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 $\sim$100 Gbit inch$^{-2}$ 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$^{-2}$.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 π−\pi-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 $\pi-$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 $\Delta$ 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 Nα\alpha Scattering: A Tool For Identifying The Two Pion Exchange Component Of The NN Potential

We study elastic N$\alpha$ 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$\alpha$ scattering to discriminate the existing models for the NN interaction.Comment: 19 pages, 6 PostScript figures, RevTeX, to be appear in Phys. Rev.