20,691 research outputs found
Harish-Chandra integrals as nilpotent integrals
Recently the correlation functions of the so-called
Itzykson-Zuber/Harish-Chandra integrals were computed (by one of the authors
and collaborators) for all classical groups using an integration formula that
relates integrals over compact groups with respect to the Haar measure and
Gaussian integrals over a maximal nilpotent Lie subalgebra of their
complexification. Since the integration formula a posteriori had the same form
for the classical series, a conjecture was formulated that such a formula
should hold for arbitrary semisimple Lie groups. We prove this conjecture using
an abstract Lie-theoretic approach.Comment: 10 page
2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals
We prove that the 2-hermitean matrix model and the complex-matrix model obey
the same loop equations, and as a byproduct, we find a formula for
Itzykzon-Zuber's type integrals over the unitary group. Integrals over U(n) are
rewritten as gaussian integrals over triangular matrices and then computed
explicitly. That formula is an efficient alternative to the former
Shatashvili's formula.Comment: 29 pages, Late
Mobility of Bloch Walls via the Collective Coordinate Method
We have studied the problem of the dissipative motion of Bloch walls
considering a totally anisotropic one dimensional spin chain in the presence of
a magnetic field. Using the so-called "collective coordinate method" we
construct an effective Hamiltonian for the Bloch wall coupled to the magnetic
excitations of the system. It allows us to analyze the Brownian motion of the
wall in terms of the reflection coefficient of the effective potential felt by
the excitations due to the existence of the wall. We find that for finite
values of the external field the wall mobility is also finite. The spectrum of
the potential at large fields is investigated and the dependence of the damping
constant on temperature is evaluated. As a result we find the temperature and
magnetic field dependence of the wall mobility.Comment: 20 pages, 5 figure
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