On the invariant properties of quantum uncertainty relations with respect to parameters of virtual photons responsible for interaction processes in quantum particle systems

2017 ◽  
Vol 381 (4) ◽  
pp. 233-238 ◽  
Author(s):  
V.N. Murzin
Keyword(s):  
Quantum Particle ◽  
Particle Systems ◽  
Uncertainty Relations ◽  
Quantum Uncertainty ◽  
Interaction Processes ◽  
Virtual Photons ◽  
Invariant Properties

scholarly journals HIDDEN SCALE IN QUANTUM MECHANICS

2009 ◽  
Vol 24 (27) ◽  
pp. 2203-2211 ◽  
Author(s):  
PULAK RANJAN GIRI
Keyword(s):  
Wave Packet ◽  
Quantum Particle ◽  
Dimensional Space ◽  
Free Particle ◽  
Three Dimensional ◽  
Particle Systems ◽  
Quantum Mechanical ◽  
Scale Invariant ◽  
Mechanical Models ◽  
Three Dimensional Space

We show that the intriguing localization of a free particle wave-packet is possible due to a hidden scale present in the system. Self-adjoint extensions (SAE) is responsible for introducing this scale in quantum mechanical models through the nontrivial boundary conditions. We discuss a couple of classically scale invariant free particle systems to illustrate the issue. In this context it has been shown that a free quantum particle moving on a full line may have localized wave-packet around the origin. As a generalization, it has also been shown that particles moving on a portion of a plane or on a portion of a three-dimensional space can have unusual localized wave-packet.

Quantum uncertainty relations and stochastic mechanics

1984 ◽  
Vol 79 (2) ◽  
pp. 175-186 ◽  
Author(s):  
S. De Martino ◽  
S. De Siena
Keyword(s):  
Uncertainty Relations ◽  
Stochastic Mechanics ◽  
Quantum Uncertainty

scholarly journals Uncertainty Relations in Hydrodynamics

2020 ◽  
Author(s):  
Gyell Gonçalves de Matos ◽  
Takeshi Kodama ◽  
Tomoi Koide
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Relation ◽  
Quantum Particle ◽  
Navier Stokes ◽  
Pitaevskii Equation ◽  
Uncertainty Relations ◽  
Derived Relations ◽  
Stochastic Variational Method ◽  
Virtual Trajectory ◽  
Fourier Equation

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

scholarly journals Uncertainty relations: An operational approach to the error-disturbance tradeoff

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 20 ◽  
Author(s):  
Joseph M. Renes ◽  
Volkher B. Scholz ◽  
Stefan Huber
Keyword(s):  
Quantum Theory ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Actual Measurement ◽  
Quantum Uncertainty ◽  
Joint Measurability ◽  
Finite Dimensional ◽  
Wave Particle Duality ◽  
Heisenberg Type ◽  
Conceptual Difficulties

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever. This definition itself does not rely on the formalism of quantum theory, avoiding many of the conceptual difficulties of usual definitions. We then derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems, as well as for the case of position and momentum. Our relations may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment. We also show that Englert's wave-particle duality relation [PRL 77, 2154 (1996)] can be viewed as an error-disturbance uncertainty relation.

scholarly journals Universal quantum uncertainty relations: Minimum-uncertainty wave packet depends on measure of spread

2019 ◽  
Vol 383 (16) ◽  
pp. 1850-1855
Author(s):  
Anindita Bera ◽  
Debmalya Das ◽  
Aditi Sen(De) ◽  
Ujjwal Sen
Keyword(s):  
Wave Packet ◽  
Uncertainty Relations ◽  
Quantum Uncertainty ◽  
Universal Quantum ◽  
Minimum Uncertainty

scholarly journals Uncertainty Relations: Curiosities and Inconsistencies

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1640
Author(s):  
Krzysztof Urbanowski
Keyword(s):  
Quantum Theory ◽  
Lower Bound ◽  
Uncertainty Relation ◽  
Quantum Particle ◽  
Uncertainty Relations ◽  
Rigorous Analysis ◽  
Special Cases ◽  
The Status ◽  
Symmetric Quantum ◽  
Standard Deviations

Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables A and B and such vectors that the lower bound for the product of standard deviations ΔA and ΔB calculated for these vectors is zero: ΔA·ΔB≥0. Here we discuss examples of such cases and some other inconsistencies which can be found performing a rigorous analysis of the uncertainty relations in some special cases. As an illustration of such cases matrices (2×2) and (3×3) and the position–momentum uncertainty relation for a quantum particle in the box are considered. The status of the uncertainty relation in PT–symmetric quantum theory and the problems associated with it are also studied.

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