10,649 research outputs found
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
Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect
The formulae for Planck length, Hawking temperature and Unruh-Davies
temperature are derived by using only laws of classical physics together with
the Heisenberg principle. Besides, it is shown how the Hawking relation can be
deduced from the Unruh relation by means of the principle of equivalence; the
deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure
Algebraic analysis of quantum search with pure and mixed states
An algebraic analysis of Grover's quantum search algorithm is presented for
the case in which the initial state is an arbitrary pure quantum state of n
qubits. This approach reveals the geometrical structure of the quantum search
process, which turns out to be confined to a four-dimensional subspace of the
Hilbert space. This work unifies and generalizes earlier results on the time
evolution of the amplitudes during the quantum search, the optimal number of
iterations and the success probability. Furthermore, it enables a direct
generalization to the case in which the initial state is a mixed state,
providing an exact formula for the success probability.Comment: 13 page
Energy properness and Sasakian-Einstein metrics
In this paper, we show that the existence of Sasakian-Einstein metrics is
closely related to the properness of corresponding energy functionals. Under
the condition that admitting no nontrivial Hamiltonian holomorphic vector
field, we prove that the existence of Sasakian-Einstein metric implies a
Moser-Trudinger type inequality. At the end of this paper, we also obtain a
Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page
Techniques for measuring atmospheric aerosols at the High Resolution Fly's Eye experiment
We describe several techniques developed by the High Resolution Fly's Eye
experiment for measuring aerosol vertical optical depth, aerosol horizontal
attenuation length, and aerosol phase function. The techniques are based on
measurements of side-scattered light generated by a steerable ultraviolet laser
and collected by an optical detector designed to measure fluorescence light
from cosmic-ray air showers. We also present a technique to cross-check the
aerosol optical depth measurement using air showers observed in stereo. These
methods can be used by future air fluorescence experiments.Comment: Accepted for publication in Astroparticle Physics Journal 16 pages, 9
figure
Grover's Quantum Search Algorithm for an Arbitrary Initial Mixed State
The Grover quantum search algorithm is generalized to deal with an arbitrary
mixed initial state. The probability to measure a marked state as a function of
time is calculated, and found to depend strongly on the specific initial state.
The form of the function, though, remains as it is in the case of initial pure
state. We study the role of the von Neumann entropy of the initial state, and
show that the entropy cannot be a measure for the usefulness of the algorithm.
We give few examples and show that for some extremely mixed initial states
carrying high entropy, the generalized Grover algorithm is considerably faster
than any classical algorithm.Comment: 4 pages. See http://www.cs.technion.ac.il/~danken/MSc-thesis.pdf for
extended discussio
A General SU(2) Formulation for Quantum Searching with Certainty
A general quantum search algorithm with arbitrary unitary transformations and
an arbitrary initial state is considered in this work. To serach a marked state
with certainty, we have derived, using an SU(2) representation: (1) the
matching condition relating the phase rotations in the algorithm, (2) a concise
formula for evaluating the required number of iterations for the search, and
(3) the final state after the search, with a phase angle in its amplitude of
unity modulus. Moreover, the optimal choices and modifications of the phase
angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure
Realization of generalized quantum searching using nuclear magnetic resonance
According to the theoretical results, the quantum searching algorithm can be
generalized by replacing the Walsh-Hadamard(W-H) transform by almost any
quantum mechanical operation. We have implemented the generalized algorithm
using nuclear magnetic resonance techniques with a solution of chloroform
molecules. Experimental results show the good agreement between theory and
experiment.Comment: 11 pages,3 figure. Accepted by Phys. Rev. A. Scheduled Issue: 01 Mar
200
The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations
In this paper we derived the precise formula in a sine function form of the
norm of the amplitude in the desired state, and by means of he precise formula
we presented the necessary and sufficient phase condition for any quantum
algorithm with arbitrary phase rotations. We also showed that the phase
condition: identical rotation angles, is a sufficient but not a necessary phase
condition.Comment: 16 pages. Modified some English sentences and some proofs. Removed a
table. Corrected the formula for kol on page 10. No figure
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