| The first considers asymmetry-driven Hamiltonian ratchet effects in context of quantum chaos. It is shown, in the Liouville framework, that a biased net effective force can emerge in initially symmetric systems subject to a force of zero mean. This arises via an asymmetric system distortion in both classical and quantum mechanics. However, differences in time-periodicity and chaos between the two mechanics lead to differences in the evolution of the effective force in time.;The second part obtains the canonical commutation relation of quantum mechanics assuming, in addition to the standard assumptions of the quantum Hilbert space, only that position and momentum are functionally independent. This exposes the fundamental interpretation of the commutation relation as an expression of independence, and thereby establishes its analogy with the classical Poisson bracket. Operator techniques used in these arguments are discussed at length. |
