4,698 research outputs found
A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limit
The original formulation of the Bohr-van Leeuwen (BvL) theorem states that,
in a uniform magnetic field and in thermal equilibrium, the magnetization of an
electron gas in the classical Drude-Lorentz model vanishes identically. This
stems from classical statistics which assign the canonical momenta all values
ranging from to what makes the free energy density
magnetic-field-independent. When considering a classical (Maxwell-Boltzmann)
interacting electron gas, it is usually admitted that the BvL theorem holds
upon condition that the potentials modeling the interactions are
particle-velocities-independent and do not cause the system to rotate after
turning on the magnetic field. From a rigorous viewpoint, when treating large
macroscopic systems one expects the BvL theorem to hold provided the
thermodynamiclimit of the free energy density exists (and the equivalence of
ensemble holds). This requires suitable assumptions on the many-body
interactions potential and on the possible external potentials to prevent the
system from collapsing or flying apart. Starting from quantum statistical
mechanics, the purpose of this article is to give, within the linear-response
theory, a proof of the BvL theorem in the semiclassical limit when considering
a dilute electron gas in the canonical conditions subjected to a class of
translational invariant external potentials.Comment: 50 pages. Revised version. Accepted for publication in R.M.
A rigorous proof of the Landau-Peierls formula and much more
We present a rigorous mathematical treatment of the zero-field orbital
magnetic susceptibility of a non-interacting Bloch electron gas, at fixed
temperature and density, for both metals and semiconductors/insulators. In
particular, we obtain the Landau-Peierls formula in the low temperature and
density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.Comment: 30 pages - Accepted for publication in A.H.
Correlation of clusters: Partially truncated correlation functions and their decay
In this article, we investigate partially truncated correlation functions
(PTCF) of infinite continuous systems of classical point particles with pair
interaction. We derive Kirkwood-Salsburg-type equations for the PTCF and write
the solutions of these equations as a sum of contributions labelled by certain
forests graphs, the connected components of which are tree graphs. We
generalize the method introduced by R.A. Minlos and S.K. Poghosyan (1977) in
the case of truncated correlations. These solutions make it possible to derive
strong cluster properties for PTCF which were obtained earlier for lattice spin
systems.Comment: 31 pages, 2 figures. 2nd revision. Misprints corrected and 1 figure
adde
Macpherson, A. G. et Macpherson, J. B., édit. (1981): The Natural Environment of Newfoundland. Past and Present, Dept. of Geography, Memorial University of Newfoundland, 265 p., 85 fig., 17 x 23 cm, 17,50$.
Aids given to beginning teachers in Rhode Island: their source and their usefulness.
Thesis (Ed.M.)--Boston Universit
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