7,208 research outputs found
Commuting Position and Momentum Operators, Exact Decoherence and Emergent Classicality
Inspired by an old idea of von Neumann, we seek a pair of commuting operators
X,P which are, in a specific sense, "close" to the canonical non-commuting
position and momentum operators, x,p. The construction of such operators is
related to the problem of finding complete sets of orthonormal phase space
localized states, a problem severely constrained by the Balian-Low theorem.
Here these constraints are avoided by restricting attention to situations in
which the density matrix is reasonably decohered (i.e., spread out in phase
space). Commuting position and momentum operators are argued to be of use in
discussions of emergent classicality from quantum mechanics. In particular,
they may be used to give a discussion of the relationship between exact and
approximate decoherence in the decoherent histories approach to quantum theory.Comment: 28 pages, RevTe
Decoherence of Histories and Hydrodynamic Equations for a Linear Oscillator Chain
We investigate the decoherence of histories of local densities for linear
oscillators models. It is shown that histories of local number, momentum and
energy density are approximately decoherent, when coarse-grained over
sufficiently large volumes. Decoherence arises directly from the proximity of
these variables to exactly conserved quantities (which are exactly decoherent),
and not from environmentally-induced decoherence. We discuss the approach to
local equilibrium and the subsequent emergence of hydrodynamic equations for
the local densities.Comment: 37 pages, RevTe
Quantum Backflow States from Eigenstates of the Regularized Current Operator
We present an exhaustive class of states with quantum backflow -- the
phenomenon in which a state consisting entirely of positive momenta may have
negative current and the probability flows in the opposite direction to the
momentum. They are characterized by a general function of momenta subject to
very weak conditions. Such a family of states is of interest in the light of a
recent experimental proposal to measure backflow. We find one particularly
simple state which has surprisingly large backflow -- about 41 percent of the
lower bound on flux derived by Bracken and Melloy. We study the eigenstates of
a regularized current operator and we show how some of these states, in a
certain limit, lead to our class of backflow states. This limit also clarifies
the correspondence between the spectrum of the regularized current operator,
which has just two non-zero eigenvalues in our chosen regularization, and the
usual current operator.Comment: 16 pages, 2 figure
The role of the quantum properties of gravitational radiation in the dete ction of gravitational waves
The role that the quantum properties of a gravitational wave could play in
the detection of gravitational radiation is analyzed. It is not only
corroborated that in the current laser-interferometric detectors the resolution
of the experimental apparatus could lie very far from the corresponding quantum
threshold (thus the backreaction effect of the measuring device upon the
gravitational wave is negligible), but it is also suggested that the
consideration of the quantum properties of the wave could entail the definition
of dispersion of the measurement outputs. This dispersion would be a function
not only of the sensitivity of the measuring device, but also of the
interaction time (between measuring device and gravitational radiation) and of
the arm length of the corresponding laser- interferometer. It would have a
minimum limit, and the introduction of the current experimental parameters
insinuates that the dispersion of the existing proposals could lie very far
from this minimum, which means that they would show a very large dispersion.Comment: 19 pages, Latex (use epsfig.sty
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