58,521 research outputs found
Ordering Events in Minkowski Space
We are given k points (events) in (n+1)-dimensional Minkowski space. Using
the theory of hyperplane arrangments and chromatic polynomials, we obtain
information the number of different orders in which the events can occur in
different reference frames if the events are sufficiently generic. We consider
the question of what sets of orderings of the points are possible and show a
connection with sphere orders and the allowable sequences of Goodman and
Pollack.Comment: 17 page
Alternating subgroups of Coxeter groups
We study combinatorial properties of the alternating subgroup of a Coxeter
group, using a presentation of it due to Bourbaki.Comment: 39 pages, 3 figure
Structure of the thermodynamic arrow of time in classical and quantum theories
In this work we analyse the structure of the thermodynamic arrow of time,
defined by transformations that leave the thermal equilibrium state unchanged,
in classical (incoherent) and quantum (coherent) regimes. We note that in the
infinite-temperature limit the thermodynamic ordering of states in both regimes
exhibits a lattice structure. This means that when energy does not matter and
the only thermodynamic resource is given by information, the thermodynamic
arrow of time has a very specific structure. Namely, for any two states at
present there exists a unique state in the past consistent with them and with
all possible joint pasts. Similarly, there also exists a unique state in the
future consistent with those states and with all possible joint futures. We
also show that the lattice structure in the classical regime is broken at
finite temperatures, i.e., when energy is a relevant thermodynamic resource.
Surprisingly, however, we prove that in the simplest quantum scenario of a
two-dimensional system, this structure is preserved at finite temperatures. We
provide the physical interpretation of these results by introducing and
analysing the history erasure process, and point out that quantum coherence may
be a necessary resource for the existence of an optimal erasure process.Comment: 14 pages, 10 figures. Published version. Expanded discussion and a
new section on history erasure process adde
Fixed points of involutive automorphisms of the Bruhat order
Applying a classical theorem of Smith, we show that the poset property of
being Gorenstein over is inherited by the subposet of fixed
points under an involutive poset automorphism. As an application, we prove that
every interval in the Bruhat order on (twisted) involutions in an arbitrary
Coxeter group has this property, and we find the rank function. This implies
results conjectured by F. Incitti. We also show that the Bruhat order on the
fixed points of an involutive automorphism induced by a Coxeter graph
automorphism is isomorphic to the Bruhat order on the fixed subgroup viewed as
a Coxeter group in its own right.Comment: 16 pages. Appendix added, minor revisions; to appear in Adv. Mat
- …