Topic

# Conical surface

About: Conical surface is a research topic. Over the lifetime, 18666 publications have been published within this topic receiving 125324 citations. The topic is also known as: conic surface & generalized cone.

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01 Jul 2004

1,127 citations

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TL;DR: In this article, the authors discuss computational tools for finding and characterizing the conical intersections in such systems, and show that these purely accidental intersections are more frequently than previously thought and in unexpected situations, making the geometric phase effect and the occurrence of efficient nonadiabatic transitions more commonplace phenomena.

Abstract: In the Born-Oppenheimer approximation for molecular dynamics as generalized by Born and Huang, nuclei move on multiple potential-energy surfaces corresponding to different electronic states. These surfaces may intersect at a point in the nuclear coordinates with the topology of a double cone. These conical intersections have important consequences for the dynamics. When an adiabatic electronic wave function is transported around a closed loop in nuclear coordinate space that encloses a conical intersection point, it acquires an additional geometric, or Berry, phase. The Schr\"odinger equation for nuclear motion must be modified accordingly. A conical intersection also permits efficient nonadiabatic transitions between potential-energy surfaces. Most examples of the geometric phase in molecular dynamics have been in situations in which a molecular point-group symmetry required the electronic degeneracy and the consequent conical intersection. Similarly, it has been commonly assumed that the conical intersections facilitating nonadiabatic transitions were largely symmetry driven. However, conical intersections also occur in the absence of any symmetry considerations. This review discusses computational tools for finding and characterizing the conical intersections in such systems. Because these purely accidental intersections are difficult to anticipate, they may occur more frequently than previously thought and in unexpected situations, making the geometric phase effect and the occurrence of efficient nonadiabatic transitions more commonplace phenomena. [S0034-6861(96)00404-7]

855 citations

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TL;DR: This Letter shows how the dispersion relation of surface plasmon polaritons propagating along a perfectly conducting wire can be tailored by corrugating its surface with a periodic array of radial grooves, opening the way to important applications such as energy concentration on cylindrical wires and superfocusing using conical structures.

Abstract: In this Letter, we show how the dispersion relation of surface plasmon polaritons (SPPs) propagating along a perfectly conducting wire can be tailored by corrugating its surface with a periodic array of radial grooves. In this way, highly localized SPPs can be sustained in the terahertz region of the electromagnetic spectrum. Importantly, the propagation characteristics of these spoof SPPs can be controlled by the surface geometry, opening the way to important applications such as energy concentration on cylindrical wires and superfocusing using conical structures.

729 citations

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TL;DR: In this article, the authors show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born-Oppenheimer approximation both in the absence and the presence of conical intersections.

Abstract: We show how the presence of a conical intersection in the adiabatic potential energy hypersurface can be handled by including a new vector potential in the nuclear‐motion Schrodinger equation. We show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born–Oppenheimer approximation both in the absence and the presence of conical intersections. The treatment of nuclear‐motion wave functions in the presence of conical intersections and the treatment of nuclear‐interchange symmetry in general both require careful consideration of the phases of the electronic and nuclear‐motion wave functions, and this is discussed in detail.

724 citations

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TL;DR: In this article, the Berger-Nirenberg problem on surfaces with conical singularities was studied and conditions under which a function on a Riemann surface is the Gaussian curvature of some conformal metric with a prescribed set of singularities of conical types.

Abstract: We study the Berger-Nirenberg problem on surfaces with conical singularities, i.e, we discuss conditions under which a function on a Riemann surface is the Gaussian curvature of some conformal metric with a prescribed set of singularities of conical types.

558 citations