13,448 research outputs found
Scaling Symmetries of Scatterers of Classical Zero-Point Radiation
Classical radiation equilibrium (the blackbody problem) is investigated by
the use of an analogy. Scaling symmetries are noted for systems of classical
charged particles moving in circular orbits in central potentials V(r)=-k/r^n
when the particles are held in uniform circular motion against radiative
collapse by a circularly polarized incident plane wave. Only in the case of a
Coulomb potential n=1 with fixed charge e is there a unique scale-invariant
spectrum of radiation versus frequency (analogous to zero-point radiation)
obtained from the stable scattering arrangement. These results suggest that
non-electromagnetic potentials are not appropriate for discussions of classical
radiation equilibrium.Comment: 13 page
Hydrodynamic reductions of the heavenly equation
We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.Comment: 14 page
Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation
By numerical calculation, the Planck spectrum with zero-point radiation is
shown to satisfy a natural maximum-entropy principle whereas alternative
choices of spectra do not. Specifically, if we consider a set of
conducting-walled boxes, each with a partition placed at a different location
in the box, so that across the collection of boxes the partitions are uniformly
spaced across the volume, then the Planck spectrum correspond to that spectrum
of random radiation (having constant energy kT per normal mode at low
frequencies and zero-point energy (1/2)hw per normal mode at high frequencies)
which gives maximum uniformity across the collection of boxes for the radiation
energy per box. The analysis involves Casimir energies and zero-point radiation
which do not usually appear in thermodynamic analyses. For simplicity, the
analysis is presented for waves in one space dimension.Comment: 11 page
Quantum Key Distribution with Classical Bob
Secure key distribution among two remote parties is impossible when both are
classical, unless some unproven (and arguably unrealistic)
computation-complexity assumptions are made, such as the difficulty of
factorizing large numbers. On the other hand, a secure key distribution is
possible when both parties are quantum.
What is possible when only one party (Alice) is quantum, yet the other (Bob)
has only classical capabilities? We present a protocol with this constraint,
and prove its robustness against attacks: we prove that any attempt of an
adversary to obtain information (and even a tiny amount of information)
necessarily induces some errors that the legitimate users could notice.Comment: 4 and a bit pages, 1 figure, RevTe
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