3,147 research outputs found
Everett's Theory of the Universal Wave Function
This is a tutorial for the many-worlds theory by Everett, which includes some
of my personal views. It has two main parts.The first main part shows the
emergence of many worlds in a universe consisting of only a Mach-Zehnder
interferometer. The second main part is an abridgment of Everett's long thesis,
where his theory was originally elaborated in detail with clarity and rigor.
Some minor comments are added in the abridgment in light of recent
developments. Even if you do not agree to Everett's view, you will still learn
a great deal from his generalization of the uncertainty relation, his unique
way of defining entanglement (or canonical correlation), his formulation of
quantum measurement using Hamiltonian, and his relative state.Comment: 18 pages, 3 figure
On the Bahadur representation of sample quantiles for dependent sequences
We establish the Bahadur representation of sample quantiles for linear and
some widely used nonlinear processes. Local fluctuations of empirical processes
are discussed. Applications to the trimmed and Winsorized means are given. Our
results extend previous ones by establishing sharper bounds under milder
conditions and thus provide new insight into the theory of empirical processes
for dependent random variables.Comment: Published at http://dx.doi.org/10.1214/009053605000000291 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
M-estimation of linear models with dependent errors
We study asymptotic properties of -estimates of regression parameters in
linear models in which errors are dependent. Weak and strong Bahadur
representations of the -estimates are derived and a central limit theorem is
established. The results are applied to linear models with errors being
short-range dependent linear processes, heavy-tailed linear processes and some
widely used nonlinear time series.Comment: Published at http://dx.doi.org/10.1214/009053606000001406 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Ehrenfest breakdown of the mean-field dynamics of Bose gases
The mean-field dynamics of a Bose gas is shown to break down at time where is the Lyapunov exponent of the mean-field
theory, is the number of bosons, and is a system-dependent constant.
The breakdown time is essentially the Ehrenfest time that
characterizes the breakdown of the correspondence between classical and quantum
dynamics. This breakdown can be well described by the quantum fidelity defined
for reduced density matrices. Our results are obtained with the formalism in
particle-number phase space and are illustrated with a triple-well model. The
logarithmic quantum-classical correspondence time may be verified
experimentally with Bose-Einstein condensates.Comment: 6 pages, 4 figure
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