scholarly journals Generalized analogs of the Heisenberg uncertainty inequality

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Ashish Bansal ◽  
Ajay Kumar
Keyword(s):  
Heisenberg Uncertainty ◽  
Uncertainty Inequality ◽  
Heisenberg Uncertainty Inequality

Heisenberg uncertainty inequality for certain Lie groups

2019 ◽  
Vol 12 (04) ◽  
pp. 1950065 ◽  
Author(s):  
Kais Smaoui
Keyword(s):  
Lie Groups ◽  
Nilpotent Lie Groups ◽  
Heisenberg Uncertainty ◽  
Motion Groups ◽  
Simply Connected ◽  
Uncertainty Inequality ◽  
Heisenberg Uncertainty Inequality

We establish analogues of Heisenberg uncertainty inequality for some classes of Lie groups, such as connected and simply connected nilpotent Lie groups, diamond Lie groups and Heisenberg motion groups.

scholarly journals On the uncertainty inequality as applied to discrete signals

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
Y. V. Venkatesh ◽  
S. Kumar Raja ◽  
G. Vidyasagar
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Sampling Theorem ◽  
Discrete Signals ◽  
Bandlimited Signal ◽  
Time Signals ◽  
Shannon Sampling Theorem ◽  
Heisenberg Uncertainty ◽  
Comparison Of The Results ◽  
Uncertainty Inequality

Given a continuous-time bandlimited signal, the Shannon sampling theorem provides an interpolation scheme forexactly reconstructingit from its discrete samples. We analyze the relationship between concentration (orcompactness) in thetemporal/spectral domainsof the (i) continuous-time and (ii) discrete-time signals. The former is governed by the Heisenberg uncertainty inequality which prescribes a lower bound on the product ofeffectivetemporal and spectral spreads of the signal. On the other hand, the discrete-time counterpart seems to exhibit some strange properties, and this provides motivation for the present paper. We consider the following problem:for a bandlimited signal, can the uncertainty inequality be expressed in terms of the samples, using thestandard definitions of the temporal and spectral spreads of the signal?In contrast with the results of the literature, we present a new approach to solve this problem. We also present a comparison of the results obtained using the proposed definitions with those available in the literature.

scholarly journals Dispersion properties of electrostatic oscillations in quantum plasmas

2009 ◽  
Vol 76 (1) ◽  
pp. 7-17 ◽  
Author(s):  
BENGT ELIASSON ◽  
PADMA KANT SHUKLA
Keyword(s):  
Low Frequency ◽  
Electron Plasma ◽  
Quantum Plasma ◽  
Plasma Oscillations ◽  
Heisenberg Uncertainty Principle ◽  
Electrostatic Wave ◽  
Dense Plasmas ◽  
Astrophysical Objects ◽  
Heisenberg Uncertainty ◽  
Semiconductor Plasmas

AbstractWe present a derivation of the dispersion relation for electrostatic oscillations in a zero-temperature quantum plasma, in which degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations. The Poisson equation determines the electrostatic wave potential. We consider parameters ranging from semiconductor plasmas to metallic plasmas and electron densities of compressed matter such as in laser compression schemes and dense astrophysical objects. Owing to the wave diffraction caused by overlapping electron wave function because of the Heisenberg uncertainty principle in dense plasmas, we have the possibility of Landau damping of the high-frequency electron plasma oscillations at large enough wavenumbers. The exact dispersion relations for the electron plasma oscillations are solved numerically and compared with the ones obtained by using approximate formulas for the electron susceptibility in the high- and low-frequency cases.

On impact of a priori classical knowledge of discriminated states on the optimal unambiguous discrimination

2008 ◽  
Vol 8 (10) ◽  
pp. 951-964
Author(s):  
M. Zhang ◽  
Z.-T. Zhou ◽  
H.-Y. Dai ◽  
D.-W. Hu
Keyword(s):  
A Priori ◽  
Quantum States ◽  
A Priori Knowledge ◽  
Single System ◽  
Heisenberg Uncertainty Principle ◽  
Unambiguous Discrimination ◽  
Fundamental Limitations ◽  
Heisenberg Uncertainty ◽  
Classical Knowledge ◽  
Priori Knowledge

Due to the fundamental limitations related to the Heisenberg uncertainty principle and the non-cloning theorem, it is impossible, even in principle, to determine the quantum state of a single system without a priori knowledge of it. To discriminate nonorthogonal quantum states in some optimal way, a priori knowledge of the discriminated states has to be relied upon. In this paper, we thoroughly investigate some impact of a priori classical knowledge of two quantum states on the optimal unambiguous discrimination. It is exemplified that a priori classical knowledge of the discriminated states, incomplete or complete, can be utilized to improve the optimal success probabilities, whereas the lack of a prior classical knowledge can not be compensated even by more resources.

scholarly journals Prediction for the cosmological constant and constraints on SUSY GUTs in resummed quantum gravity

2018 ◽  
Vol 33 (29) ◽  
pp. 1830028
Author(s):  
B. F. L. Ward
Keyword(s):  
General Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Planck Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

Working in the context of the Planck scale cosmology formulation of Bonanno and Reuter, we use our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as [Formula: see text]. We show that SUSY GUT models are constrained by the closeness of this estimate to experiment. We also address various consistency checks on the calculation. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of [Formula: see text].

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