3,106 research outputs found
Adaiabtic theorems and reversible isothermal processes
Isothermal processes of a finitely extended, driven quantum system in contact
with an infinite heat bath are studied from the point of view of quantum
statistical mechanics. Notions like heat flux, work and entropy are defined for
trajectories of states close to, but distinct from states of joint thermal
equilibrium. A theorem characterizing reversible isothermal processes as
quasi-static processes (''isothermal theorem'') is described. Corollaries
concerning the changes of entropy and free energy in reversible isothermal
processes and on the 0th law of thermodynamics are outlined
Spin - or, actually: Spin and Quantum Statistics
The history of the discovery of electron spin and the Pauli principle and the
mathematics of spin and quantum statistics are reviewed. Pauli's theory of the
spinning electron and some of its many applications in mathematics and physics
are considered in more detail. The role of the fact that the tree-level
gyromagnetic factor of the electron has the value g = 2 in an analysis of
stability (and instability) of matter in arbitrary external magnetic fields is
highlighted. Radiative corrections and precision measurements of g are
reviewed. The general connection between spin and statistics, the CPT theorem
and the theory of braid statistics are described.Comment: 50 pages, no figures, seminar on "spin
Absence of spontaneous magnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactions
The Mermin-Wagner theorem is strengthened so as to rule out magnetic
long-range order at T>0 in one- or two-dimensional Heisenberg and XY systems
with long-range interactions decreasing as R^{-alpha} with a sufficiently large
exponent alpha. For oscillatory interactions, ferromagnetic long-range order at
T>0 is ruled out if alpha >= 1 (D=1) or alpha > 5/2 (D=2). For systems with
monotonically decreasing interactions ferro- or antiferromagnetic long-range
order at T>0 is ruled out if alpha >= 2D.Comment: RevTeX, 4 pages. Further (p)reprints available from
http://www.mpi-halle.de/~theory ; v2: revised versio
Spectral and Localization Properties for the One-Dimensional Bernoulli Discrete Dirac Operator
A 1D Dirac tight-binding model is considered and it is shown that its
nonrelativistic limit is the 1D discrete Schr?odinger model. For random
Bernoulli potentials taking two values (without correlations), for typical
realizations and for all values of the mass, it is shown that its spectrum is
pure point, whereas the zero mass case presents dynamical delocalization for
specific values of the energy. The massive case presents dynamical localization
(excluding some particular values of the energy). Finally, for general
potentials the dynamical moments for distinct masses are compared, especially
the massless and massive Bernoulli cases.Comment: no figure; 24 pages; to appear in Journal of Mathematical Physic
The Spin-Statistics Theorem for Anyons and Plektons in d=2+1
We prove the spin-statistics theorem for massive particles obeying braid
group statistics in three-dimensional Minkowski space. We start from first
principles of local relativistic quantum theory. The only assumption is a gap
in the mass spectrum of the corresponding charged sector, and a restriction on
the degeneracy of the corresponding mass.Comment: 21 pages, 2 figures. Citation added; Minor modifications of Appendix
A model with simultaneous first and second order phase transitions
We introduce a two dimensional nonlinear XY model with a second order phase
transition driven by spin waves, together with a first order phase transition
in the bond variables between two bond ordered phases, one with local
ferromagnetic order and another with local antiferromagnetic order. We also
prove that at the transition temperature the bond-ordered phases coexist with a
disordered phase as predicted by Domany, Schick and Swendsen. This last result
generalizes the result of Shlosman and van Enter (cond-mat/0205455). We argue
that these phenomena are quite general and should occur for a large class of
potentials.Comment: 7 pages, 7 figures using pstricks and pst-coi
The Conformal Spin and Statistics Theorem
We prove the equality between the statistics phase and the conformal
univalence for a superselection sector with finite index in Conformal Quantum
Field Theory on . A relevant point is the description of the PCT symmetry
and the construction of the global conjugate charge.Comment: plain tex, 22 page
Non-Gaussian statistics of electrostatic fluctuations of hydration shells
We report the statistics of electric field fluctuations produced by SPC/E
water inside a Kihara solute given as a hard-sphere core with a Lennard-Jones
layer at its surface. The statistics of electric field fluctuations, obtained
from numerical simulations, are studied as a function of the magnitude of a
point dipole placed close to the solute-water interface. The free energy
surface as a function of the electric field projected on the dipole direction
shows a cross-over with the increasing dipole magnitude. While it is a
single-well harmonic function at low dipole values, it becomes a double-well
surface at intermediate dipole moment magnitudes, transforming to a single-well
surface, with a non-zero minimum position, at still higher dipoles. A broad
intermediate region where the interfacial waters fluctuate between the two
minima is characterized by intense field fluctuations, with non-Gaussian
statistics and the variance far exceeding the linear-response expectations. The
excited state of the surface water is found to be lifted above the ground state
by the energy required to break approximately two hydrogen bonds. This state is
pulled down in energy by the external electric field of the solute dipole,
making it readily accessible to thermal excitations. The excited state is a
localized surface defect in the hydrogen-bond network creating a stress in the
nearby network, but otherwise relatively localized in the region closest to the
solute dipole
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