Spontaneous symmetry breaking. Consider the bottom of an empty wine bottle, a symmetrical upward dome with a trough for sediment. If a ball is put in a particular position at the peak of the dome, the circumstances are symmetrical with respect to rotating the wine bottle. But the ball may spontaneously break this symmetry and move into the trough, a point of lowest energy. The bottle and the ball continue to have symmetry, but the system does not.[4] Most simple phases of matter and phase-transitions, like crystals, magnets, and conventional superconductors can be simply understood from the viewpoint of spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the fractional quantum Hall effect.
Spontaneous symmetry breaking in physics[edit] Spontaneous symmetry breaking simplified: - At high energy levels (left) the ball settles in the center, and the result is symmetrical. Particle physics[edit] Chiral symmetry[edit] Higgs mechanism[edit] Condensed matter physics[edit] , where such that . Spin (physics) In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.[1][2] Spin is a solely quantum-mechanical phenomenon; it does not have a counterpart in classical mechanics (despite the term spin being reminiscent of classical phenomena such as a planet spinning on its axis).[2] Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. Orbital angular momentum is the quantum-mechanical counterpart to the classical notion of angular momentum: it arises when a particle executes a rotating or twisting trajectory (such as when an electron orbits a nucleus).[3][4] The existence of spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which particles are observed to possess angular momentum that cannot be accounted for by orbital angular momentum alone.[5] where h is the Planck constant.
Self-organization. Self-organization occurs in a variety of physical, chemical, biological, robotic, social and cognitive systems. Common examples include crystallization, the emergence of convection patterns in a liquid heated from below, chemical oscillators, swarming in groups of animals, and the way neural networks learn to recognize complex patterns.
Overview[edit] The most robust and unambiguous examples[1] of self-organizing systems are from the physics of non-equilibrium processes. Self-organization is also relevant in chemistry, where it has often been taken as being synonymous with self-assembly. The concept of self-organization is central to the description of biological systems, from the subcellular to the ecosystem level. Self-organization usually relies on three basic ingredients:[3] Strong dynamical non-linearity, often though not necessarily involving positive and negative feedbackBalance of exploitation and explorationMultiple interactions Principles of self-organization[edit] Examples[edit]
Magnetism. A magnetic quadrupole Magnetism is a class of physical phenomena that includes forces exerted by magnets on other magnets. It has its origin in electric currents and the fundamental magnetic moments of elementary particles. These give rise to a magnetic field that acts on other currents and moments. All materials are influenced to some extent by a magnetic field.
The strongest effect is on permanent magnets, which have persistent magnetic moments caused by ferromagnetism. Most materials do not have permanent moments. Some are attracted to a magnetic field (paramagnetism); others are repulsed by a magnetic field (diamagnetism); others have a much more complex relationship with an applied magnetic field (spin glass behavior and antiferromagnetism). The magnetic state (or phase) of a material depends on temperature (and other variables such as pressure and the applied magnetic field) so that a material may exhibit more than one form of magnetism depending on its temperature, etc. Electrical conduction. Definition[edit] Resistors or conductors with uniform cross-section[edit] A piece of resistive material with electrical contacts on both ends. where R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω) is the length of the piece of material (measured in metres, m) A is the cross-sectional area of the specimen (measured in square metres, m2).
The reason resistivity is defined this way is that it makes resistivity an intrinsic property, unlike resistance. In a hydraulic analogy, passing current through a high-resistivity material is like pushing water through a pipe full of sand, while passing current through a low-resistivity material is like pushing water through an empty pipe. The above equation can be transposed to get Pouillet's law (named after Claude Pouillet): The resistance of a given material will increase with the length, but decrease with increasing cross-sectional area.
The formula and General definition[edit] Conductivity is the inverse: [edit] Phase (matter) Not to be confused with State of matter In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform.[1] Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air over the water is a third phase. The glass of the jar is another separate phase. (See State of Matter#Glass) The term phase is sometimes used as a synonym for state of matter, but there can be several immiscible phases of the same state of matter. A small piece of rapidly melting argon ice shows the transition from solid to liquid.
Distinct phases may also exist within a given state of matter.