5 research outputs found

### Functional Classical Mechanics and Rational Numbers

The notion of microscopic state of the system at a given moment of time as a
point in the phase space as well as a notion of trajectory is widely used in
classical mechanics. However, it does not have an immediate physical meaning,
since arbitrary real numbers are unobservable. This notion leads to the known
paradoxes, such as the irreversibility problem. A "functional" formulation of
classical mechanics is suggested. The physical meaning is attached in this
formulation not to an individual trajectory but only to a "beam" of
trajectories, or the distribution function on phase space. The fundamental
equation of the microscopic dynamics in the functional approach is not the
Newton equation but the Liouville equation for the distribution function of the
single particle. The Newton equation in this approach appears as an approximate
equation describing the dynamics of the average values and there are
corrections to the Newton trajectories. We give a construction of probability
density function starting from the directly observable quantities, i.e., the
results of measurements, which are rational numbers.Comment: 8 page

### Derivation of the Boltzmann equation and entropy production in functional mechanics

A derivation of the Boltzmann equation from the Liouville equation by the use
of the Grad limiting procedure in a finite volume is proposed. We introduce two
scales of space-time: macro- and microscale and use the BBGKY hierarchy and the
functional formulation of classical mechanics. According to the functional
approach to mechanics, a state of a system of particles is formed from the
measurements, which are rational numbers. Hence, one can speak about the
accuracy of the initial probability density function in the Liouville equation.
We assume that the initial data for the microscopic density functions are
assigned by the macroscopic one (so, one can say about a kind of hierarchy and
subordination of the microscale to the macroscale) and derive the Boltzmann
equation, which leads to the entropy production.Comment: 14 page

### Eurasian-Scale Experimental Satellite-based Quantum Key Distribution with Detector Efficiency Mismatch Analysis

The Micius satellite is the pioneering initiative to demonstrate quantum
teleportation, entanglement distribution, quantum key distribution (QKD), and
quantum-secured communications experiments at the global scale. In this work,
we report on the results of the 600-mm-aperture ground station design which has
enabled the establishment of a quantum-secured link between the Zvenigorod and
Nanshan ground stations using the Micius satellite. As a result of a quantum
communications session, an overall sifted key of 2.5 Mbits and a total final
key length of 310 kbits have been obtained. We present an extension of the
security analysis of the realization of satellite-based QKD decoy-state
protocol by taking into account the effect of the detection-efficiency mismatch
for four detectors. We also simulate the QKD protocol for the satellite passage
and by that validate our semi-empirical model for a realistic receiver, which
is in good agreement with the experimental data. Our results pave the way to
the considerations of realistic imperfection of the QKD systems, which are
important in the context of their practical security.Comment: 8+2 pages, 5+2 figure