What is it about?
Loschmidt Echo concept evolved from precise experiments like the Erwin Hahn's "spin echo", which is an implementation of a quantum "time machine" at atomic level. Because of influence of the sorroundings and experimental imperfection, one can not make the magnetic state of an atom beyond a time scale T2. This time scale is precisely the contrast you see in a Magnetic Resonance Image. The concept of Loschmidt Echo was introduced by Jalabert and Pastawski in 2001, in general this time-scale could be called T3. This article reviews the technical developments since then. In particular it allows to introduce the concept of dynamical chaos in quantum physics where T3 could be identified with the intrinsic instability of the system.
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Why is it important?
Loschmidt Echo is the best way to quantify the "Butterfly effect" in classical and quantum realms. Conceptually it allows compatibilization of classical and quantum realms. Jalabert and Pastawski have probed that quantum 1/T3 is identical to a Lyapunov exponent in classical realm, in cases where this correspondence exist.
Perspectives
Applications of Loschmidt Echo are ubiquitous. You might recheck your long sume by substracting each item an seeing if the result is zero, the same will be valid in any complex calculation. You might prevent deterioration of a stored quantum memory by applying a "time reversal" procedure in intervals shorter than T3. Applications are everywhere.
Professor Horacio M. Pastawski
Instituto de Física Enrique Gaviola- Conicet- Universidad Nacional de Córdoba
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This page is a summary of: Loschmidt echo, Scholarpedia, January 2012, Scholarpedia,
DOI: 10.4249/scholarpedia.11687.
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