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Geographic disparities refer to the uneven distribution of resources, opportunities, and outcomes across different regions, often influenced by factors such as socioeconomic status, infrastructure, and policy decisions. These disparities can manifest in various domains, including health, education, and economic development, leading to significant impacts on quality of life and social equity.
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Topological phases of matter are states of matter that are characterized by global properties that remain invariant under continuous deformations, distinguishing them from conventional phases like solids, liquids, and gases. These phases are largely described by topological invariants and exhibit phenomena such as robust edge states and quantized conductance, making them of great interest in condensed matter physics and potential applications in quantum computing.
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A symmetry group is a mathematical concept used to describe the set of all transformations that can be applied to an object without changing its overall structure. These transformations include operations such as rotations, reflections, and translations, and the group structure provides a framework to analyze the symmetry properties of geometric objects, physical systems, and even abstract algebraic structures.
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Surface states are electronic states found at the surface of materials, which can significantly influence the material's properties and behavior. These states arise due to the disruption of the periodic potential at the surface, leading to unique electronic structures that differ from the bulk material.
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A phase transition is a transformation between different states of matter, such as solid, liquid, and gas, driven by changes in external conditions like temperature and pressure. It involves critical phenomena and can be characterized by abrupt changes in physical properties, such as density or magnetization, at specific transition points.
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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.
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Quantum entanglement is a phenomenon where particles become interconnected in such a way that the state of one particle instantaneously influences the state of another, regardless of the distance between them. This non-local interaction challenges classical intuitions about separability and locality, and is a cornerstone of quantum mechanics with implications for quantum computing and cryptography.
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Topological phases are states of matter that extend beyond the traditional classification based on symmetry breaking and are characterized by topological invariants that remain unchanged under continuous deformations. These phases exhibit robust edge states and exotic quantum phenomena, such as the quantum Hall effect, that are protected by the system's topology rather than its symmetry.
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Topological materials possess unique electronic properties that stem from their topological order, distinguished by surface states that are protected against disruptions. These materials have promising applications in quantum computing and electronics, as their robust characteristics offer new ways to manage electron flow without loss.
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