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We theoretically study the local density of states in superconductingproximity structure where two superconducting terminals are attached to a sidesurface of a normal-metal wire. Using the quasiclassical Green's functionmethod, the energy spectrum is obtained for both of spin-singlet $s$-wave andspin-triplet $p$-wave junctions. In both of the cases, the decay length of theproximity effect at the zero temperature is limited by a depairing effect dueto inelastic scatterings. In addition to the depairing effect, in $p$-wavejunctions, the decay length depends sensitively on the transparency at thejunction interfaces, which is a unique property to odd-parity superconductorswhere the anomalous proximity effect occurs.

Effects of the phase coherence on the local density of states in superconducting proximity structures