130,378 research outputs found
Conceptual Problems in Scattering from Localized non-Hermitian Potentials
We highlight the conceptual issues that arise when one applies the
quasi-Hermitian framework to analyze scattering from localized non-Hermitian
potentials, in particular complex square-wells or delta-functions. When treated
in the framework of conventional quantum mechanics, these potentials are
generally considered as effective theories, in which probability is not
conserved because of processes that have been ignored. However, if they are
treated as fundamental theories, the Hilbert-space metric must be changed. In
order for the newly-defined probability to be conserved, it must differ from
the standard one, even at asymptotically large distances from the scattering
centre, and the mechanism for this is the non-locality of the new metric, as we
show in detail in the model of a single complex delta function. However,
properties of distant bound-state systems, which do not interact physically
with the non-Hermitian scattering potential, should not be affected. We analyze
a model Hamiltonian that supports this contention.Comment: The emphasis has been changed from v1, recognizing that it makes
physical sense that the wave functions of scattering states are fundamentally
changed in the quasi-Hermitian framework. In contrast, bound states should
not be significantly affected by the introduction of a distant non-Hermitian
scattering potentia
Hit or Miss? The Effect of Assassinations on Institutions and War
Assassinations are a persistent feature of the political landscape. Using a new data set of assassination attempts on all world leaders from 1875 to 2004, we exploit inherent randomness in the success or failure of assassination attempts to identify assassination's effects. We find that, on average, successful assassinations of autocrats produce sustained moves toward democracy. We also find that assassinations affect the intensity of small-scale conflicts. The results document a contemporary source of institutional change, inform theories of conflict, and show that small sources of randomness can have a pronounced effect on history.
The Anatomy of Start-Stop Growth
This paper investigates the remarkable extremes of growth experiences within countries and examines the changes that occur when growth starts and stops. We find three main results. First, all but the very richest countries experience both growth miracles and failures over substantial periods. Second, growth accounting reveals that physical capital accumulation plays a negligible role in growth take-offs and a larger but still modest role in growth collapses. The implied role of productivity in these shifts is also directly reflected in employment reallocations and changes in trade. Third, growth accelerations and collapses are asymmetric phenomena. Collapses typically feature reduced manufacturing and investment amidst increasing price instability, whereas growth takeoffs are primarily associated with large and steady expansions in international trade. This asymmetry suggests that the roads into and out of rapid growth expansions may not be the same. The results stand in contrast to much growth theory and conventional wisdom: despite much talk of poverty traps, even very poor countries regularly grow rapidly, and the role of aggregate investment in growth accelerations is negligible.
Interactions of Hermitian and non-Hermitian Hamiltonians
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian
Hamiltonians, each of which individually has a real energy spectrum, is
explored by means of a number of soluble models. It is found that in all cases
the energy remains real for small values of the coupling constant, but becomes
complex if the coupling becomes stronger than some critical value. For a
quadratic non-Hermitian PT-symmetric Hamiltonian coupled to an arbitrary real
Hermitian PT-symmetric Hamiltonian, the reality of the ground-state energy for
small enough coupling constant is established up to second order in
perturbation theory.Comment: 9 pages, 0 figure
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