5,301 research outputs found
KMS, etc
A general form of the ``Wick rotation'', starting from imaginary-time Green
functions of quantum-mechanical systems in thermal equilibrium at positive
temperature, is established. Extending work of H. Araki, the role of the KMS
condition and of an associated anti-unitary symmetry operation, the ``modular
conjugation'', in constructing analytic continuations of Green functions from
real- to imaginary times, and back, is clarified.
The relationship between the KMS condition for the vacuum with respect to
Lorentz boosts, on one hand, and the spin-statistics connection and the PCT
theorem, on the other hand, in local, relativistic quantum field theory is
recalled.
General results on the reconstruction of local quantum theories in various
non-trivial gravitational backgrounds from ``Euclidian amplitudes'' are
presented. In particular, a general form of the KMS condition is proposed and
applied, e.g., to the Unruh- and the Hawking effects.
This paper is dedicated to Huzihiro Araki on the occasion of his seventieth
birthday, with admiration, affection and best wishes.Comment: 56 pages, submitted to J. Math. Phy
Polaron action for multimode dispersive phonon systems
Path-integral approach to the tight-binding polaron is extended to multiple
optical phonon modes of arbitrary dispersion and polarization. The non-linear
lattice effects are neglected. Only one electron band is considered. The
electron-phonon interaction is of the density-displacement type, but can be of
arbitrary spatial range and shape. Feynman's analytical integration of ion
trajectories is performed by transforming the electron-ion forces to the basis
in which the phonon dynamical matrix is diagonal. The resulting polaron action
is derived for the periodic and shifted boundary conditions in imaginary time.
The former can be used for calculating polaron thermodynamics while the latter
for the polaron mass and spectrum. The developed formalism is the analytical
basis for numerical analysis of such models by path-integral Monte Carlo
methods.Comment: 9 page
Stellar evolution of massive stars at very low metallicities
Recently, measurements of abundances in extremely metal poor (EMP) stars have
brought new constraints on stellar evolution models. In an attempt to explain
the origin of the abundances observed, we computed pre--supernova evolution
models, explosion models and the related nucleosynthesis. In this paper, we
start by presenting the pre-SN models of rotating single stars with
metallicities ranging from solar metallicity down to almost metal free. We then
review key processes in core-collapse and bounce, before we integrate them in a
simplistic parameterization for 3D MHD models, which are well underway and
allow one to follow the evolution of the magnetic fields during collapse and
bounce. Finally, we present explosive nucleosynthesis results including
neutrino interactions with matter, which are calculated using the outputs of
the explosion models.
The main results of the pre-SN models are the following. First, primary
nitrogen is produced in large amount in models with an initial metallicity
. Second, at the same metallicity of and for models with
an initial mass larger than about 60 Mo, rotating models may experience heavy
mass loss (up to more than half of the initial mass of the star). The chemical
composition of these winds can qualitatively reproduce the abundance patterns
observed at the surface of carbon-rich EMP stars. Explosive nucleosynthesis
including neutrino-matter interactions produce improved abundances for iron
group elements, in particular for scandium and zinc. It also opens the way to a
new neutrino and proton rich process (p-process) able to contribute to the
nucleosynthesis of elements with A > 64. (Abridged)Comment: 29 pages, 10 figures, Reviews of Modern Astronomy 19, proceedings for
79th Annual Scientific Meeting of the Deutsche Astronomische Gesellschaft
200
Stochastically positive structures on Weyl algebras. The case of quasi-free states
We consider quasi-free stochastically positive ground and thermal states on
Weyl algebras in Euclidean time formulation. In particular, we obtain a new
derivation of a general form of thermal quasi-free state and give conditions
when such state is stochastically positive i.e. when it defines periodic
stochastic process with respect to Euclidean time, so called thermal process.
Then we show that thermal process completely determines modular structure
canonically associated with quasi-free state on Weyl algebra. We discuss a
variety of examples connected with free field theories on globally hyperbolic
stationary space-times and models of quantum statistical mechanics.Comment: 46 pages, amste
Long-range magnetic fields in the ground state of the Standard Model plasma
In thermal equilibrium the ground state of the plasma of Standard Model
particles is determined by temperature and exactly conserved combinations of
baryon and lepton numbers. We show that at non-zero values of the global
charges a translation invariant and homogeneous state of the plasma becomes
unstable and the system transits into a new state, containing a large-scale
magnetic field. The origin of this effect is the parity-breaking character of
weak interactions and chiral anomaly. This situation can occur in the early
Universe and may play an important role in its subsequent evolution.Comment: 6 pages. Comments are welcom
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
Expression and alternative splicing of the neural cell adhesion molecule NCAM in human granulosa cells during luteinization
Freshly aspirated human granulosa cells from pre-ovulatory follicles and granulosa cells luteinized in culture possess the neural cell adhesion molecule (NCAM) of approximate molecular mass of 140,000 and NCAM mRNA as confirmed by S1-nuclease protection assays and RT-PCR. Moreover, in the process of luteinization the NCAM isoform pattern is modified. Isoforms containing an insert of 10 amino acids (termed VASE) in the extracellular domain of NCAM were supplemented by alternatively spliced isoforms without this insert. NCAM immunoreactivity, at light and electron microscope levels, was associated with the cell membrane of most granulosa cells which formed clusters. During time in culture an increasing subpopulation of granulosa cells, devoid of NCAM immunoreactivity, spread out and formed monolayers. This differential expression and the alternative splicing of NCAM during luteinization of granulosa cells raise the possibility that NCAM could be involved in folliculogenesis and the formation of the corpus luteum in the human
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