1,491 research outputs found
High orders of the perturbation theory for hydrogen atom in magnetic field
The states of hydrogen atom with principal quantum number and zero
magnetic quantum number in constant homogeneous magnetic field are
considered. The coefficients of energy eigenvalues expansion up to 75th order
in powers of are obtained for these states. The series for energy
eigenvalues and wave functions are summed up to values of the order
of atomic magnetic field. The calculations are based on generalization of the
moment method, which may be used in other cases of the hydrogen atom
perturbation by a polynomial in coordinates potential.Comment: 16 pages, LaTeX, 6 figures (ps, eps
The Usability of Ambiguity Detection Methods for Context-Free Grammars
One way of verifying a grammar is the detection of ambiguities. Ambiguities are not always unwanted, but they can only be controlled if their sources are known. Unfortunately, the ambiguity problem for context-free grammars is undecidable in the general case. Various ambiguity detection methods (ADMs) exist, but they can never be perfect. In this paper we explore three ADMs to test whether they still can be of any practical value: the derivation generator AMBER, the LR(k) test and the Noncanonical Unambiguity test. We benchmarked their implementations on a collection of ambiguous and unambiguous grammars of different sizes and compa
Data driven optimal filtering for phase and frequency of noisy oscillations: application to vortex flowmetering
A new method for extracting the phase of oscillations from noisy time series
is proposed. To obtain the phase, the signal is filtered in such a way that the
filter output has minimal relative variation in the amplitude (MIRVA) over all
filters with complex-valued impulse response. The argument of the filter output
yields the phase. Implementation of the algorithm and interpretation of the
result are discussed. We argue that the phase obtained by the proposed method
has a low susceptibility to measurement noise and a low rate of artificial
phase slips. The method is applied for the detection and classification of mode
locking in vortex flowmeters. A novel measure for the strength of mode locking
is proposed.Comment: 12 pages, 10 figure
Minimum error discrimination of Pauli channels
We solve the problem of discriminating with minimum error probability two
given Pauli channels. We show that, differently from the case of discrimination
between unitary transformations, the use of entanglement with an ancillary
system can strictly improve the discrimination, and any maximally entangled
state allows to achieve the optimal discrimination. We also provide a simple
necessary and sufficient condition in terms of the structure of the channels
for which the ultimate minimum error probability can be achieved without
entanglement assistance. When such a condition is satisfied, the optimal input
state is simply an eigenstate of one of the Pauli matrices.Comment: 8 pages, no figure
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