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In condensed matter physics, an AKLT model, also known as an Affleck-Kennedy-Lieb-Tasaki model is an extension of the one-dimensional quantum Heisenberg spin model.The proposal and exact solution of this model by Ian Affleck, Elliott H. Lieb, Tom Kennedy and Hal Tasaki [] [1] provided crucial insight into the physics of the spin-1 Heisenberg chain.
SnapPea is free software designed to help mathematicians, in particular low-dimensional topologists, study hyperbolic 3-manifolds. The primary developer is Jeffrey Weeks, who created the first version [1] as part of his doctoral thesis, [2] supervised by William Thurston. It is not to be confused with the unrelated android malware with the same ...
However, the Hamiltonian still exists. In the case where the cometric is degenerate at every point q of the configuration space manifold Q, so that the rank of the cometric is less than the dimension of the manifold Q, one has a sub-Riemannian manifold. The Hamiltonian in this case is known as a sub-Riemannian Hamiltonian. Every such ...
Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. [ 1 ] The term "symplectic", introduced by Hermann Weyl , [ 2 ] is a calque of "complex"; previously, the "symplectic group" had been called the "line ...
An -action on a symplectic manifold (,) is called Hamiltonian if it is symplectic and if there exists a momentum map. A momentum map is often also required to be G {\displaystyle G} -equivariant , where G {\displaystyle G} acts on g ∗ {\displaystyle {\mathfrak {g}}^{*}} via the coadjoint action , and sometimes this requirement is included in ...
In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle of a manifold. In physics, it is used to create a correspondence between the velocity of a point in a mechanical system and its momentum, thus providing a bridge between Lagrangian mechanics and Hamiltonian mechanics (on the manifold ).
The Dicke model is a quantum mechanical model that describes the coupling between a single-mode cavity and two-level systems, or equivalently spin-1/2 degrees of freedom. . The model was first introduced in 1973 by K. Hepp and E. H. Lieb
Symplectic manifolds arise from classical mechanics; in particular, they are a generalization of the phase space of a closed system. [1] In the same way the Hamilton equations allow one to derive the time evolution of a system from a set of differential equations, the symplectic form should allow one to obtain a vector field describing the flow of the system from the differential of a ...