35,319 research outputs found
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
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