6,338 research outputs found
How much complementarity?
Bohr placed complementary bases at the mathematical centre point of his view
of quantum mechanics. On the technical side then my question translates into
that of classifying complex Hadamard matrices. Recent work (with Barros e Sa)
shows that the answer depends heavily on the prime number decomposition of the
Hilbert space. By implication so does the geometry of quantum state space.Comment: 6 pages; talk at the Vaxjo conference on Foundations of Probability
and Physics, 201
A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples
We enumerate all circulant good matrices with odd orders divisible by 3 up to
order 70. As a consequence of this we find a previously overlooked set of good
matrices of order 27 and a new set of good matrices of order 57. We also find
that circulant good matrices do not exist in the orders 51, 63, and 69, thereby
finding three new counterexamples to the conjecture that such matrices exist in
all odd orders. Additionally, we prove a new relationship between the entries
of good matrices and exploit this relationship in our enumeration algorithm.
Our method applies the SAT+CAS paradigm of combining computer algebra
functionality with modern SAT solvers to efficiently search large spaces which
are specified by both algebraic and logical constraints
Global Existence of Solutions of the Semiclassical Einstein Equation for Cosmological Spacetimes
We study the solutions of the semiclassical Einstein equation in flat
cosmological spacetimes driven by a massive conformally coupled scalar field.
In particular, we show that it is possible to give initial conditions at finite
time to get a state for the quantum field which gives finite expectation values
for the stress-energy tensor. Furthermore, it is possible to control this
expectation value by means of a global estimate on regular cosmological
spacetimes. The obtained estimates permit to write a theorem about the
existence and uniqueness of the local solutions encompassing both the spacetime
metric and the matter field simultaneously. Finally, we show that one can
always extend local solutions up to a point where the scale factor becomes
singular or the Hubble function reaches a critical value ,
which both correspond to a divergence of the scalar curvature, namely a
spacetime singularity.Comment: 20 pages; corrected reference
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