Einstein's Equations in the Presence of Signature Change

We discuss Einstein's field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no surface layer, precisely when the extrinsic curvature is continuous, in agreement with the standard result for constant signature.Comment: REVTeX, 8 pages; to appear in JM

Time-symmetric boundary conditions and quantum foundations

Despite the widely-held premise that initial boundary conditions (BCs) corresponding to measurements/interactions can fully specify a physical subsystem, a literal reading of Hamilton's principle would imply that both initial and final BCs are required (or more generally, a BC on a closed hypersurface in spacetime). Such a time-symmetric perspective of BCs, as applied to classical fields, leads to interesting parallels with quantum theory. This paper will map out some of the consequences of this counter-intuitive premise, as applied to covariant classical fields. The most notable result is the contextuality of fields constrained in this manner, naturally bypassing the usual arguments against so-called "realistic" interpretations of quantum phenomena.Comment: 16 pages. With 0906.5409, companion paper to pirsa.org/09060031. v2: Minor edit, updates to reference

Doped high-Tc cuprate superconductors elucidated in the light of zeros and poles of electronic Green's function

We study electronic structure of hole- and electron-doped Mott insulators in the two-dimensional Hubbard model to reach a unified picture for the normal state of cuprate high-Tc superconductors. By using a cluster extension of the dynamical mean-field theory, we demonstrate that structure of coexisting zeros and poles of the single-particle Green's function holds the key to understand Mott physics in the underdoped region. We show evidence for the emergence of non-Fermi-liquid phase caused by the topological quantum phase transition of Fermi surface by analyzing low-energy charge dynamics. The spectra calculated in a wide range of energy and momentum reproduce various anomalous properties observed in experiments for the high-Tc cuprates. Our results reveal that the pseudogap in hole-doped cuprates has a d-wave-like structure only below the Fermi level, while it retains non-d-wave structure with a fully opened gap above the Fermi energy even in the nodal direction due to a zero surface extending over the entire Brillouin zone. In addition to the non-d-wave pseudogap, the present comprehensive identifications of the spectral asymmetry as to the Fermi energy, the Fermi arc, and the back-bending behavior of the dispersion, waterfall, and low-energy kink, in agreement with the experimental anomalies of the cuprates, do not support that these originate from (the precursors of) symmetry breakings such as the preformed pairing and the d-density wave fluctuations, but support that they are direct consequences of the proximity to the Mott insulator. Several possible experiments are further proposed to prove or disprove our zero mechanism.Comment: 17 pages, 15 figure

The Weyl-Lanczos Equations and the Lanczos Wave Equation in 4 Dimensions as Systems in Involution

Using the work by Bampi and Caviglia, we write the Weyl-Lanczos equations as an exterior differential system. Using Janet-Riquier theory, we compute the Cartan characters for all spacetimes with a diagonal metric and for the plane wave spacetime since all spacetimes have a plane wave limit. We write the Lanczos wave equation as an exterior differential system and, with assistance from Janet-Riquier theory, we find that it forms a system in involution. This result can be derived from the scalar wave equation itself. We compute its Cartan characters and compare them with those of the Weyl-Lanczos equations.Comment: 18 pages, latex, no figures, references correcte

Cylindrical thin-shell wormholes and energy conditions

We prove the impossibility of cylindrical thin-shell wormholes supported by matter satisfying the energy conditions everywhere, under reasonable assumptions about the asymptotic behaviour of the - in general different - metrics at each side of the throat. In particular, we reproduce for singular sources previous results corresponding to flat and conical asymptotics, and extend them to a more general asymptotic behaviour. Besides, we establish necessary conditions for the possibility of non exotic cylindrical thin-shell wormholes.Comment: 9 pages; slightly improved version of the article accepted in Int. J. Mod. Phys.

Brane-worlds in T-dual Bulks

We consider brane-world models with a Schwarzschild-AdS black hole bulk. In the particular case of a flat black hole horizon geometry, we study the behaviour of the brane cosmological equations when T-duality transformations act on the bulk. We find that the scale factor is inverted and that either the Friedmann equation or the energy conservation equation are unchanged. However, these become both invariant if we include a tension in the brane action. In this case, the T-duality in the bulk is completely equivalent to the scale factor duality on the brane.Comment: 11 pages, Latex, (v2) minor corrections, references adde

Double Time Window Targeting Technique: Real time DMRG dynamics in the PPP model

We present a generalized adaptive time-dependent density matrix renormalization group (DMRG) scheme, called the {\it double time window targeting} (DTWT) technique, which gives accurate results with nominal computational resources, within reasonable computational time. This procedure originates from the amalgamation of the features of pace keeping DMRG algorithm, first proposed by Luo {\it et. al}, [Phys.Rev. Lett. {\bf 91}, 049701 (2003)], and the time-step targeting (TST) algorithm by Feiguin and White [Phys. Rev. B {\bf 72}, 020404 (2005)]. Using the DTWT technique, we study the phenomena of spin-charge separation in conjugated polymers (materials for molecular electronics and spintronics), which have long-range electron-electron interactions and belong to the class of strongly correlated low-dimensional many-body systems. The issue of real time dynamics within the Pariser-Parr-Pople (PPP) model which includes long-range electron correlations has not been addressed in the literature so far. The present study on PPP chains has revealed that, (i) long-range electron correlations enable both the charge and spin degree of freedom of the electron, to propagate faster in the PPP model compared to Hubbard model, (ii) for standard parameters of the PPP model as applied to conjugated polymers, the charge velocity is almost twice that of the spin velocity and, (iii) the simplistic interpretation of long-range correlations by merely renormalizing the {\it U} value of the Hubbard model fails to explain the dynamics of doped holes/electrons in the PPP model.Comment: Final (published) version; 39 pages, 13 figures, 1 table; 2 new references adde