Conserved quantum probability currents on stochastic phase space

1981 ◽  
Vol 59 (6) ◽  
pp. 807-811 ◽  
Author(s):  
S. T. Ali ◽  
R. Gagnon ◽  
E. Prugovečki
Keyword(s):  
Phase Space ◽  
Probability Density ◽  
Configuration Space ◽  
Continuity Equation ◽  
Quantum Probability ◽  
Space Representation ◽  
Configuration Representation

It is shown that the continuity equation in stochastic phase space is satisfied if the configuration space representation ξ(x) of the resolution generator is real. It is also shown that the probability density and current merge into the standard ones if ξ(n)(x) is a sequence of real resolution generators which converges to the Dirac δ-function for n → x. A relation between the current on Γξ and the stochastic current in configuration representation is also derived.

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

Phase space representation of pseudo oscillator

1969 ◽  
Vol 29 (5) ◽  
pp. 245-246 ◽  
Author(s):  
A.K. Jaiswal ◽  
C.L. Mehta
Keyword(s):  
Phase Space ◽  
Space Representation ◽  
Phase Space Representation

Automated classification of human lung sound signals using phase space representation of intrinsic mode function

2021 ◽  
Author(s):  
Sibghatullah I. Khan ◽  
Vikram Palodiya ◽  
Lavanya Poluboyina
Keyword(s):  
Phase Space ◽  
Human Lung ◽  
Feature Space ◽  
Normal Lung ◽  
Space Representation ◽  
Support Vector ◽  
Lung Sounds ◽  
Lung Sound ◽  
Phase Space Representation

Abstract Bronchiectasis and chronic obstructive pulmonary disease (COPD) are common human lung diseases. In general, the expert pulmonologistcarries preliminary screening and detection of these lung abnormalities by listening to the adventitious lung sounds. The present paper is an attempt towards the automatic detection of adventitious lung sounds ofBronchiectasis,COPD from normal lung sounds of healthy subjects. For classification of the lung sounds into a normaland adventitious category, we obtain features from phase space representation (PSR). At first, the empirical mode decomposition (EMD) is applied to lung sound signals to obtain intrinsic mode functions (IMFs). The IMFs are then further processed to construct two dimensional (2D) and three dimensional (3D) PSR. The feature space includes the 95% confidence ellipse area and interquartile range (IQR) of Euclidian distances computed from 2D and 3D PSRs, respectively. The process is carried out for the first four IMFs correspondings to normal and adventitious lung sound signals. The computed features depicta significant ability to discriminate the two categories of lung sound signals.To perform classification, we use the least square support vector machine with two kernels, namely, polynomial and radial basis function (RBF).Simulation outcomes on ICBHI 2017 lung sound dataset show the ability of the proposed method in effectively classifying normal and adventitious lung sound signals. LS-SVM is employing RBF kernel provides the highest classification accuracy of 97.67 % over feature space constituted by first, second, and fourth IMF.

scholarly journals Predicting the cumulative medical load of COVID-19 outbreaks after the peak in daily fatalities

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0247272
Author(s):  
Claudius Gros ◽  
Roser Valenti ◽  
Lukas Schneider ◽  
Benedikt Gutsche ◽  
Dimitrije Marković
Keyword(s):  
Phase Space ◽  
Sir Model ◽  
Reaction Model ◽  
Space Representation ◽  
Cumulative Number ◽  
Short Term ◽  
Before And After ◽  
The Status ◽  
Short And Long Term

The distinct ways the COVID-19 pandemic has been unfolding in different countries and regions suggest that local societal and governmental structures play an important role not only for the baseline infection rate, but also for short and long-term reactions to the outbreak. We propose to investigate the question of how societies as a whole, and governments in particular, modulate the dynamics of a novel epidemic using a generalization of the SIR model, the reactive SIR (short-term and long-term reaction) model. We posit that containment measures are equivalent to a feedback between the status of the outbreak and the reproduction factor. Short-term reaction to an outbreak corresponds in this framework to the reaction of governments and individuals to daily cases and fatalities. The reaction to the cumulative number of cases or deaths, and not to daily numbers, is captured in contrast by long-term reaction. We present the exact phase space solution of the controlled SIR model and use it to quantify containment policies for a large number of countries in terms of short and long-term control parameters. We find increased contributions of long-term control for countries and regions in which the outbreak was suppressed substantially together with a strong correlation between the strength of societal and governmental policies and the time needed to contain COVID-19 outbreaks. Furthermore, for numerous countries and regions we identified a predictive relation between the number of fatalities within a fixed period before and after the peak of daily fatality counts, which allows to gauge the cumulative medical load of COVID-19 outbreaks that should be expected after the peak. These results suggest that the proposed model is applicable not only for understanding the outbreak dynamics, but also for predicting future cases and fatalities once the effectiveness of outbreak suppression policies is established with sufficient certainty. Finally, we provide a web app (https://itp.uni-frankfurt.de/covid-19/) with tools for visualising the phase space representation of real-world COVID-19 data and for exporting the preprocessed data for further analysis.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Quantum Process ◽  
Hidden Variable ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years, Man’ko and coauthors have successfully reconciled quantum and classic probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely, that mathematically, the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables, and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classic probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic hidden variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. Uncovering this variable confirms the possibility that it could be the stochastic archetype of quantum probability.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Classical Probability ◽  
Quantum Process ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years Man’ko and co-authors have successfully reconciled quantum and classical probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely that mathematically the interference term in the squared amplitude of superposed wavefunctions has the form of a variance of a sum of correlated random variables and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classical probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. This hidden generic variable appears to be such an archetype.

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