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We consider a ballistic Mach-Zehnder interferometer for electrons propagatingchirally in one dimension (such as in an integer Quantum Hall effect edgechannel). In such a system, dephasing occurs when the finite range of theinteraction potential is taken into account. Using the tools of bosonization,we discuss the decay of coherence as a function of propagation distance andenergy. We supplement the exact solution by a semiclassical approach that isphysically transparent and is exact at high energies. In particular, we studyin more detail the recently predicted universal power-law decay of thecoherence at high energies, where the exponent does not depend on theinteraction strength. In addition, we compare against Keldysh perturbationtheory, which works well for small interaction strength at short propagationdistances.

Dephasing by electron-electron interactions in a ballistic Mach-Zehnder interferometer