The Infamous Boundary

Paolo Facchi A, Giancarlo Garnero, Giuseppe Marmo +2 more

W. David Wick

John Bell coined the phrase ``Infamous Boundary" for the point where classical physics splits off from quantum physics. Many authors, including the present one, have advanced theories with the intention of defining and locating this ``shifty split"; most propose that it lies somewhere on the scale of apparatus. But what if it resides at the level of macromolecules? I show here that this question is intimately connected to the choice of thermal ensembles and to the so-called `Hund's Paradox' in quantum chemistry. I propose an experimental set-up that could in principle reveal the IB lurking in asymmetric macromolecules.

Colin Bruce Jack

The "infamous boundary" is the apparent dichotomy between the quantum behaviour of microscopic systems and the classical behaviour of macroscopic systems. A lifetime after the invention of quantum theory, the problem of "quantum collapse" remains unsolved. Wavelike, probabilistic behaviour at the quantum level is resolved into specific outcomes at the observer's end of the measuring apparatus in an instantaneous way that appears to transcend the normal laws of physics.

Alexei S. Trifonov

F. Brosens

The propagator of N interacting fermions in a scalar potential can, in the coordinate space, be written as a Feynman-Kac functional over a symmetrized process, i.e., as a superposition of Euclidean-time path integrals over the diffusion process of N free fermions. Exploiting the properties of the permutation group allows to reduce the coordinate space by a factor , ! N leading to a state space in which the propagator is positive. The expression for the state space is numerically inaccessible because of an intricate limit to be taken, reflecting the infamous fermion sign problem. However, by analytical methods the state space can be expressed in terms of standard, numerically tractable, N N × determinants. A well-defined Markov process is defined on the state space, namely Brownian motion with superimposed potential-dependent exponential weights and absorbing boundary conditions. This leads to a random process by stable diffusion of purely positive walkers which generate the Feynman-Kac functional in the state space.