Related papers: Fundamental lower size limit in wavelength selecti…
The paper establishes explicit lower bounds for the lattice cell size of periodic structures (metamaterials and photonic crystals) capable of supporting backward waves and producing negative refraction. At optical frequencies, this result…
The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough…
Both the radiation efficiency and bandwidth of electrically small antennas are dramatically reduced as the size decreases. Fundamental limitations on the bandwidth of small antennas have been thoroughly treated in the past. However, upper…
Methods on reducing resonant frequencies and electrical sizes of resonators are reported in this paper. Theoreti-cal and numerical analysis has been used and the results for the broadside-coupled resonators from both studies exhibit good…
We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape for the various scalings of $d = n^{\alpha}$, $\alpha\in(0,1)$, for the input…
In this paper, the uncertainty principle of discrete signals associated with Quaternion Fourier transform is investigated. It suggests how sparsity helps in the recovery of missing frequency.
The Heisenberg uncertainty relation is derived for relativistic electrons described by the Dirac equation. The standard nonrelativistic lower bound $3/2\hbar$ is attained only in the limit and the wave function that reproduces this value is…
We numerically demonstrate a new type of waveform-selective metasurface that senses the difference in incoming waveforms or pulse widths at the same frequency. Importantly, the proposed structure contains precise rectifier circuits that,…
Several variations of the Heisenberg uncertainty inequality are derived on the basis of "noise-resolution duality" recently proposed by the authors. The same approach leads to a related inequality that provides an upper limit for the…
The Heisenberg uncertainty principle sets a lower bound on the sensitivity of continuous optical measurements of force. This bound, the standard quantum limit, can only be reached when a mechanical oscillator subjected to the force is…
We test the validity of the Generalized Heisenberg's Uncertainty principle in the presence of strong gravitational fields nearby rotating black holes; Heisenberg's principle is supposed to require additional correction terms when gravity is…
On-chip optical resonators have the promise of revolutionizing numerous fields including metrology and sensing; however, their optical losses have always lagged behind their larger discrete resonator counterparts based on crystalline…
Subwavelength dielectric structures offer an attractive low loss alternative to plasmonic structures for the development of resonant optics functionality such as metamaterials. Nonspherical like rectangular structures are of most interest…
An indirect measurement model is constructed for an approximately repeatable, precise position measuring apparatus that violates the assertion, sometimes called the Heisenberg uncertainty principle, that any position measuring apparatus…
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.
In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in…
We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof…
This is an article written in a popular science style, in which I will explain: (1) the famous Heisenberg uncertainty principle, expressing the experimental incompatibility of certain properties of micro-physical entities; (2) the Compton…
The effects of Lorentz-violating operators of nonrenormalizable dimension in optical resonate cavities are studied. Optical-frequency experiments are shown to provide sensitivity to nondispersive nonbirefringent violations that is many…
Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement…