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The solar system is a gravitationally bound system comprising the Sun and the objects that orbit it, including planets, moons, asteroids, comets, and meteoroids. It formed approximately 4.6 billion years ago from the gravitational collapse of a region within a large molecular cloud.
The Berry phase is a quantum mechanical phase factor acquired over the course of a cycle, when a system is subjected to adiabatic processes and the parameters in its Hamiltonian are varied cyclically. It is a geometric phase, distinct from the dynamic phase, and plays a crucial role in various physical phenomena, including the Aharonov-Bohm effect and topological insulators.
Topological order is a way of arranging the vertices of a directed acyclic graph (DAG) such that for every directed edge from vertex u to vertex v, u comes before v in the ordering. It is crucial in scenarios like task scheduling, where certain tasks must be completed before others.
Bulk-Boundary Correspondence is a principle in theoretical physics that proposes a duality between a higher-dimensional 'bulk' space and its lower-dimensional boundary, often used in the study of quantum gravity and string theory. This correspondence allows for complex calculations in the bulk to be simplified by examining the boundary, giving a powerful tool for understanding phenomena like black holes and quantum field theories.
The Chern number is a topological invariant that characterizes distinct phases of matter in condensed matter physics, particularly in systems exhibiting the quantum Hall effect. It reflects the global properties of a system's band structure, indicating how many times the wavefunctions wrap around a parameter space, and is crucial for understanding topological insulators and quantized conductance.
Weyl semimetals are quantum materials where the electronic band structure leads to the presence of Weyl fermions as emergent quasiparticles. These materials exhibit unique topological properties and feature phenomena such as surface Fermi arcs and the chiral anomaly, making them of great interest in condensed matter physics and potential applications in quantum computing.
Symmetry-protected topological (SPT) states are phases of matter that possess non-trivial topological properties, protected by the presence of certain symmetries, and unlike traditional topological insulators, they become indistinguishable from a trivial state when these symmetries are broken. These states have garnered significant interest due to their robust edge states that could be utilized in quantum computing and other technologies that require stable quantum properties, immune to localized perturbations.
Non-Abelian anyons are exotic quasiparticles that arise in certain two-dimensional systems and have the unique property that interchanging them results in a change to the system's quantum state that depends on the order of the exchanges. This property makes non-Abelian anyons promising candidates for fault-tolerant quantum computation, as they can potentially perform operations that are inherently robust against local errors.
Spin-orbit coupling is a quantum mechanical phenomenon where an electron's spin interacts with its orbital motion around a nucleus, leading to shifts in energy levels and splitting of spectral lines. This interaction is crucial for understanding fine structure in atomic spectra, magnetic properties of materials, and the behavior of electrons in semiconductors and topological insulators.
A Van Hove singularity is a feature in the electronic density of states of a solid where there is a divergent or non-analytic point due to the topology of the topology of the energy bands. This singularity can significantly influence the physical properties of materials, like superconductivity and magnetism, by enhancing electron interactions at specific energy levels.
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