10,304 research outputs found
Nonlinear screening and stopping power in two-dimensional electron gases
We have used density functional theory to study the nonlinear screening
properties of a two-dimensional (2D) electron gas. In particular, we consider
the screening of an external static point charge of magnitude Z as a function
of the distance of the charge from the plane of the gas. The self-consistent
screening potentials are then used to determine the 2D stopping power in the
low velocity limit based on the momentum transfer cross-section. Calculations
as a function of Z establish the limits of validity of linear and quadratic
response theory calculations, and show that nonlinear screening theory already
provides significant corrections in the case of protons. In contrast to the 3D
situation, we find that the nonlinearly screened potential supports a bound
state even in the high density limit. This behaviour is elucidated with the
derivation of a high density screening theorem which proves that the screening
charge can be calculated perturbatively in the high density limit for arbitrary
dimensions. However, the theorem has particularly interesting implications in
2D where, contrary to expectations, we find that perturbation theory remains
valid even when the perturbing potential supports bound states.Comment: 23 pages, 15 figures in RevTeX
Mixture Based Outlier Filtration
Success/failure of adaptive control algorithms â especially those designed using the Linear Quadratic Gaussian criterion â depends on the quality of the process data used for model identification. One of the most harmful types of process data corruptions are outliers, i.e. âwrong dataâ lying far away from the range of real data. The presence of outliers in the data negatively affects an estimation of the dynamics of the system. This effect is magnified when the outliers are grouped into blocks. In this paper, we propose an algorithm for outlier detection and removal. It is based on modelling the corrupted data by a two-component probabilistic mixture. The first component of the mixture models uncorrupted process data, while the second models outliers. When the outlier component is detected to be active, a prediction from the uncorrupted data component is computed and used as a reconstruction of the observed data. The resulting reconstruction filter is compared to standard methods on simulated and real data. The filter exhibits excellent properties, especially in the case of blocks of outliers.
Nonlinear screening in two-dimensional electron gases
We have performed self-consistent calculations of the nonlinear screening of
a point charge Z in a two-dimensional electron gas using a density functional
theory method. We find that the screened potential for a Z=1 charge supports a
bound state even in the high density limit where one might expect perturbation
theory to apply. To explain this behaviour, we prove a theorem to show that the
results of linear response theory are in fact correct even though bound states
exist.Comment: 4 pages, 4 figure
Parametrization of semi-dynamical quantum reflection algebra
We construct sets of structure matrices for the semi-dynamical reflection
algebra, solving the Yang-Baxter type consistency equations extended by the
action of an automorphism of the auxiliary space. These solutions are
parametrized by dynamical conjugation matrices, Drinfel'd twist representations
and quantum non-dynamical -matrices. They yield factorized forms for the
monodromy matrices.Comment: LaTeX, 24 pages. Misprints corrected, comments added in Conclusion on
construction of Hamiltonian
Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution
In non relativistic quantum mechanics time enters as a parameter in the
Schroedinger equation. However, there are various situations where the need
arises to view time as a dynamical variable. In this paper we consider the
dynamical role of time through the construction of a Lyapunov variable - i.e.,
a self-adjoint quantum observable whose expectation value varies monotonically
as time increases. It is shown, in a constructive way, that a certain class of
models admit a Lyapunov variable and that the existence of a Lyapunov variable
implies the existence of a transformation mapping the original quantum
mechanical problem to an equivalent irreversible representation. In addition,
it is proved that in the irreversible representation there exists a natural
time ordering observable splitting the Hilbert space at each t>0 into past and
future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604.
Discussion expanded to include the case of Hamiltonians with an infinitely
degenerate spectru
Functional renormalization group with a compactly supported smooth regulator function
The functional renormalization group equation with a compactly supported
smooth (CSS) regulator function is considered. It is demonstrated that in an
appropriate limit the CSS regulator recovers the optimized one and it has
derivatives of all orders. The more generalized form of the CSS regulator is
shown to reduce to all major type of regulator functions (exponential,
power-law) in appropriate limits. The CSS regulator function is tested by
studying the critical behavior of the bosonized two-dimensional quantum
electrodynamics in the local potential approximation and the sine-Gordon scalar
theory for d<2 dimensions beyond the local potential approximation. It is shown
that a similar smoothing problem in nuclear physics has already been solved by
introducing the so called Salamon-Vertse potential which can be related to the
CSS regulator.Comment: JHEP style, 11 pages, 2 figures, proofs corrected, accepted for
publication by JHE
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