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