Related papers: The Uncertainty Principle and Classical Amplitudes
We present a detailed analysis of the scattering of charged particles by the magnetic field of a long solenoid of constant magnetic flux and finite radius. We study the relativistic and non-relativistic quantum and classical scenarios. The…
Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude,…
We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution.…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature…
Unitarity is the fundamental property of the S-matrix while its usage for a scattering of unstable particles has been subtle as unstable particles do not appear in the asymptotic states. Defining unstable-particle amplitudes as residues of…
Scanning gate microscopy measurements in a circular ballistic cavity with a tip placed near its center yield a non-monotonic dependence of the conductance on the tip voltage. Detailed numerical quantum calculations reproduce these…
The decomposition of a one-loop scattering amplitude into elementary functions with rational coefficients introduces spurious singularities which afflict individual coefficients but cancel in the complete amplitude. These cancellations…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
Theory of scattering of a quantum-mechanical particle on a cosmic string is developed. S-matrix and scattering amplitude are determined as functions of the flux and the tension of the string. We reveal that, in the case of the nonvanishing…
We consider scattering of a free quantum particle on a singular potential with rather arbitrary shape of the support of the potential. In the classical limit $\hbar=0$ this problem reduces to the well known problem of chaotic scattering.…
Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied…
The scattering amplitudes of string theory exhibit many extraordinary properties. But are they the unique mathematical objects to do so? Recently, it has been shown how the spectrum and amplitudes of open string theory follow directly from…
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we…
The fact that we rarely directly observe much quantum uncertainty is often attributed to decoherence. However, decoherence does not reduce the quantum uncertainty in the full quantum state. Whether or not it reduces the quantum…
In [arXiv:1906.10100], the authors argued that the Newman-Janis algorithm on the space of classical solutions in general relativity and electromagnetism could be used in the space of scattering amplitudes to map an amplitude with external…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…
As an undergraduate exercise, in an article (2012 Am. J. Phys. $\bf{80}$ 780-14), quantum and classical uncertainties for dimensionless variables of position and momentum were evaluated in three potentials: infinite well, bouncing ball, and…
The relationship between the classical and quantum theories of gravity is reexamined. The value of the gravitational potential defined with the help of the two-particle scattering amplitudes is shown to be in disagreement with the classical…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…