Related papers: Harmonic inversion helps to beat time-energy uncer…
The very old problem of extracting frequencies from time signals is addressed in the case of signals that are very short as compared to their intrinsic time scales. The solution of the problem is not only important to the classic signal…
We give a short review of known exact inequalities that can be interpreted as "energy-time" and "frequency-time" uncertainty relations. In particular we discuss a precise form of signals minimizing the physical frequency-time uncertainty…
All energy measurements of a quantum system are prone to inaccuracies. In particular, if such measurements are carried over a finite period of time the accuracy of the result is affected by the length of that period. Here I show an upper…
Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation…
The uncertainty principle is a cornerstone of modern physics, and its implications have a fundamental impact on theoretical and applied quantum mechanics. The aim of this thesis is to study and apply the uncertainty relations between time…
The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information…
Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the…
In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…
The time-energy uncertainty relation is often invoked as a heuristic explanation for virtual particles in interacting quantum field theories. However, this interpretation breaks down upon closer scrutiny for several reasons. Although…
Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta…
Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…
Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to…
The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…
Precise understanding of the dynamics of trapped particles is crucial for nascent quantum technologies, including atomic clocks and quantum simulators. Here we present a framework to systematically include quantum effects arising from the…
The generation of time signals is a fundamental task in science. Here we study the relation between the quality of a time signal and the physics of the system that generates it. According to quantum theory, any time signal can be decomposed…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
Minimization of the expectation value of energy under the constraints imposed by the uncertainty principle can be a convenient method of solving quantum-mechanical problems.
Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations,…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
The ability to control and direct acoustic energy is essential for many engineering applications such as vibration and noise control, invisibility cloaking, acoustic sensing, energy harvesting, and phononic switching and rectification. The…