The Ricardo puzzle

This paper tackles the puzzle of Ricardo’s stubborn commitment to a labor theory of value that he himself saw as no more than an approximation to reality and which was heavily opposed by Malthus, his most respected contemporary. We show it is wrong to think that the theory had no analytical use. Quite to the contrary, it was the only defence Ricardo could find against Malthus’ destructive criticism, which introduced an unacceptable degree of indetermination in his theory of profits. By adopting the labor theory of value, Ricardo drastically simplified the method of proof of his main proposition, which otherwise seemed to present unsurmountable analytical difficulties. The irony is that the proposition was correct, quite independently of the labor theory of value, but Ricardo was just unable to prove it.

Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces

The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a multi-dimensional (usually two-dimensional) parameter space in which paths can be defined for adiabatic changes in the Hamiltonian, i.e., without closing the gap. Here, we extend the concept of Thouless pumps of band insulators by considering a larger, three-dimensional parameter space. We show that the connectivity of this parameter space is crucial for defining quantum pumps, demonstrating that, as opposed to the conventional two-dimensional case, pumped quantities depend not only on the initial and final points of Hamiltonian evolution but also on the class of the chosen path and preserved symmetries. As such, we distinguish the scenarios of closed/open paths of Hamiltonian evolution, finding that different closed cycles can lead to the pumping of different quantum numbers, and that different open paths may point to distinct scenarios for surface physics. As explicit examples, we consider models similar to simple models used to describe topological insulators, but with doubled degrees of freedom compared to a minimal topological insulator model. The extra fermionic flavors from doubling allow for extra gapping terms/adiabatic parameters - besides the usual topological mass which preserves the topology-protecting discrete symmetries - generating an enlarged adiabatic parameter-space. We consider cases in one and three \emph{spatial} dimensions, and our results in three dimensions may be realized in the context of crystalline topological insulators, as we briefly discuss.Comment: 21 pages, 7 Figure