Carrier dynamics and coherent acoustic phonons in nitride heterostructures

We model generation and propagation of coherent acoustic phonons in piezoelectric InGaN/GaN multi-quantum wells embedded in a \textit{pin} diode structure and compute the time resolved reflectivity signal in simulated pump-probe experiments. Carriers are created in the InGaN wells by ultrafast pumping below the GaN band gap and the dynamics of the photoexcited carriers is treated in a Boltzmann equation framework. Coherent acoustic phonons are generated in the quantum well via both deformation potential electron-phonon and piezoelectric electron-phonon interaction with photogenerated carriers, with the latter mechanism being the dominant one. Coherent longitudinal acoustic phonons propagate into the structure at the sound speed modifying the optical properties and giving rise to a giant oscillatory differential reflectivity signal. We demonstrate that coherent optical control of the differential reflectivity can be achieved using a delayed control pulse.Comment: 14 pages, 11 figure

Concise theory of chiral lipid membranes

A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur \textit{et al.}, Science \textbf{264}, 945 (1994); M.S. Spector \textit{et al.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{et al.}, Proc. Natl. Acad. Sci. USA \textbf{102}, 7438 (2005)] on self-assembled chiral lipid membranes of DC$_{8,9}$PC. A torus with the ratio between its two generated radii larger than $\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations, and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0$^\circ$ and 35$^\circ$, which are close to the most frequent values 5$^\circ$ and 28$^\circ$ observed in the experiment [N. Mahajan \textit{et al.}, Langmuir \textbf{22}, 1973 (2006)]. Additionally, the present theory can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions. The ratio between the width and pitch of twisted ribbons is predicted to be proportional to the relative concentration difference of left- and right-handed enantiomers in the low relative concentration difference region, which is in good agreement with the experiment [R. Oda \textit{et al.}, Nature (London) \textbf{399}, 566 (1999)].Comment: 14 pages, 7 figure

Oscillatons formed by non linear gravity

Oscillatons are solutions of the coupled Einstein-Klein-Gordon (EKG) equations that are globally regular and asymptotically flat. By means of a Legendre transformation we are able to visualize the behaviour of the corresponding objects in non-linear gravity where the scalar field has been absorbed by means of the conformal mapping.Comment: Revtex file, 6 pages, 3 eps figure; matches version published in PR

Euler numbers of four-dimensional rotating black holes with the Euclidean signature

For a black hole's spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the spacetime manifolds of black holes. Using this formula, we obtain that the Euler numbers of Kerr and Kerr-Newman black holes are 2. We also obtain that the Euler number of the Kerr-Sen metric in the heterotic string theory with one boost angle nonzero is 2 that is in accordence with its topology.Comment: 15 pages, Latex, arxiv-id for the refs. supplemente

Singular sources in gravity and homotopy in the space of connections

Suppose a Lagrangian is constructed from its fields and their derivatives. When the field configuration is a distribution, it is unambiguously defined as the limit of a sequence of smooth fields. The Lagrangian may or may not be a distribution, depending on whether there is some undefined product of distributions. Supposing that the Lagrangian is a distribution, it is unambiguously defined as the limit of a sequence of Lagrangians. But there still remains the question: Is the distributional Lagrangian uniquely defined by the limiting process for the fields themselves? In this paper a general geometrical construction is advanced to address this question. We describe certain types of singularities, not by distribution valued tensors, but by showing that the action functional for the singular fields is (formally) equivalent to another action built out of \emph{smooth} fields. Thus we manage to make the problem of the lack of a derivative disappear from a system which gives differential equations. Certain ideas from homotopy and homology theory turn out to be of central importance in analyzing the problem and clarifying finer aspects of it. The method is applied to general relativity in first order formalism, which gives some interesting insights into distributional geometries in that theory. Then more general gravitational Lagrangians in first order formalism are considered such as Lovelock terms (for which the action principle admits space-times more singular than other higher curvature theories).Comment: 21 pages, 9 figures, RevTe

Self-gravitating branes of codimension 4 in Lovelock gravity

We construct a familly of exact solutions of Lovelock equations describing codimension four branes with discrete symmetry in the transverse space. Unlike what is known from pure Einstein gravity, where such brane solutions of higher codimension are singular, the solutions we find, for the complete Lovelock theory, only present removable singularities. The latter account for a localised tension-like energy-momentum tensor on the brane, in analogy with the case of a codimension two self-gravitating cosmic string in pure Einstein gravity. However, the solutions we discuss present two main distinctive features : the tension of the brane receives corrections from the induced curvature of the brane's worldsheet and, in a given Lovelock theory, the spectrum of possible values of the tension is discrete. These solutions provide a new framework for the study of higher codimension braneworlds.Comment: 22 page

de Sitter group and Einstein-Hilbert Lagrangian

Axial vector torsion in the Einstein-Cartan space $U_{4}$ is considered here. By picking a particular term from the SO(4,1) Pontryagin density and then modifying it in a SO(3,1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then considering torsion and torsion-less connection as independent fields, it has been found that $\kappa$ and $\lambda$ of Einstein-Hilbert Lagrangian, appear as integration constants in such a way that $\kappa$ has been found to be linked with the topological Nieh-Yan density of $U_{4}$ space.Comment: 14 page

Pseudo-forces in quantum mechanics

Dynamical evolution is described as a parallel section on an infinite dimensional Hilbert bundle over the base manifold of all frames of reference. The parallel section is defined by an operator-valued connection whose components are the generators of the relativity group acting on the base manifold. In the case of Galilean transformations we show that the property that the curvature for the fundamental connection must be zero is just the Heisenberg equations of motion and the canonical commutation relation in geometric language. We then consider linear and circular accelerating frames and show that pseudo-forces must appear naturally in the Hamiltonian.Comment: 6 pages, 1 figure, revtex, new section added, to appear in PR