1,267 research outputs found
Topologically non-trivial quantum layers
Given a complete non-compact surface embedded in R^3, we consider the
Dirichlet Laplacian in a layer of constant width about the surface. Using an
intrinsic approach to the layer geometry, we generalise the spectral results of
an original paper by Duclos et al. to the situation when the surface does not
possess poles. This enables us to consider topologically more complicated
layers and state new spectral results. In particular, we are interested in
layers built over surfaces with handles or several cylindrically symmetric
ends. We also discuss more general regions obtained by compact deformations of
certain layers.Comment: 15 pages, 6 figure
Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula
Consider a three dimensional system which looks like a cross-connected pipe
system, i.e. a small sample coupled to a finite number of leads. We investigate
the current running through this system, in the linear response regime, when we
adiabatically turn on an electrical bias between leads. The main technical tool
is the use of a finite volume regularization, which allows us to define the
current coming out of a lead as the time derivative of its charge. We finally
prove that in virtually all physically interesting situations, the conductivity
tensor is given by a Landauer-B{\"u}ttiker type formula.Comment: 20 pages, submitte
Tissue fusion over non-adhering surfaces
Tissue fusion eliminates physical voids in a tissue to form a continuous
structure and is central to many processes in development and repair. Fusion
events in vivo, particularly in embryonic development, often involve the
purse-string contraction of a pluricellular actomyosin cable at the free edge.
However in vitro, adhesion of the cells to their substrate favors a closure
mechanism mediated by lamellipodial protrusions, which has prevented a
systematic study of the purse-string mechanism. Here, we show that monolayers
can cover well-controlled mesoscopic non-adherent areas much larger than a cell
size by purse-string closure and that active epithelial fluctuations are
required for this process. We have formulated a simple stochastic model that
includes purse-string contractility, tissue fluctuations and effective friction
to qualitatively and quantitatively account for the dynamics of closure. Our
data suggest that, in vivo, tissue fusion adapts to the local environment by
coordinating lamellipodial protrusions and purse-string contractions
Comparison of latching control strategies for a heaving wave energy device in random sea
International audienceThis paper investigates semi-analytically the latching control applied to a mechanical oscillator; and numerically three strategies of latching control for a point absorber wave energy converter oscillating in the heave mode only. By solving the equation of motion of a mechanical damped oscillator, it is shown that latching control can magnify the amplitude of the motion whatever the frequency of the excitation force, and how it can improve the efficiency of the system, in term of absorbed energy, for excitation frequencies apart from the natural frequency. Assuming that the excitation force is known in the close future and that the body is locked in position at the current time step, equations of motion of the body are solved numerically in the time domain fordifferent initial conditions (i.e. latching durations). For all these simulations, three criteria—one for each strategy—are tested and the latching time leading to the best result is selected. Time domainsimulation results are presented for a heaving buoy in small-amplitude regular and random waves. In regular waves, the same results as for the case of a mechanical oscillator are recovered for the wave energy converter. In random sea, results show that for all the three proposed strategies, efficiency of the wave energy converter is considerably improved in terms of absorbed energy. Numerical study of the period of the controlled system shows that the delay of prediction of the excitation force in the future seems to be bounded by the natural period of the system
Bound States in Mildly Curved Layers
It has been shown recently that a nonrelativistic quantum particle
constrained to a hard-wall layer of constant width built over a geodesically
complete simply connected noncompact curved surface can have bound states
provided the surface is not a plane. In this paper we study the weak-coupling
asymptotics of these bound states, i.e. the situation when the surface is a
mildly curved plane. Under suitable assumptions about regularity and decay of
surface curvatures we derive the leading order in the ground-state eigenvalue
expansion. The argument is based on Birman-Schwinger analysis of Schroedinger
operators in a planar hard-wall layer.Comment: LaTeX 2e, 23 page
Universal topological phase of 2D stabilizer codes
Two topological phases are equivalent if they are connected by a local
unitary transformation. In this sense, classifying topological phases amounts
to classifying long-range entanglement patterns. We show that all 2D
topological stabilizer codes are equivalent to several copies of one universal
phase: Kitaev's topological code. Error correction benefits from the
corresponding local mappings.Comment: 4 pages, 3 figure
H2 molecule in strong magnetic fields
The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant
magnetic field is asymptotic, in norm-resolvent sense, to an effective
Hamiltonian which has the form of a multi-particle Schr\"odinger operator with
interactions given by one-dimensional \delta-potentials. We study this
effective Hamiltonian in the case of the H2 -molecule and establish existence
of the ground state. We also show that the inter-nuclear equilibrium distance
tends to 0 as the field-strength tends to infinity
Pulse-driven quantum dynamics beyond the impulsive regime
We review various unitary time-dependent perturbation theories and compare
them formally and numerically. We show that the Kolmogorov-Arnold-Moser
technique performs better owing to both the superexponential character of
correction terms and the possibility to optimize the accuracy of a given level
of approximation which is explored in details here. As an illustration, we
consider a two-level system driven by short pulses beyond the sudden limit.Comment: 15 pages, 5 color figure
On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum
of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha,
with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay
as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously
differentiable in the strong sense and such that the matrix entries with
respect to the spectral decomposition of H obey the estimate
|V(t)_{m,n}|0,
p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be
arbitrarily small provided p is sufficiently large and \epsilon is small
enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the
diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where
\sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the
Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was
discussed earlier in the literature by Howland
Une méthode de calcul des coefficients de réflexion et de transmission d'une houle bidimensionnelle en milieu confiné
International audienc
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