1,426 research outputs found
Entanglement, which-way measurements, and a quantum erasure
We present a didactical approach to the which-way experiment and the
counterintuitive effect of the quantum erasure for one-particle quantum
interferences. The fundamental concept of entanglement plays a central role and
highlights the complementarity between quantum interference and knowledge of
which path is followed by the particle.Comment: 5 pages, 4 figures; with some clarifications and added reference
Extended Edge States in Finite Hall Systems
We study edge states of a random Schroedinger operator for an electron
submitted to a magnetic field in a finite macroscopic two dimensional system of
linear dimensions equal to L. The y direction is L-periodic and in the x
direction the electron is confined by two smoothly increasing parallel boundary
potentials. We prove that, with large probability, for an energy range in the
first spectral gap of the bulk Hamiltonian, the spectrum of the full
Hamiltonian consists only on two sets of eigenenergies whose eigenfuntions have
average velocities which are strictly positive/negative, uniformly with respect
to the size of the system. Our result gives a well defined meaning to the
notion of edge states for a finite cylinder with two boundaries, and extends
previous studies on systems with only one boundary.Comment: 24 pages, 1 figure; Submitte
Neutrino current in a gravitational plane wave collision background
The behaviour of a massless Dirac field on a general spacetime background
representing two colliding gravitational plane waves is discussed in the
Newman-Penrose formalism. The geometrical properties of the neutrino current
are analysed and explicit results are given for the special Ferrari-Ibanez
solution.Comment: 17 pages, 6 Postscript figures, accepted by International Journal of
Modern Physics
The preload force affects the perception threshold of muscle vibration-induced movement illusions
On the Hydrodynamic Equilibrium of a Rod in a Lattice Fluid
We model the behavior of a big (Brazil) nut in a medium of smaller nuts with
a stochastic asymmetric simple exclusion dynamics of a polymer-monomer lattice
system. The polymer or `rod' can move up or down in an external negative field,
occupying N horizontal lattice sites where the monomers cannot enter. The
monomers (at most one per site) or `fluid particles' are moving symmetrically
in the horizontal plane and asymmetrically in the vertical direction, also with
a negative field. For a fixed position of the rod, this lattice fluid is in
equilibrium with a vertical height profile reversible for the monomers' motion.
Upon `shaking' (speeding up the monomers) the motion of the `rod' dynamically
decouples from that of the monomers resulting in a reversible random walk for
the rod around an average height proportional to log N.Comment: 19 pages, 2 figure
Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems
We study the spectrum of a random Schroedinger operator for an electron
submitted to a magnetic field in a finite but macroscopic two dimensional
system of linear dimensions equal to L. The y direction is periodic and in the
x direction the electron is confined by two smooth increasing boundary
potentials. The eigenvalues of the Hamiltonian are classified according to
their associated quantum mechanical current in the y direction. Here we look at
an interval of energies inside the first Landau band of the random operator for
the infinite plane. In this energy interval, with large probability, there
exist O(L) eigenvalues with positive or negative currents of O(1). Between each
of these there exist O(L^2) eigenvalues with infinitesimal current
O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the
integer quantum Hall effect.Comment: 29 pages, no figure
Aspects of two dimensional magnetic Schrödinger operatorsquantum hall systems and magnetic Stark resonances
In this PhD thesis we deal with two mathematical problems arising from quantum mechanics. We consider a spinless non relativistic quantum particle whose configuration space is a two dimensional surface S. We also suppose that the particle feels the effect of an homogeneous magnetic field perpendicular to the surface S. In the first case S = R × SL1, the infinite cylinder of circumference L, corresponding to periodic boundary conditions, while in the second one S = R2. In both cases the particle feels the effect of an additional suitable potential. We are thus left with the study of two specific classes of Schrödinger operators. The operator of the first class generates the dynamics of the particle when it is submitted to an Anderson-type random potential, as well as to a non random potential confining the particle along the cylinder axis in an interval of length L. In this case we describe the spectrum and classify it by the quantum mechanical current carried by the corresponding eigenfunctions. We prove that there are spectral regions in which all the eigenvalues have an order one current with respect to L, and spectral regions where eigenvalues with order one current and eigenvalues with infinitesimal current with respect to L are intermixed. These results are relevant for the theory of the integer quantum Hall effect. The second Schrödinger operator class corresponds to the physical situation where the potential is the sum of a "local" potential and of a potential due to a weak constant electric field F. In this case we show that the resonant states, induced by the electric field, decay exponentially at a rate given by the imaginary part of the eigenvalues of some non self-adjoint operator. Moreover we prove an upper bound on this imaginary part that turns out to be of order exp(-1/F2) as F goes to zero. Therefore the lifetime of the resonant states is at least of order exp(-1/F2)
Archimedes' law and its corrections for an active particle in a granular sea
We study the origin of buoyancy forces acting on a larger particle moving in
a granular medium subject to horizontal shaking and its corrections before
fluidization. In the fluid limit Archimedes' law is verified; before the limit
memory effects counteract buoyancy, as also found experimentally. The origin of
the friction is an excluded volume effect between active particles, which we
study more exactly for a random walker in a random environment. The same
excluded volume effect is also responsible for the mutual attraction between
bodies moving in the granular medium. Our theoretical modeling proceeds via an
asymmetric exclusion process, i.e., via a dissipative lattice gas dynamics
simulating the position degrees of freedom of a low density granular sea.Comment: 22 pages,5 figure
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