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In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. [1] It was devised by Wu-Pei Su, John Robert Schrieffer, and Alan J. Heeger in 1979, to describe the increase of electrical conductivity of polyacetylene polymer chain when doped, based on the existence of solitonic defects.
Of course, this is not the case in general – the standard model includes the non-Abelian SU(2) and SU(3) groups (such groups lead to what is called a Yang–Mills gauge theory). We need to introduce three gauge fields corresponding to each of the subgroups SU(3) × SU(2) × U(1) .
In mathematics of stochastic systems, the Runge–Kutta method is a technique for the approximate numerical solution of a stochastic differential equation. It is a generalisation of the Runge–Kutta method for ordinary differential equations to stochastic differential equations (SDEs). Importantly, the method does not involve knowing ...
Unlike the Dirac monopole, the 't Hooft–Polyakov monopole is a smooth solution with a finite total energy. The solution is localized around r = 0 {\displaystyle r=0} . Very far from the origin, the gauge group G {\displaystyle G} is broken to H {\displaystyle H} , and the 't Hooft–Polyakov monopole reduces to the Dirac monopole.
In their foundational paper on the topic of gauge theories, Robert Mills and Chen-Ning Yang developed (essentially independent of the mathematical literature) the theory of principal bundles and connections in order to explain the concept of gauge symmetry and gauge invariance as it applies to physical theories. [1]
For example, the second-order equation y′′ = −y can be rewritten as two first-order equations: y′ = z and z′ = −y. In this section, we describe numerical methods for IVPs, and remark that boundary value problems (BVPs) require a different set of tools. In a BVP, one defines values, or components of the solution y at more than one ...
Francis Edward Su is an American mathematician. He joined the Harvey Mudd College faculty in 1996, and is currently Benediktsson-Karwa Professor of Mathematics. Su served as president of the Mathematical Association of America from 2015–2017 [ 1 ] and is serving as a Vice President of the American Mathematical Society from 2020-2023. [ 2 ]
Adding repetition to the game introduces a focal point at the Nash equilibrium solution of 0. This was shown by Camerer as, “[when] the game is played multiple times with the same group, the average moves close to 0.” [ 5 ] Introducing the iterative aspect to the game forces all players onto higher levels of thinking which allows them all ...