227 research outputs found
Hamilton-Jacobi Formulation of KS Entropy for Classical and Quantum Dynamics
A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is
developed. It is numerically efficient and reveals a close relation between the
KS invariant and the classical action. This formulation is extended to the
quantum domain using the Madelung-Bohm orbits associated with the Schroedinger
equation. The resulting quantum KS invariant for a given orbit equals the mean
decay rate of the probability density along the orbit, while its ensemble
average measures the mean growth rate of configuration-space information for
the quantum system.Comment: preprint, 8 pages (revtex
Verschraenkung versus Stosszahlansatz: Disappearance of the Thermodynamic Arrow in a High-Correlation Environment
The crucial role of ambient correlations in determining thermodynamic
behavior is established. A class of entangled states of two macroscopic systems
is constructed such that each component is in a state of thermal equilibrium at
a given temperature, and when the two are allowed to interact heat can flow
from the colder to the hotter system. A dilute gas model exhibiting this
behavior is presented. This reversal of the thermodynamic arrow is a
consequence of the entanglement between the two systems, a condition that is
opposite to molecular chaos and shown to be unlikely in a low-entropy
environment. By contrast, the second law is established by proving Clausius'
inequality in a low-entropy environment. These general results strongly support
the expectation, first expressed by Boltzmann and subsequently elaborated by
others, that the second law is an emergent phenomenon that requires a
low-entropy cosmological environment, one that can effectively function as an
ideal information sink.Comment: 4 pages, REVTeX
Stable ultrahigh-density magneto-optical recordings using introduced linear defects
The stability of data bits in magnetic recording media at ultrahigh densities
is compromised by thermal `flips' -- magnetic spin reversals -- of nano-sized
spin domains, which erase the stored information. Media that are magnetized
perpendicular to the plane of the film, such as ultrathin cobalt films or
multilayered structures, are more stable against thermal self-erasure than
conventional memory devices. In this context, magneto-optical memories seem
particularly promising for ultrahigh-density recording on portable disks, and
bit densities of 100 Gbit inch have been demonstrated using recent
advances in the bit writing and reading techniques. But the roughness and
mobility of the magnetic domain walls prevents closer packing of the magnetic
bits, and therefore presents a challenge to reaching even higher bit densities.
Here we report that the strain imposed by a linear defect in a magnetic thin
film can smooth rough domain walls over regions hundreds of micrometers in
size, and halt their motion. A scaling analysis of this process, based on the
generic physics of disorder-controlled elastic lines, points to a simple way by
which magnetic media might be prepared that can store data at densities in
excess of 1 Tbit inch.Comment: 5 pages, 4 figures, see also an article in TRN News at
http://www.trnmag.com/Stories/041801/Defects_boost_disc_capacity_041801.htm
How to obtain a covariant Breit type equation from relativistic Constraint Theory
It is shown that, by an appropriate modification of the structure of the
interaction potential, the Breit equation can be incorporated into a set of two
compatible manifestly covariant wave equations, derived from the general rules
of Constraint Theory. The complementary equation to the covariant Breit type
equation determines the evolution law in the relative time variable. The
interaction potential can be systematically calculated in perturbation theory
from Feynman diagrams. The normalization condition of the Breit wave function
is determined. The wave equation is reduced, for general classes of potential,
to a single Pauli-Schr\"odinger type equation. As an application of the
covariant Breit type equation, we exhibit massless pseudoscalar bound state
solutions, corresponding to a particular class of confining potentials.Comment: 20 pages, Late
A note on entropic uncertainty relations of position and momentum
We consider two entropic uncertainty relations of position and momentum
recently discussed in literature. By a suitable rescaling of one of them, we
obtain a smooth interpolation of both for high-resolution and low-resolution
measurements respectively. Because our interpolation has never been mentioned
in literature before, we propose it as a candidate for an improved entropic
uncertainty relation of position and momentum. Up to now, the author has
neither been able to falsify nor prove the new inequality. In our opinion it is
a challenge to do either one.Comment: 2 pages, 2 figures, 2 references adde
The Haroche-Ramsey experiment as a generalized measurement
A number of atomic beam experiments, related to the Ramsey experiment and a
recent experiment by Brune et al., are studied with respect to the question of
complementarity. Three different procedures for obtaining information on the
state of the incoming atom are compared. Positive operator-valued measures are
explicitly calculated. It is demonstrated that, in principle, it is possible to
choose the experimental arrangement so as to admit an interpretation as a joint
non-ideal measurement yielding interference and ``which-way'' information.
Comparison of the different measurements gives insight into the question of
which information is provided by a (generalized) quantum mechanical
measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned
by the operators of the POVM, are determined for different measurement
arrangements and different values of the parameters.Comment: REVTeX, 22 pages, 5 figure
The Gluon Exchange Interaction Between Constituent Quarks
The interaction mediated by irreducible pion and gluon exchange between
constituent quarks is calculated and shown to have a strong tensor component,
which tends to cancel the pion exchange tensor interaction between quarks. Its
spin-spin component is somewhat weaker than the pion exchange spin-spin
interaction, while its central and spin-orbit components are small in
comparison to the corresponding single gluon exchange interactions. The
combination of the gluon exchange interaction with the single pion
exchange interaction and a weak gluon exchange interaction between constituent
quarks has the qualitative features required for understanding the hyperfine
splittings of the spectra of the nucleon and the resonances.Comment: LaTeX, 17 pages, 5 Postscript figure
Apparent wave function collapse caused by scattering
Some experimental implications of the recent progress on wave function
collapse are calculated. Exact results are derived for the center-of-mass wave
function collapse caused by random scatterings and applied to a range of
specific examples. The results show that recently proposed experiments to
measure the GRW effect are likely to fail, since the effect of naturally
occurring scatterings is of the same form as the GRW effect but generally much
stronger. The same goes for attempts to measure the collapse caused by quantum
gravity as suggested by Hawking and others. The results also indicate that
macroscopic systems tend to be found in states with (Delta-x)(Delta-p) =
hbar/sqrt(2), but microscopic systems in highly tiltedly squeezed states with
(Delta-x)(Delta-p) >> hbar.Comment: Final published version. 20 pages, Plain TeX, no figures. Online at
http://astro.berkeley.edu/~max/collapse.html (faster from the US), from
http://www.mpa-garching.mpg.de/~max/collapse.html (faster from Europe) or
from [email protected]
Validity of the second law in nonextensive quantum thermodynamics
The second law of thermodynamics in nonextensive statistical mechanics is
discussed in the quantum regime. Making use of the convexity property of the
generalized relative entropy associated with the Tsallis entropy indexed by q,
Clausius' inequality is shown to hold in the range of q between zero and two.
This restriction on the range of the entropic index, q, is purely quantum
mechanical and there exists no upper bound of q for validity of the second law
in classical theory.Comment: 12 pages, no figure
Peripheral N Scattering: A Tool For Identifying The Two Pion Exchange Component Of The NN Potential
We study elastic N scattering and produce a quantitative correlation
between the range of the effective potential and the energy of the system. This
allows the identification of the waves and energies for which the scattering
may be said to be peripheral. We then show that the corresponding phase shifts
are sensitive to the tail of the NN potential, which is due to the exchange of
two pions. However, the present uncertainties in the experimental phase shifts
prevent the use of N scattering to discriminate the existing models
for the NN interaction.Comment: 19 pages, 6 PostScript figures, RevTeX, to be appear in Phys. Rev.
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