scholarly journals Assessing the validity of the thermodynamic uncertainty relation in quantum systems

2018 ◽  
Vol 98 (15) ◽  
Author(s):  
Bijay Kumar Agarwalla ◽  
Dvira Segal
Keyword(s):  
Uncertainty Relation ◽  
Quantum Systems

What is Time–Energy Uncertainty?

2020 ◽  
pp. 92-104
Author(s):  
Gershon Kurizki ◽  
Goren Gordon
Keyword(s):  
Schrodinger Equation ◽  
Uncertainty Relation ◽  
Energy State ◽  
Human Experience ◽  
Quantum Systems ◽  
General Question ◽  
Energy Measurement ◽  
Quantum Observable ◽  
The Subject ◽  
Short Time

Henry scores a surprise win over Eve thanks to his quantum rocket that is powered by a quantum-chargeable battery. This gadget is subject to the time–energy uncertainty relation that may result in the battery having more energy than expected. This occurs if an energy measurement within a short time “collapses” the battery randomly to the highest energy state. Intriguingly, time is not a quantum observable. This raises the question that was hotly debated by Bohr and Einstein: how can time be uncertain and affect the energy uncertainty? The more general question is: what is the meaning of time, energy and their uncertainty in physics and in human experience? Attempts to define time have been the subject of philosophical controversy throughout millennia. The appendix to this chapter introduces the Schrödinger equation that governs the dynamics of quantum systems and their time–energy uncertainty.

scholarly journals Local States in One-Dimensional Symmetrical Quantum Systems

1979 ◽  
Vol 34 (12) ◽  
pp. 1452-1457 ◽  
Author(s):  
Jürgen Brickmann
Keyword(s):  
Half Space ◽  
Uncertainty Relation ◽  
Quantum Systems ◽  
Quantum States ◽  
Uncertainty Measure ◽  
One Dimensional ◽  
Quantum Dynamical ◽  
Local Quantum ◽  
Local Properties ◽  
Energy Moments

Abstract Local quantum states, which play an important role in quantum dynamical treatments, are expanded analytically with respect to a basis of eigen functions of a symmetrical Hamiltonian ℋ̂(x) = ℋ̂(- x). Exact local states (ELS) in one-dimensional symmetrical quantum systems are therein defined as quantum states which are local eigenstates of the Hamiltonian ℋ̂(x) on one half space ℝ+ or ℝ- and are identically equal to zero on the other half space. Local properties like the projection operator on one half space can be given in terms of ELS-basis, but it is shown that the energy moments 〈(〈ℋ̂ 〉 - 〈ℋ̂)k〉 with respect to the ELS do not converge. Consequently, if one uses the ELS as quasistationary initial states, as has been done recently by some authors [5], the lifetimes of these states cannot be estimated from time energy uncertainty relation using the second energy moment as an energy uncertainty measure. A harmonic oscillator system and a symmetrical double oscillator are treated as examples.

scholarly journals Uncertainty Relation for Errors Focusing on General POVM Measurements with an Example of Two-State Quantum Systems

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1222
Author(s):  
Jaeha Lee ◽  
Izumi Tsutsui
Keyword(s):  
Quantum Measurement ◽  
Uncertainty Principle ◽  
Positive Operator ◽  
Pure State ◽  
Uncertainty Relation ◽  
Measure Theory ◽  
Quantum Systems ◽  
Quantum Measurements ◽  
Positive Operator Valued Measures ◽  
Informative Case

A novel uncertainty relation for errors of general quantum measurement is presented. The new relation, which is presented in geometric terms for maps representing measurement, is completely operational and can be related directly to tangible measurement outcomes. The relation violates the naïve bound ℏ/2 for the position-momentum measurement, whilst nevertheless respecting Heisenberg’s philosophy of the uncertainty principle. The standard Kennard–Robertson uncertainty relation for state preparations expressed by standard deviations arises as a corollary to its special non-informative case. For the measurement on two-state quantum systems, the relation is found to offer virtually the tightest bound possible; the equality of the relation holds for the measurement performed over every pure state. The Ozawa relation for errors of quantum measurements will also be examined in this regard. In this paper, the Kolmogorovian measure-theoretic formalism of probability—which allows for the representation of quantum measurements by positive-operator valued measures (POVMs)—is given special attention, in regard to which some of the measure-theory specific facts are remarked along the exposition as appropriate.

On the information and uncertainty relation of canonical quantum systems with SL(2R) invariance

1996 ◽  
Vol 7 (5) ◽  
pp. 659-668 ◽  
Author(s):  
Maricel Agop ◽  
Cristina Buzea ◽  
Caˇlin Gh. Buzea ◽  
Liliana Chirilaˇ ◽  
Servilia Oancea
Keyword(s):  
Uncertainty Relation ◽  
Quantum Systems ◽  
Canonical Quantum

scholarly journals Information Geometry in Classical and Quantum Systems

2018 ◽  
Author(s):  
Eun-jin Kim
Keyword(s):  
Stochastic Systems ◽  
Uncertainty Relation ◽  
Quantum Systems ◽  
Probability Density Functions ◽  
Probabilistic Description ◽  
Equilibrium Process ◽  
Far From Equilibrium ◽  
The Difference ◽  
Information Change

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic processes and geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate classical and quantum systems and demonstrate the utility of the information length as a unique Lagrangian diagnostic to quantify the information change as a system continuously evolves in time and to map out attractor structure. We further elucidate quantum effects (uncertainty relation) and the dual role of the width of PDF in quantum systems.

Sign in / Sign up

Export Citation Format

Share Document