Novel Systems and Methods for Quantum
... Precise control over quantum systems can enable the realization of fascinating applications such as powerful computers, secure communication devices, and simulators
that can elucidate the physics of complex condensed matter systems. However, the
fragility of quantum eﬀects makes it very diﬃcult to h ...
tgd as a generalized number theory
... 3.4.6 Infinite primes and the structure of many-sheeted space-time . . . . . . . . . . 197
3.4.7 How infinite integers could correspond to p-adic effective topologies? . . . . . . 198
3.4.8 An alternative interpretation for the hierarchy of functions defined by infinite
primes . . . . . . . . . . . ...
reactive molecular collisions
... Apart from the practical problems that must be faced when implementing a classical trajectory calculation, there is always the conceptual
question: Howreliable is classical mechanics for treating nuclear motion in molecular systems? Truhlar & Muckerman(14) present a discussion of this point in their ...
Topological phases and polaron physics in ultra cold quantum gases
... the physics is well understood at moderate energies! The interplay of many indistinguishable
particles – of the order of 1023 – gives rise to rich physics, which some – including the author
– ultimately believe to include even as complex phenomena as human life.
One key challenge today is to underst ...
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.