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Open Quantum Systems Decoherence
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Does the complex deformation of the Riemann equation exhibit shocks?
arXiv
Authors: Carl M. Bender, Joshua Feinberg
Year
2007
Paper ID
49052
Status
Preprint
Abstract Read
~2 min
Abstract Words
71
Citations
N/A
Abstract
The Riemann equation ut+uux=0, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is cPcT symmetric. A one-parameter cPcT-invariant complex deformation of this equation, ut-iu\(iux\)^ε= 0 (ε real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless ε is an odd integer.
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- The Riemann equation ut+uux=0, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time.
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