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Lossless Quantum Data Compression and Secure Direct
Lossless Quantum Data Compression and Secure Direct

Quantum coherent biomolecular energy transfer with spatially
Quantum coherent biomolecular energy transfer with spatially

Quantum States of Neutrons in the Gravitational Field
Quantum States of Neutrons in the Gravitational Field

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A conformal field theory approach to the fractional quantum Hall

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Helium atom - ChaosBook.org

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Applying elementary principles from quantum physics

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... I had used the mathematics of the example of the mass point between two walls, and of the wave-packets that belong to it, in my lectures in such a way that the transformation formula of the theta-function comes into play. But that is a mere detail. Pauli’s remark stimulated Born to return to the pro ...
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Toward the Unification of Physics and Number Theory

ABSTRACT Title of Document:
ABSTRACT Title of Document:

Quantum Circuits Engineering: Efficient Simulation and
Quantum Circuits Engineering: Efficient Simulation and

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Quantum group

In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects.The term ""quantum group"" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a `bicrossproduct' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo.In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.Just as groups often appear as symmetries, quantum groups act on many other mathematical objects and it has become fashionable to introduce the adjective quantum in such cases; for example there are quantum planes and quantum Grassmannians.
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