27,993 research outputs found
Time-Dependent Invariants and Green's Functions in the Probability Representation of Quantum Mechanics
In the probability representation of quantum mechanics, quantum states are
represented by a classical probability distribution, the marginal distribution
function (MDF), whose time dependence is governed by a classical evolution
equation. We find and explicitly solve, for a wide class of Hamiltonians, new
equations for the Green's function of such an equation, the so-called classical
propagator. We elucidate the connection of the classical propagator to the
quantum propagator for the density matrix and to the Green's function of the
Schr\"odinger equation. Within the new description of quantum mechanics we give
a definition of coherence solely in terms of properties of the MDF and we test
the new definition recovering well known results. As an application, the forced
parametric oscillator is considered . Its classical and quantum propagator are
found, together with the MDF for coherent and Fock states.Comment: 29 pages, RevTex, 6 eps-figures, to appear on Phys. Rev.
Near-field interaction between domain walls in adjacent Permalloy nanowires
The magnetostatic interaction between two oppositely charged transverse
domain walls (DWs)in adjacent Permalloy nanowires is experimentally
demonstrated. The dependence of the pinning strength on wire separation is
investigated for distances between 13 and 125 nm, and depinning fields up to 93
Oe are measured. The results can be described fully by considering the
interaction between the full complex distribution of magnetic charge within
rigid, isolated DWs. This suggests the DW internal structure is not appreciably
disturbed by the pinning potential, and that they remain rigid although the
pinning strength is significant. This work demonstrates the possibility of
non-contact DW trapping without DW perturbation and full continuous flexibility
of the pinning potential type and strength. The consequence of the interaction
on DW based data storage schemes is evaluated.Comment: 4 pages, 4 figures, 1 page supplimentary material (supporting.ps
Proof of Bose-Einstein Condensation for Interacting Gases with a One-Particle Spectral Gap
Using a specially tuned mean-field Bose gas as a reference system, we
establish a positive lower bound on the condensate density for continuous Bose
systems with superstable two-body interactions and a finite gap in the
one-particle excitations spectrum, i.e. we prove for the first time standard
homogeneous Bose-Einstein condensation for such interacting systems
The partition function versus boundary conditions and confinement in the Yang-Mills theory
We analyse dependence of the partition function on the boundary condition for
the longitudinal component of the electric field strength in gauge field
theories. In a physical gauge the Gauss law constraint may be resolved
explicitly expressing this component via an integral of the physical
transversal variables. In particular, we study quantum electrodynamics with an
external charge and SU(2) gluodynamics. We find that only a charge distribution
slowly decreasing at spatial infinity can produce a nontrivial dependence in
the Abelian theory. However, in gluodynamics for temperatures below some
critical value the partition function acquires a delta-function like dependence
on the boundary condition, which leads to colour confinement.Comment: 14 pages, RevTeX, submitted to Phys. Rev.
Lie symmetries for two-dimensional charged particle motion
We find the Lie point symmetries for non-relativistic two-dimensional charged
particle motion. These symmetries comprise a quasi-invariance transformation, a
time-dependent rotation, a time-dependent spatial translation and a dilation.
The associated electromagnetic fields satisfy a system of first-order linear
partial differential equations. This system is solved exactly, yielding four
classes of electromagnetic fields compatible with Lie point symmetries
Microlensing of Relativistic Knots in the Quasar HE1104-1805
We present 3 years of photometry of the ``Double Hamburger'' lensed quasar,
HE1104-1805, obtained on 102 separate nights using the OGLE 1.3-m telescope.
Both the A and B images show variations, but with substantial differences in
the lighcurves at all time delays. At the 310 day delay reported by Wisotzki
and collaborators the difference lightcurve has an rms amplitude of 0.060 mag.
The structure functions for the A and B images are quite different, with image
A more than twice as variable as image B (a factor of 4 in structure function)
on timescales of less than a month. Adopting microlensing as a working
hypothesis for the uncorrelated variability, the short timescale argues for the
relativistic motion of one or more components of the source. We argue that the
small amplitude of the fluctuations is due to the finite size of the source
with respect to the microlenses.Comment: As accepted for publication in ApJ. 22 pages. The discussion of
microlensing at high optical depth has been shortened and a few minor points
have been clarifie
A Magnetic Resonance Realization of Decoherence-Free Quantum Computation
We report the realization, using nuclear magnetic resonance techniques, of
the first quantum computer that reliably executes an algorithm in the presence
of strong decoherence. The computer is based on a quantum error avoidance code
that protects against a class of multiple-qubit errors. The code stores two
decoherence-free logical qubits in four noisy physical qubits. The computer
successfully executes Grover's search algorithm in the presence of arbitrarily
strong engineered decoherence. A control computer with no decoherence
protection consistently fails under the same conditions.Comment: 5 pages with 3 figures, revtex4, accepted by Physical Review Letters;
v2 minor revisions to conten
On A Cosmological Invariant as an Observational Probe in the Early Universe
k-essence scalar field models are usually taken to have lagrangians of the
form with some general function of
. Under certain conditions this lagrangian
in the context of the early universe can take the form of that of an oscillator
with time dependent frequency. The Ermakov invariant for a time dependent
oscillator in a cosmological scenario then leads to an invariant quadratic form
involving the Hubble parameter and the logarithm of the scale factor. In
principle, this invariant can lead to further observational probes for the
early universe. Moreover, if such an invariant can be observationally verified
then the presence of dark energy will also be indirectly confirmed.Comment: 4 pages, Revte
Degeneracy in exotic gravitational lensing
We present three different theoretically foreseen, but unusual, astrophysical
situations where the gravitational lens equation ends up being the same, thus
producing a degeneracy problem. These situations are (a) the case of
gravitational lensing by exotic stresses (matter violating the weak energy
condition and thus having a negative mass, particular cases of wormholes
solutions can be used as an example), (b) scalar field gravitational lensing
(i.e. when considering the appearance of a scalar charge in the lensing
scenario), and (c) gravitational lensing in closed universes (with
antipodes).The reasons that lead to this degeneracy in the lens equations, the
possibility of actually encountering it in the real universe, and eventually
the ways to break it, are discussed.Comment: Accepted for publication in Modern Physics Letters
Solving order constraints in logarithmic space.
We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space
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