Related Experiment Video
Updated: May 4, 2026
13:44
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
42.6K
Geometric phase effects in dynamics near conical intersections: symmetry breaking and spatial localization.
Ilya G Ryabinkin1, Artur F Izmaylov1
1Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
Physical Review Letters
|December 17, 2013
Summary
Finite systems with conical intersections show spontaneous symmetry breaking, localizing eigenstates. This robust phenomenon, with a geometric phase origin, slows quantum nuclear dynamics at low temperatures.
Area of Science:
- Quantum mechanics
- Chemical physics
- Condensed matter theory
Background:
- Conical intersections are critical points in molecular potential energy surfaces where electronic states become degenerate.
- Symmetry breaking is a fundamental concept in physics, leading to distinct phases and properties.
- Understanding quantum dynamics is crucial for predicting chemical reaction rates and material behavior.
Purpose of the Study:
- To investigate spontaneous symmetry breaking in finite systems featuring conical intersections.
- To explore the manifestation of symmetry breaking as spatial localization of eigenstates.
- To analyze the impact of this localization on quantum nuclear dynamics.
Main Methods:
- Theoretical modeling of finite systems with conical intersections.
- Analysis of eigenstate properties, focusing on localization and delocalization.
- Investigation of the geometric phase origin of the observed localization.
- Study of the transition between localized and delocalized regimes.
- Simulation of low-energy quantum nuclear dynamics at varying temperatures.
Main Results:
- Demonstrated spontaneous symmetry breaking in finite systems with conical intersections.
- Observed spatial localization of eigenstates as a direct consequence of symmetry breaking.
- Established the geometric phase origin of this localization, proving its robustness against parameter variations.
- Characterized the transition between localized and delocalized eigenstates as analogous to a continuous phase transition.
- Found that eigenstate localization significantly slows down low-energy quantum nuclear dynamics at low temperatures.
Conclusions:
- Finite systems with conical intersections can undergo spontaneous symmetry breaking, leading to robust eigenstate localization.
- This localization, rooted in geometric phase effects, impacts quantum dynamics by slowing nuclear motion at low temperatures.
- The observed transition dynamics resemble a continuous phase transition, offering insights into fundamental physical phenomena.
Related Concept Videos
01:27Gauss's Law: Planar Symmetry
7.6K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
7.6K
01:30Dynamics of Circular Motion
21.6K
An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
21.6K
01:26Gauss's Law: Spherical Symmetry
7.2K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has...
7.2K
01:26Orthogonal Trajectories
303
Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
303
01:16Eccentric Axial Loading in a Plane of Symmetry
763
Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
763
01:23Curvilinear Motion: Rectangular Components
1.6K
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
1.6K