8,112 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
A tight analysis of Kierstead-Trotter algorithm for online unit interval coloring
Kierstead and Trotter (Congressus Numerantium 33, 1981) proved that their
algorithm is an optimal online algorithm for the online interval coloring
problem. In this paper, for online unit interval coloring, we show that the
number of colors used by the Kierstead-Trotter algorithm is at most , where is the size of the maximum clique in a given
graph , and it is the best possible.Comment: 4 page
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
Entropy growth of shift-invariant states on a quantum spin chain
We study the entropy of pure shift-invariant states on a quantum spin chain.
Unlike the classical case, the local restrictions to intervals of length
are typically mixed and have therefore a non-zero entropy which is,
moreover, monotonically increasing in . We are interested in the asymptotics
of the total entropy. We investigate in detail a class of states derived from
quasi-free states on a CAR algebra. These are characterised by a measurable
subset of the unit interval. As the entropy density is known to vanishes,
is sublinear in . For states corresponding to unions of finitely many
intervals, is shown to grow slower than . Numerical
calculations suggest a behaviour. For the case with infinitely many
intervals, we present a class of states for which the entropy increases
as where can take any value in .Comment: 18 pages, 2 figure
The - divergence and Mixing times of quantum Markov processes
We introduce quantum versions of the -divergence, provide a detailed
analysis of their properties, and apply them in the investigation of mixing
times of quantum Markov processes. An approach similar to the one presented in
[1-3] for classical Markov chains is taken to bound the trace-distance from the
steady state of a quantum processes. A strict spectral bound to the convergence
rate can be given for time-discrete as well as for time-continuous quantum
Markov processes. Furthermore the contractive behavior of the
-divergence under the action of a completely positive map is
investigated and contrasted to the contraction of the trace norm. In this
context we analyse different versions of quantum detailed balance and, finally,
give a geometric conductance bound to the convergence rate for unital quantum
Markov processes
Universal fermionization of bosons on permutative representations of the Cuntz algebra
Bosons and fermions are described by using canonical generators of Cuntz
algebras on any permutative representation. We show a fermionization of bosons
which universally holds on any permutative representation of the Cuntz algebra
. As examples, we show fermionizations on the Fock space and the
infinite wedge.Comment: 12 page
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