Topic
Hamiltonian (control theory)
About: Hamiltonian (control theory) is a research topic. Over the lifetime, 4713 publications have been published within this topic receiving 67415 citations. The topic is also known as: Hamiltonian function.
Papers published on a yearly basis
Papers
More filters
04 Oct 2019
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.
Abstract: Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.
1,962 citations
TL;DR: Wilson's lattice gauge model is presented as a canonical Hamiltonian theory and the structure of the model is reduced to the interactions of an infinite collection of coupled rigid rotators as mentioned in this paper.
Abstract: Wilson's lattice gauge model is presented as a canonical Hamiltonian theory. The structure of the model is reduced to the interactions of an infinite collection of coupled rigid rotators. The gauge-invariant configuration space consists of a collection of strings with quarks at their ends. The strings are lines of non-Abelian electric flux. In the strong-coupling limit the dynamics is best described in terms of these strings. Quark confinement is a result of the inability to break a string without producing a pair.
1,388 citations
TL;DR: The relations between the different sets of optimality conditions arising in Pontryagin's maximum principle are shown and the application of these maximum principle conditions is demonstrated by solving some illustrative examples.
Abstract: This paper gives a survey of the various forms of Pontryagin’s maximum principle for optimal control problems with state variable inequality constraints. The relations between the different sets of optimality conditions arising in these forms are shown. Furthermore, the application of these maximum principle conditions is demonstrated by solving some illustrative examples.
937 citations
28 Jan 2000
TL;DR: In this article, a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution, is given, where the evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian and a final Hamiltonian, whose ground state encodes the satisfying assignment.
Abstract: We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. To ensure that the system evolves to the desired final ground state, the evolution time must be big enough. The time required depends on the minimum energy difference between the two lowest states of the interpolating Hamiltonian. We are unable to estimate this gap in general. We give some special symmetric cases of the satisfiability problem where the symmetry allows us to estimate the gap and we show that, in these cases, our algorithm runs in polynomial time.
713 citations
TL;DR: The quantization of self-dual two-dimensional Lagrangeans which describe systems that are not explicitly canonical are discussed, and some remarks on the most efficient method for exhibiting the canonical structure are made.
Abstract: Recent Letters and Comments discuss the quantization of self-dual two-dimensional Lagrangeans which describe systems that are not explicitly canonical. We make some remarks on the most efficient method for exhibiting the canonical structure.
661 citations