Recent content by C. H. Fleming

Isn't the QED Hamiltonian in the Coulomb gauge given in Chapters 7,8 of Weinberg?

It was argued by Dyson that http://prola.aps.org/abstract/PR/v85/i4/p631_1" , because if one considers a negative fine structure constant \alpha then the vacuum would become unstable - that for \alpha < 0 like charge attracts and then there is no lower bound in the energy, as pair production can...

There is a paper by Parikh and Wilczek which relies upon ordinary quantum mechanical tunneling, but it is not very rigorous.

I think that the limit of small fluctuations this is the same principle. Your muscles expend energy during compensation (and do work on the box). Then the box relaxes (and does work on your muscles). However, your muscles do not operate via reversible processes. So that energy is transformed...

Your body is not in equilibrium when holding the box up. If the force of your muscles does not exactly balance with the weight of the box, then your muscles will have to compensate. There are short periods of time when the force of your muscles do not exactly balance with the weight of the box...

Also I believe I have determined that the positivity constraint for Fokker-Plank equations defined on a continuous phase space with only local operations (coordinates and derivatives) is that it be constructed from an exterior derivative (e.g. in this case, all derivatives to the left of all...

You want to say this \phi^* L_X \omega = \frac{d}{dt} \phi^* \omega The flow has time dependence, not the symplectic form, as Arnold already mentioned. From this relation you probably immediately see \frac{d}{dt} \phi^* \omega = - \gamma \phi^* \omega which is the ODE you were looking for...

I have thought about this some more. Unitary maps are analogous to Symplectomorphic maps. Neither groups are simply bijections, but they are moreover isomorphisms. There are bijections between state vectors in Hilbert space which are not unitary, but they do not preserve the state overlap...

Great progress. I see now, it is obvious that Hamiltonian motion is not necessary to satisfy the continuity of phase-space volume in the evolution of \rho. It is only sufficient. I have been thinking about this with the wrong framework: phase space instead of the cotangent space of the...

So there are volume preserving flows which cannot be described by a Hamiltonian? I have been thinking about Hamiltonian motion instead of maps between pure states like I should. In QM they are equivalent, but I've never thought about it classically.

I believe the generalization of Choi's theorem is Stinespring's theorem (although I think it is a touch too general). As you already seem to know, people do apply Lindblad's theorem to systems with unbounded operators and the end result looks the same. This is typically safe. I think Davies...

How do you apply that definition to extending the classical mechanics of finite systems to classical fields?

You will have to excuse my ignorance. Why are we mapping between nonnegative vectors? Naively I would imagine the starting point to be norm-preserving positive linear maps between positive functions of the phase-space coordinates (i.e. density functions instead of density matrices). Is there...

Consider the dynamical map: \boldsymbol{\rho}(t) = \boldsymbol{\mathcal{G}}(t,0) \boldsymbol{\rho}(0) where \boldsymbol{\rho}(t) is the density matrix of the reduced system at time t and we have a non-unitary theory (likely with a traced out environment) such that we can consider any initial...

I don't want to limit scope to the dynamical semigroup, so the stochastic process may be non-Markovian and the quantum dynamical generator might not be of Lindblad-GKS form. The algebraic generator (which is not equivalent to the dynamical generator given time dependence) should still satisfy...