88 research outputs found
Uncertainty in prediction and in inference
The concepts of uncertainty in prediction and inference are introduced
and illustrated using the diffraction of light as an example. The close re-lationship
between the concepts of uncertainty in inference and resolving
power is noted. A general quantitative measure of uncertainty in infer-ence
can be obtained by means of the so-called statistical distance between
probability distributions. When applied to quantum mechanics, this dis-tance
leads to a measure of the distinguishability of quantum states, which
essentially is the absolute value of the matrix element between the states.
The importance of this result to the quantum mechanical uncertainty prin-ciple
is noted. The second part of the paper provides a derivation of the
statistical distance on basis of the so-called method of support
A transport coefficient: the electrical conductivity
I describe the lattice determination of the electrical conductivity of the
quark gluon plasma. Since this is the first extraction of a transport
coefficient with a degree of control over errors, I next use this to make
estimates of other transport related quantities using simple kinetic theory
formulae. The resulting estimates are applied to fluctuations, ultra-soft
photon spectra and the viscosity. Dimming of ultra-soft photons is exponential
in the mean free path, and hence is a very sensitive probe of transport.Comment: Talk given in ICPAQGP 2005, SINP, Kolkat
PMH14 HEALTH CARE EXPENDITURES OF PATIENTS WITH MAJOR DEPRESSIVE DISORDER AND POST TRAUMATIC STRESS DISORDER
A computer model is presented that describes soleus H-reflex recruitment as a function of electric stimulus intensity. The model consists of two coupled non-linear transfer functions. The first transfer function describes the activation of muscle spindle (Ia) afferent terminals as a function of the electric stimulus intensity; whereas the second describes the activation of a number of motoneurons as a function of the number of active Ia afferent terminals. The effect of change in these transfer functions on the H-reflex recruitment curve is simulated. In spastic patients, a higher average maximal H-response amplitude is observed in combination with a decreased H-reflex threshold. Vibration of the Achilles tendon reduces the H-reflex amplitude, presumably by reducing the excitatory afferent input. Vibratory inhibition is diminished in spasticity. In the model, the afferent-motoneuron transfer function was modified to represent the possible alterations occurring in spasticity. The simulations show that vibratory suppression of the H-reflex is determined only in part by the inhibition level of the afferent input. With a constant level of presynaptic inhibition, the suppression of reflexes of different sizes may vary. A lowering of the motoneuron activation thresholds in spastic patients will directly contribute to a decrease of vibratory inhibition in spasticit
The Time-Energy Uncertainty Relation
The time energy uncertainty relation has been a controversial issue since the
advent of quantum theory, with respect to appropriate formalisation, validity
and possible meanings. A comprehensive account of the development of this
subject up to the 1980s is provided by a combination of the reviews of Jammer
(1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are
concerned with different specific aspects of the subject. The purpose of this
chapter is to show that different types of time energy uncertainty relation can
indeed be deduced in specific contexts, but that there is no unique universal
relation that could stand on equal footing with the position-momentum
uncertainty relation. To this end, we will survey the various formulations of a
time energy uncertainty relation, with a brief assessment of their validity,
and along the way we will indicate some new developments that emerged since the
1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition
of "Time in quantum mechanics") contains minor corrections, new examples and
pointers to some additional relevant literatur
Control of quantum interference in the quantum eraser
We have implemented an optical quantum eraser with the aim of studying this
phenomenon in the context of state discrimination. An interfering single photon
is entangled with another one serving as a which-path marker. As a consequence,
the visibility of the interference as well as the which-path information are
constrained by the overlap (measured by the inner product) between the
which-path marker states, which in a more general situation are non-orthogonal.
In order to perform which-path or quantum eraser measurements while analyzing
non-orthogonal states, we resort to a probabilistic method for the unambiguous
modification of the inner product between the two states of the which-path
marker in a discrimination-like process.Comment: Submitted to New Journal of Physics, March 200
Time of arrival in the presence of interactions
We introduce a formalism for the calculation of the time of arrival t at a
space point for particles traveling through interacting media. We develop a
general formulation that employs quantum canonical transformations from the
free to the interacting cases to construct t in the context of the Positive
Operator Valued Measures. We then compute the probability distribution in the
times of arrival at a point for particles that have undergone reflection,
transmission or tunneling off finite potential barriers. For narrow Gaussian
initial wave packets we obtain multimodal time distributions of the reflected
packets and a combination of the Hartman effect with unexpected retardation in
tunneling. We also employ explicitly our formalism to deal with arrivals in the
interaction region for the step and linear potentials.Comment: 20 pages including 5 eps figure
A closer look at the uncertainty relation of position and momentum
We consider particles prepared by the von Neumann-L\"uders projection. For
those particles the standard deviation of the momentum is discussed. We show
that infinite standard deviations are not exceptions but rather typical. A
necessary and sufficient condition for finite standard deviations is given.
Finally, a new uncertainty relation is derived and it is shown that the latter
cannot be improved.Comment: 3 pages, introduction shortened, content unchange
Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process
The accuracy of the Arthurs-Kelly model of a simultaneous measurement of
position and momentum is analysed using concepts developed by Braginsky and
Khalili in the context of measurements of a single quantum observable. A
distinction is made between the errors of retrodiction and prediction. It is
shown that the distribution of measured values coincides with the initial state
Husimi function when the retrodictive accuracy is maximised, and that it is
related to the final state anti-Husimi function (the P representation of
quantum optics) when the predictive accuracy is maximised. The disturbance of
the system by the measurement is also discussed. A class of minimally
disturbing measurements is characterised. It is shown that the distribution of
measured values then coincides with one of the smoothed Wigner functions
described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final
published versio
Time in Quantum Mechanics and Quantum Field Theory
W. Pauli pointed out that the existence of a self-adjoint time operator is
incompatible with the semibounded character of the Hamiltonian spectrum. As a
result, people have been arguing a lot about the time-energy uncertainty
relation and other related issues. In this article, we show in details that
Pauli's definition of time operator is erroneous in several respects.Comment: 20 page
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