Improvement and extension of a radar forest backscattering model

Radar modeling of mangal forest stands, in the Sundarbans area of Southern Bangladesh, was developed. The modeling employs radar system parameters such as wavelength, polarization, and incidence angle, with forest data on tree height, spacing, biomass, species combinations, and water content (including slightly conductive water) both in leaves and trunks of the mangal. For Sundri and Gewa tropical mangal forests, five model components are proposed, which are required to explain the contributions of various forest species combinations in the attenuation and scattering of mangal vegetated nonflooded or flooded surfaces. Statistical data of simulated images (HH components only) were compared with those of SIR-B images both to refine the modeling procedures and to appropriately characterize the model output. The possibility of delineation of flooded or non-flooded boundaries is discussed

S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Lower dimensional volumes and the Kastler-Kalau-Walze type theorem for Manifolds with Boundary

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume ${\rm Vol}^{(2,2)}$ for 5-dimensional and 6-dimensional spin manifolds with boundary and we also get the Kastler-Kalau-Walze type theorem in this case

High Fidelity State Transfer Over an Unmodulated Linear XY Spin Chain

We provide a class of initial encodings that can be sent with a high fidelity over an unmodulated, linear, XY spin chain. As an example, an average fidelity of ninety-six percent can be obtained using an eleven-spin encoding to transmit a state over a chain containing ten-thousand spins. An analysis of the magnetic field dependence is given, and conditions for field optimization are provided.Comment: Replaced with published version. 8 pages, 5 figure

Quantum criticality in a generalized Dicke model

We employ a generalized Dicke model to study theoretically the quantum criticality of an extended two-level atomic ensemble interacting with a single-mode quantized light field. Effective Hamiltonians are derived and diagonalized to investigate numerically their eigenfrequencies for different quantum phases in the system. Based on the analysis of the eigenfrequencies, an intriguing quantum-phase transition from a normal phase to a superradiant phase is revealed clearly, which is quite different from that observed with a standard Dicke model.Comment: 6 pages, 3 figure

Correlated metallic state in honeycomb lattice: Orthogonal Dirac semimetal

A novel gapped metallic state coined orthogonal Dirac semimetal is proposed in the honeycomb lattice in terms of $Z_{2}$ slave-spin representation of Hubbard model. This state corresponds to the disordered phase of slave-spin and has the same thermaldynamical and transport properties as usual Dirac semimetal but its singe-particle excitation is gapped and has nontrivial topological order due to the $Z_{2}$ gauge structure. The quantum phase transition from this orthogonal Dirac semimetal to usual Dirac semimetal is described by a mean-field decoupling with complementary fluctuation analysis and its criticality falls into the universality class of 2+1D Ising model while a large anomalous dimension for the physical electron is found at quantum critical point (QCP), which could be considered as a fingerprint of our fractionalized theory when compared to other non-fractionalized approaches. As byproducts, a path integral formalism for the $Z_{2}$ slave-spin representation of Hubbard model is constructed and possible relations to other approaches and the sublattice pairing states, which has been argued to be a promising candidate for gapped spin liquid state found in the numerical simulation, are briefly discussed. Additionally, when spin-orbit coupling is considered, the instability of orthogonal Dirac semimetal to the fractionalized quantum spin Hall insulator (fractionalized topological insulator) is also expected. We hope the present work may be helpful for future studies in $Z_{2}$ slave-spin theory and related non-Fermi liquid phases in honeycomb lattice.Comment: 12 pages,no figures, more discussions added. arXiv admin note: text overlap with arXiv:1203.063

Alternative Kondo breakdown mechanism: Orbital-selective orthogonal metal transition

In a recent paper of Nandkishore and Senthil [arxiv:1201.5998 (2012)], a concept of orthogonal metal has been introduced to reinterpret the disordered state of slave-spin representation in the Hubbard model as an exotic gapped metallic state. We extend this concept to study the corresponding quantum phase transition in the extended Anderson lattice model. It is found that the disordered state of slave spins in this model is an orbital-selective orthogonal metal, a generalization of the concept of the orthogonal metal in the Hubbard model. Near the quantum critical point the essential behaviors are dominated by a z = 3 critical mode, which is in contrast to the naive expectation in the Hubbard model. The result provides alternative Kondo breakdown mechanism for heavy fermion compounds underlying the physics of the orbital-selective orthogonal metal in the disordered state, which is different from the conventional Kondo breakdown mechanism with the fractionalized Fermi liquid picture. This work is expected to be useful in understanding the quantum criticality happening in some heavy fermion materials and other related strongly correlated systems.Comment: 11 pages, no figures, significantly revised and reference added. Comparison with conventional Kondo breakdown mechanism is discussed in a new sectio