Hopf mapping from 2 dimensions Quantum Mechanics (QM) to 3 dimensions Classical Mechanics (CM) is examined in terms of a formalism started by Feynman which has linkage to the (CM) equations of motion have linkage to t...Hopf mapping from 2 dimensions Quantum Mechanics (QM) to 3 dimensions Classical Mechanics (CM) is examined in terms of a formalism started by Feynman which has linkage to the (CM) equations of motion have linkage to the Serret-Frenet form (for differential equations). We argue that in doing so we may then link QM representations of qubits to a solved version of the rotating rod problem. Furthermore since a “generic” solid body rotation equivalent to the rotating rod problem has linkage to Gravitational Wave (GW) generation, as given by Lightman et al., it is a way to tie qubits (quantum information) to GW generation. We then make observations as to what the results mean in terms of QM initial states and the power of GW production from early universe conditions.展开更多
The N involutive integrals of motion with linearly independent gradients for the nonlin earized eigenvalue problem corresponding to the classical Boussinesq (CB) hierarchy are given. It is shown that when n=1,2,3, the...The N involutive integrals of motion with linearly independent gradients for the nonlin earized eigenvalue problem corresponding to the classical Boussinesq (CB) hierarchy are given. It is shown that when n=1,2,3, the nonlinearized time parts of Lax systems for the CB hierarchy are transformed into three finite-dimensional integrable Hamiltonian systems under the constraint of the nonlinearized spatial part.展开更多
文摘Hopf mapping from 2 dimensions Quantum Mechanics (QM) to 3 dimensions Classical Mechanics (CM) is examined in terms of a formalism started by Feynman which has linkage to the (CM) equations of motion have linkage to the Serret-Frenet form (for differential equations). We argue that in doing so we may then link QM representations of qubits to a solved version of the rotating rod problem. Furthermore since a “generic” solid body rotation equivalent to the rotating rod problem has linkage to Gravitational Wave (GW) generation, as given by Lightman et al., it is a way to tie qubits (quantum information) to GW generation. We then make observations as to what the results mean in terms of QM initial states and the power of GW production from early universe conditions.
文摘The N involutive integrals of motion with linearly independent gradients for the nonlin earized eigenvalue problem corresponding to the classical Boussinesq (CB) hierarchy are given. It is shown that when n=1,2,3, the nonlinearized time parts of Lax systems for the CB hierarchy are transformed into three finite-dimensional integrable Hamiltonian systems under the constraint of the nonlinearized spatial part.
