Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.

Time evolution of Bloch electrons in a homogeneous electric field

Abstract: The theory of a Bloch electron moving in the presence of a homogeneous electric field is reviewed and objections to the conventional derivations are discussed. A new derivation of the time development of a Bloch electron moving in a homogeneous, but time-dependent, electric field is presented using a vector potential to describe the field rather than the usual scalar potential. This new treatment avoids all the basic assumptions of the conventional derivations and demonstrates that a Bloch electron will oscillate in a single band with the Bloch period if a homogeneous electric field is abruptly turned on, with a tunneling probability into other bands given by the conventional expression. It is also shown that the calculated optical absorption will have the same ladderlike structure that would be obtained if Wannier-Stark quantized energy levels are assumed, although the present calculation makes no such assumption. The previous objections to the existence of Bloch oscillations for electrons in a perfect periodic potential are examined and found to be irrelevant provided the tunneling probability per Bloch oscillation period is much less than one, a condition that is generally satisfied for typical elemental and compound semiconductors for electric fields smaller than ${10}^{6}$ V/cm.

Instability in cosmological topologically massive gravity at the chiral point

Abstract: This thesis explores three different aspects of quantum gravity. First we study D3-brane black holes in Calabi-Yau compactifications of type IIB string theory. Using the OSV conjecture and a relation between topological strings and matrix models we show that some black holes have a matrix model description. This is the case if the attractor mechanism fixes the internal geometry to a conifold at the black hole horizon. We also consider black holes in a flux compactification and compare the effects of the black holes and fluxes on the internal geometry. We find that the fluxes dominate. Second, we study the scalar potential of type IIB flux compactifications. We demonstrate that monodromies of the internal geometry imply as a general feature the existence of long series of continuously connected minima. This allows for the embedding of scenarios such as chain inflation and resonance tunneling into string theory. The concept of monodromies is also extended to include geometric transitions: passing to a different Calabi-Yau topology, performing its monodromies and then returning to the original space allows for novel transformations. All constructions are performed explicitly, using both analytical and numerical techniques, in the mirror quintic Calabi-Yau. Third, we study cosmological topologically massive gravity at the chiral point, a prime candidate for quantization of gravity in three dimensions. The prospects of this scenario depend crucially of the stability of the theory. We demonstrate the presence of a negative energy bulk mode that grows logarithmically toward the AdS boundary. The AdS isometry generators have non-unitary matrix representations like in logarithmic CFT, and we propose that the CFT dual for this theory is logarithmic. In a complementing canonical analysis we also demonstrate the existence of this bulk degree of freedom, and we present consistent boundary conditions encompassing the new mode.