2,306 research outputs found
Stabilizing Non-Hermitian Systems by Periodic Driving
The time evolution of a system with a time-dependent non-Hermitian
Hamiltonian is in general unstable with exponential growth or decay. A periodic
driving field may stabilize the dynamics because the eigenphases of the
associated Floquet operator may become all real. This possibility can emerge
for a continuous range of system parameters with subtle domain boundaries. It
is further shown that the issue of stability of a driven non-Hermitian Rabi
model can be mapped onto the band structure problem of a class of lattice
Hamiltonians. As an application, we show how to use the stability of driven
non-Hermitian two-level systems (0-dimension in space) to simulate a spectrum
analogous to Hofstadter's butterfly that has played a paradigmatic role in
quantum Hall physics. The simulation of the band structure of non-Hermitian
superlattice potentials with parity-time reversal symmetry is also briefly
discussed
Dynamical quantum phase transitions in non-Hermitian lattices
In closed quantum systems, a dynamical phase transition is identified by
nonanalytic behaviors of the return probability as a function of time. In this
work, we study the nonunitary dynamics following quenches across exceptional
points in a non-Hermitian lattice realized by optical resonators. Dynamical
quantum phase transitions with topological signatures are found when an
isolated exceptional point is crossed during the quench. A topological winding
number defined by a real, noncyclic geometric phase is introduced, whose value
features quantized jumps at critical times of these phase transitions and
remains constant elsewhere, mimicking the plateau transitions in quantum Hall
effects. This work provides a simple framework to study dynamical and
topological responses in non-Hermitian systems.Comment: 7 pages, 5 figure
The physics of large-scale food crises
Investigating the ``physics'' of food crises consists in identifying features
which are common to all large-scale food crises. One element which stands out
is the fact that during a food crisis there is not only a surge in deaths but
also a correlative temporary decline in conceptions and subsequent births. As a
matter of fact, birth reduction may even start several months before the death
surge and can therefore serve as an early warning signal of an impending
crisis. This scenario is studied in three cases of large-scale food crises.
Finland (1868), India (1867--1907), China (1960--1961). It turns out that
between the regional amplitudes of death spikes and birth troughs there is a
power law relationship. This confirms what was already observed for the
epidemic of 1918 in the United States (Richmond et al. 2018b). In a second part
of the paper we explain how this relationship can be used for the investigation
of mass-mortality episodes in cases where direct death data are either
uncertain or nonexistent.Comment: 29 pages, 11 figure
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