In this paper, we study the Lehmer’s type congruences for lacunary harmonic sums.

– The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the Hilbert space or an appropriately defined phase space must be populated in terms of coherent states in order to obtain the quantum result respectively the...

Nano-electro-mechanical devices are now rapidly approaching the point where it will be possible to observe quantum mechanical behavior. However, for such behavior to be visible it is necessary to reduce the thermal motion of these devices down to temperatures in the millikelvin range. Here we consider the use of feedback control for this purpose. We analyze an experimentally realizable situatio...

The process some call ‘categorification’ consists of interpreting set-theoretic structures in mathematics as derived from category-theoretic structures. Examples include the interpretation of as the Burnside rig of the category of finite sets with product and coproduct, and of [x] in terms the category of combinatorial species. This has interesting applications to quantum mechanics, and in part...

A free quantum field and its canonical conjugate are equivalent to a family of harmonic oscillators (one oscillator for each plane wave), which is in turn equivalent to a quantum theory of free identical bosons. In this note, I will show how all of this works for the relativistic scalar field φ̂(x) and its conjugate π̂(x). And then I will turn around and show that a quantum theory of any kind of ...

The phenomenon that a quantum particle propagating in detector, such as Wilson cloud chamber, leaves track close to classical trajectory is analyzed. We introduce an idealized quantum-mechanical model of charged periodically illuminated by pulses laser light resulting repeated indirect measurements the approximate position particle. For this we present mathematically rigorous analysis appearanc...

The quantum theory of a damped harmonic oscillator has been continuously studied since 1939. For quantization, an oscillation usually uses reservoir that includes number finite and discrete oscillators. However, set oscillators is unable to study the Ohmic damping (damping proportional velocity). In this research, continuous used investigate damping. Using continuum instead will enrich results ...