215 research outputs found
Benford's Law Detects Quantum Phase Transitions similarly as Earthquakes
A century ago, it was predicted that the first significant digit appearing in
a data would be nonuniformly distributed, with the number one appearing with
the highest frequency. This law goes by the name of Benford's law. It holds for
data ranging from infectious disease cases to national greenhouse gas
emissions. Quantum phase transitions are cooperative phenomena where
qualitative changes occur in many-body systems at zero temperature. We show
that the century-old Benford's law can detect quantum phase transitions, much
like it detects earthquakes. Therefore, being certainly of very different
physical origins, seismic activity and quantum cooperative phenomena may be
detected by similar methods. The result has immediate implications in precise
measurements in experiments in general, and for realizable quantum computers in
particular. It shows that estimation of the first significant digit of measured
physical observables is enough to detect the presence of quantum phase
transitions in macroscopic systems.Comment: v1: 3 pages, 2 figures; v2: 6 (+epsilon) epl pages, 5 figures,
significant additions, previous results unchange
Ergodicity from Nonergodicity in Quantum Correlations of Low-dimensional Spin Systems
Correlations between the parts of a many-body system, and its time dynamics,
lie at the heart of sciences, and they can be classical as well as quantum.
Quantum correlations are traditionally viewed as constituted out of classical
correlations and magnetizations. While that of course remains so, we show that
quantum correlations can have statistical mechanical properties like
ergodicity, which is not inherited from the corresponding classical
correlations and magnetizations, for the transverse anisotropic quantum XY
model in one-, two-, and quasi two-dimension, for suitably chosen transverse
fields and temperatures. The results have the potential for applications in
decoherence effects in realizable quantum computers.Comment: 8 pages, 6 figures, RevTeX 4.
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