8,200 research outputs found
On the theory of electric dc-conductivity : linear and non-linear microscopic evolution and macroscopic behaviour
We consider the Schrodinger time evolution of charged particles subject to a
static substrate potential and to a homogeneous, macroscopic electric field (a
magnetic field may also be present). We investigate the microscopic velocities
and the resulting macroscopic current. We show that the microscopic velocities
are in general non-linear with respect to the electric field. One kind of
non-linearity arises from the highly non-linear adiabatic evolution and (or)
from an admixture of parts of it in so-called intermediate states, and the
other kind from non-quadratic transition rates between adiabatic states. The
resulting macroscopic dc-current may or may not be linear in the field. Three
cases can be distinguished : (a) The microscopic non-linearities can be
neglected. This is assumed to be the case in linear response theory (Kubo
formalism, ...). We give arguments which make it plausible that often such an
assumption is indeed justified, in particular for the current parallel to the
field. (b) The microscopic non-linearitites lead to macroscopic
non-linearities. An example is the onset of dissipation by increasing the
electric field in the breakdown of the quantum Hall effect. (c) The macroscopic
current is linear although the microscopic non-linearities constitute an
essential part of it and cannot be neglected. We show that the Hall current of
a quantized Hall plateau belongs to this case. This illustrates that
macroscopic linearity does not necessarily result from microscopic linearity.
In the second and third cases linear response theory is inadequate. We
elucidate also some other problems related to linear response theory.Comment: 24 pages, 6 figures, some typing errors have been corrected. Remark :
in eq. (1) of the printed article an obvious typing error remain
Relaxation Phenomena in a System of Two Harmonic Oscillators
We study the process by which quantum correlations are created when an
interaction Hamiltonian is repeatedly applied to a system of two harmonic
oscillators for some characteristic time interval. We show that, for the case
where the oscillator frequencies are equal, the initial Maxwell-Boltzmann
distributions of the uncoupled parts evolve to a new equilibrium
Maxwell-Boltzmann distribution through a series of transient Maxwell-Boltzmann
distributions. Further, we discuss why the equilibrium reached when the two
oscillator frequencies are unequal, is not a thermal one. All the calculations
are exact and the results are obtained through an iterative process, without
using perturbation theory.Comment: 22 pages, 6 Figures, Added contents, to appear in PR
Long-range interactions and the sign of natural amplitudes in two-electron systems
In singlet two-electron systems the natural occupation numbers of the
one-particle reduced density matrix are given as squares of the natural
amplitudes which are defined as the expansion coefficients of the two-electron
wave function in a natural orbital basis. In this work we relate the sign of
the natural amplitudes to the nature of the two-body interaction. We show that
long-range Coulomb-type interactions are responsible for the appearance of
positive amplitudes and give both analytical and numerical examples that
illustrate how the long-distance structure of the wave function affects these
amplitudes. We further demonstrate that the amplitudes show an avoided crossing
behavior as function of a parameter in the Hamiltonian and use this feature to
show that these amplitudes never become zero, except for special interactions
in which infinitely many of them can become zero simultaneously when changing
the interaction strength. This mechanism of avoided crossings provides an
alternative argument for the non-vanishing of the natural occupation numbers in
Coulomb systems.Comment: 10 pages, 4 figure
First-Order Provenance Games
We propose a new model of provenance, based on a game-theoretic approach to
query evaluation. First, we study games G in their own right, and ask how to
explain that a position x in G is won, lost, or drawn. The resulting notion of
game provenance is closely related to winning strategies, and excludes from
provenance all "bad moves", i.e., those which unnecessarily allow the opponent
to improve the outcome of a play. In this way, the value of a position is
determined by its game provenance. We then define provenance games by viewing
the evaluation of a first-order query as a game between two players who argue
whether a tuple is in the query answer. For RA+ queries, we show that game
provenance is equivalent to the most general semiring of provenance polynomials
N[X]. Variants of our game yield other known semirings. However, unlike
semiring provenance, game provenance also provides a "built-in" way to handle
negation and thus to answer why-not questions: In (provenance) games, the
reason why x is not won, is the same as why x is lost or drawn (the latter is
possible for games with draws). Since first-order provenance games are
draw-free, they yield a new provenance model that combines how- and why-not
provenance
Quantum Limits of Measurements Induced by Multiplicative Conservation Laws: Extension of the Wigner-Araki-Yanase Theorem
The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws
limit the accuracy of measurements. Recently, various quantitative expressions
have been found for quantum limits on measurements induced by additive
conservation laws, and have been applied to the study of fundamental limits on
quantum information processing. Here, we investigate generalizations of the WAY
theorem to multiplicative conservation laws. The WAY theorem is extended to
show that an observable not commuting with the modulus of, or equivalently the
square of, a multiplicatively conserved quantity cannot be precisely measured.
We also obtain a lower bound for the mean-square noise of a measurement in the
presence of a multiplicatively conserved quantity. To overcome this noise it is
necessary to make large the coefficient of variation (the so-called relative
fluctuation), instead of the variance as is the case for additive conservation
laws, of the conserved quantity in the apparatus.Comment: 8 pages, REVTEX; typo added, to appear in PR
Quantum Electrical Dipole in Triangular Systems: a Model for Spontaneous Polarity in Metal Clusters
Triangular symmetric molecules with mirror symmetry perpendicular to the
3-fold axis are forbidden to have a fixed electrical dipole moment. However, if
the ground state is orbitally degenerate and lacks inversion symmetry, then a
``quantum'' dipole moment does exist. The system of 3 electrons in D_3h
symmetry is our example. This system is realized in triatomic molecules like
Na_3. Unlike the fixed dipole of a molecule like water, the quantum moment does
not point in a fixed direction, but lies in the plane of the molecule and takes
quantized values +/- mu_0 along any direction of measurement in the plane. An
electric field F in the plane leads to a linear Stark splitting +/- mu_0 F}. We
introduce a toy model to study the effect of Jahn-Teller distortions on the
quantum dipole moment. We find that the quantum dipole property survives when
the dynamic Jahn-Teller effect is included, if the distortion of the molecule
is small. Linear Stark splittings are suppressed in low fields by molecular
rotation, just as the linear Stark shift of water is suppressed, but will be
revealed in moderately large applied fields and low temperatures. Coulomb
correlations also give a partial suppression.Comment: 10 pages with 7 figures included; thoroughly revised with a new
coauthor; final minor change
Comment on Viscous Stability of Relativistic Keplerian Accretion Disks
Recently Ghosh (1998) reported a new regime of instability in Keplerian
accretion disks which is caused by relativistic effects. This instability
appears in the gas pressure dominated region when all relativistic corrections
to the disk structure equations are taken into account. We show that he uses
the stability criterion in completely wrong way leading to inappropriate
conclusions. We perform a standard stability analysis to show that no unstable
region can be found when the relativistic disk is gas pressure dominated.Comment: 9 pages, 4 figures, uses aasms4.sty, submitted for ApJ Letter
Learning to predict phases of manipulation tasks as hidden states
Phase transitions in manipulation tasks often occur
when contacts between objects are made or broken. A
switch of the phase can result in the robot’s actions suddenly
influencing different aspects of its environment. Therefore, the
boundaries between phases often correspond to constraints or
subgoals of the manipulation task.
In this paper, we investigate how the phases of manipulation
tasks can be learned from data. The task is modeled as an
autoregressive hidden Markov model, wherein the hidden phase
transitions depend on the observed states. The model is learned
from data using the expectation-maximization algorithm. We
demonstrate the proposed method on both a pushing task
and a pepper mill turning task. The proposed approach was
compared to a standard autoregressive hidden Markov model.
The experiments show that the learned models can accurately
predict the transitions in phases during the manipulation tasks
Learning robot in-hand manipulation with tactile features
Dexterous manipulation enables repositioning of
objects and tools within a robot’s hand. When applying dexterous
manipulation to unknown objects, exact object models
are not available. Instead of relying on models, compliance and
tactile feedback can be exploited to adapt to unknown objects.
However, compliant hands and tactile sensors add complexity
and are themselves difficult to model. Hence, we propose acquiring
in-hand manipulation skills through reinforcement learning,
which does not require analytic dynamics or kinematics models.
In this paper, we show that this approach successfully acquires
a tactile manipulation skill using a passively compliant hand.
Additionally, we show that the learned tactile skill generalizes
to novel objects
Optimization Under Uncertainty Using the Generalized Inverse Distribution Function
A framework for robust optimization under uncertainty based on the use of the
generalized inverse distribution function (GIDF), also called quantile
function, is here proposed. Compared to more classical approaches that rely on
the usage of statistical moments as deterministic attributes that define the
objectives of the optimization process, the inverse cumulative distribution
function allows for the use of all the possible information available in the
probabilistic domain. Furthermore, the use of a quantile based approach leads
naturally to a multi-objective methodology which allows an a-posteriori
selection of the candidate design based on risk/opportunity criteria defined by
the designer. Finally, the error on the estimation of the objectives due to the
resolution of the GIDF will be proven to be quantifiableComment: 20 pages, 25 figure
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