6,800 research outputs found
Equilibrium Statistical Mechanics of Fermion Lattice Systems
We study equilibrium statistical mechanics of Fermion lattice systems which
require a different treatment compared with spin lattice systems due to the
non-commutativity of local algebras for disjoint regions.
Our major result is the equivalence of the KMS condition and the variational
principle with a minimal assumption for the dynamics and without any explicit
assumption on the potential. It holds also for spin lattice systems as well,
yielding a vast improvement over known results.
All formulations are in terms of a C*-dynamical systems for the Fermion (CAR)
algebra with all or a part of the following assumptions:
(I) The interaction is even with respect to the Fermion number.
(Automatically satisfied when (IV) below is assumed.)
(II) All strictly local elements of the algebra have the first time
derivative.
(III) The time derivatives in (II) determine the dynamics.
(IV) The interaction is lattice translation invariant.
A major technical tool is the conditional expectation from the total algebra
onto the local subalgebra for any finite subset of the lattice, which induces a
system of commuting squares. This technique overcomes the lack of tensor
product structures for Fermion systems and even simplifies many known arguments
for spin lattice systems.Comment: 103 pages, no figure. The Section 13 has become simpler and a problem
in 14.1 is settled thanks to a referee. The format has been revised according
to the suggestion of this and the other referee
Neutral Particles and Super Schwinger Terms
Z_2-graded Schwinger terms for neutral particles in 1 and 3 space dimensions
are considered.Comment: 13 page
Magnetic flares in the protoplanetary nebula and the origin of meteorite chondrules
This study proposes and analyzes a model for the chondrule forming heating events based on magnetohydrodynamic flares in the corona of the protoplanetary nebula which precipitate energy in the form of energetic plasma along magnetic field lines down toward the face of the nebula. It is found that flare energy release rates sufficient to melt the prechondrular matter, leading to the formation of the chondrules, can occur in the tenuous corona of a protostellar disk. Energy release rates sufficient to achieve melting require that the ambient magnetic field strength be in the range that has been inferred separately from independent meteorite remanent magnetization studies
Out of equilibrium correlations in the XY chain
We study the transversal XY spin-spin correlations in the non-equilibrium
steady state constructed in \cite{AP03} and prove their spatial exponential
decay close to equilibrium
Maximally entangled fermions
Fermions play an essential role in many areas of quantum physics and it is
desirable to understand the nature of entanglement within systems that consists
of fermions. Whereas the issue of separability for bipartite fermions has
extensively been studied in the present literature, this paper is concerned
with maximally entangled fermions. A complete characterization of maximally
entangled quasifree (gaussian) fermion states is given in terms of the
covariance matrix. This result can be seen as a step towards distillation
protocols for maximally entangled fermions.Comment: 13 pages, 1 figure, RevTex, minor errors are corrected, section
"Conclusions" is adde
Trace functions as Laplace transforms
We study trace functions on the form t\to\tr f(A+tB) where is a
real function defined on the positive half-line, and and are
matrices such that is positive definite and is positive
semi-definite. If is non-negative and operator monotone decreasing, then
such a trace function can be written as the Laplace transform of a positive
measure. The question is related to the Bessis-Moussa-Villani conjecture.
Key words: Trace functions, BMV-conjecture.Comment: Minor change of style, update of referenc
Structural and dynamical heterogeneities in two-dimensional melting
Using molecular dynamics simulation, we study structural and dynamical
heterogeneities at melting in two-dimensional one-component systems with 36000
particles. Between crystal and liquid we find intermediate hexatic states,
where the density fluctuations are enhanced at small wave number k as well as
those of the six-fold orientational order parameter. Their structure factors
both grow up to the smallest wave number equal to the inverse system length.
The intermediate scattering function of the density S(k,t) is found to relax
exponentially with decay rate Gamma_k ~ k^z with z~2.6 at small k in the
hexatic phase.Comment: 6 pages, 8 figure
Broken translation invariance in quasifree fermionic correlations out of equilibrium
Using the C* algebraic scattering approach to study quasifree fermionic
systems out of equilibrium in quantum statistical mechanics, we construct the
nonequilibrium steady state in the isotropic XY chain whose translation
invariance has been broken by a local magnetization and analyze the asymptotic
behavior of the expectation value for a class of spatial correlation
observables in this state. The effect of the breaking of translation invariance
is twofold. Mathematically, the finite rank perturbation not only regularizes
the scalar symbol of the invertible Toeplitz operator generating the leading
order exponential decay but also gives rise to an additional trace class Hankel
operator in the correlation determinant. Physically, in its decay rate, the
nonequilibrium steady state exhibits a left mover--right mover structure
affected by the scattering at the impurity.Comment: 30 pages, 4 figure
Edge modes in band topological insulators
We characterize gapless edge modes in translation invariant topological
insulators. We show that the edge mode spectrum is a continuous deformation of
the spectrum of a certain gluing function defining the occupied state bundle
over the Brillouin zone (BZ). Topologically non-trivial gluing functions,
corresponding to non-trivial bundles, then yield edge modes exhibiting spectral
flow. We illustrate our results for the case of chiral edge states in two
dimensional Chern insulators, as well as helical edges in quantum spin Hall
states.Comment: 4 pages, 2 figures; v4 minor change
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