Abstract
A disordered conductor in which the mean free path for inelastic electron scattering exceeds its size is called mesoscopic. Using the Landauer-Büttiker scattering approach one can express transport quantities in terms of a transfer matrix T which belongs to a non-compact group (Sp(2N,R),SU(N,N), and SO*(4N) for the orthogonal, unitary, and the symplectic transfer matrix ensembles, respectively)1. The evolution of the probability distribution of T with the length of a quasi-one-dimensional wire can be described as diffusion on the coset spaces of these groups. It is known that the semi-classical approximation for the path integral which describes diffusion on compact group manifolds is exact. Is this also true for these non-compact coset spaces?
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References
M. Caselle, Nucl. Phys. B S45A, 120 (1996)
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Endesfelder, D. (1997). Exactness of the Semi-Classical Approximation for Diffusion on Non-Compact Coset Spaces?. In: DeWitt-Morette, C., Cartier, P., Folacci, A. (eds) Functional Integration. NATO ASI Series, vol 361. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0319-8_19
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DOI: https://doi.org/10.1007/978-1-4899-0319-8_19
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