thus should be considered in future experiments.Comment: 10 pages, 2 figure

Infra-solvmanifolds of \Sol_1^4-geometry

The purpose of this paper is to classify all compact manifolds modeled on the 4-dimensional solvable Lie group $Sol_1^4$. The maximal compact subgroup of $Isom(Sol_1^4)$ is $D_4=\mathbb Z_4\rtimes\mathbb Z_2$. We shall exhibit an infra-solvmanifold with $Sol_1^4$-geometry whose holonomy is $D_4$. This implies that all possible holonomy groups do occur; $\{1\}$, $\mathbb Z_2$ (5 families), $\mathbb Z_4$, $\mathbb Z_2\times\mathbb Z_2$ (5 families),and $\mathbb Z_4\rtimes\mathbb Z_2$ (2 families). This includes the classification of 3-dimensional infra-$Sol$ manifolds

Multitype branching process with nonhomogeneous Poisson and generalized Polya immigration

In a multitype branching process, it is assumed that immigrants arrive according to a nonhomogeneous Poisson or a generalized Polya process (both processes are formulated as a nonhomogeneous birth process with an appropriate choice of transition intensities). We show that the renormalized numbers of objects of the various types alive at time $t$ for supercritical, critical, and subcritical cases jointly converge in distribution under those two different arrival processes. Furthermore, some transient moment analysis when there are only two types of particles is provided. AMS 2000 subject classifications: Primary 60J80, 60J85; secondary 60K10, 60K25, 90B15

Amplify-and-Forward Full-Duplex Relay with Power Splitting-Based SWIPT

This paper proposes a virtual harvest-transmit model and a harvest-transmit-store model for amplify-and-forward full-duplex relay (FDR) networks with power splitting-based simultaneous wireless information and power transfer. The relay node employs a battery group consisting of two rechargeable batteries. By switching periodically between two batteries for charging and discharging in two consecutive time slots of each transmission block, all the harvested energy in each block has been applied for full duplex transmission in the virtual harvest-transmit model. By employing energy scheduling, the relay node switches among the harvesting, relaying, harvesting-relaying, and idle behaviors at a block level, so that a part of the harvested energy in a block can be scheduled for future usage in the harvest-transmit-store model. A greedy switching policy is designed to implement the harvest-transmit-store model, where the FDR node transmits when its residual energy ensures decoding at the destination. Numerical results verify the outage performance of the proposed schemes.Comment: 4 pages, submit to a conferenc