Absence of Thermalization in Nonintegrable Systems

We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.Comment: 5 pages, 2 figures, to appear in PRL, improved presentation of the numerical findings, editorial change

Absence of Buckling in Nerve Fiber

In this study we give a geometrical model which employs the smoothness of nerve fibers as differentiable curves. We show that a nerve fiber may encounter large curvature due to the possible helicial bending and hence it could cause the fiber to buckle. However, its membrane structure provides a mechanism, entirely geometrical to avoid it. To overcome the challenge of emerging helix we project it into a plane.Comment: 7 pages no figure. Final version presented at The 10th International Physics Conference of the Balkan Physical Union (BPU10), 26-30 August 2018. To be published in AIP Conference Proceeding

Absence of barriers in dynamical triangulation

Due to the unrecognizability of certain manifolds there must exist pairs of triangulations of these manifolds that can only be reached from each other by going through an intermediate state that is very large. This might reduce the reliability of dynamical triangulation, because there will be states that will not be reached in practice. We investigate this problem numerically for the manifold $S^5$, which is known to be unrecognizable, but see no sign of these unreachable states.Comment: 8 pages, LaTeX2e source with postscript resul

Absence of Wigner Crystallization in Graphene

Graphene, a single sheet of graphite, has attracted tremendous attention due to recent experiments which demonstrate that carriers in it are described by massless fermions with linear dispersion. In this note, we consider the possibility of Wigner crystallization in graphene in the absence of external magnetic field. We show that the ratio of potential and kinetic energy is independent of the carrier density, the tuning parameter that usually drives Wigner crystallization and find out that for given material parameters (dielectric constant and Fermi velocity), Wigner crystallization is not possible. We comment on the how these results change in the presence of a strong external magnetic field.Comment: 3 pages, 1 figure,Submitted for PR

Absence of ferroelectricity in BiMnO3 ceramics

We performed factor-group analysis of all phonons in possible monoclinic C2/c and C2 structures of BiMnO3 and compared it with our experimental infrared and Raman spectra. We conclude that the crystal structure is centrosymmetric C2/c in the whole investigated temperature range from 10 to 550 K, therefore BiMnO3 cannot be ferroelectric. We revealed a dielectric relaxation in THz spectra above the structural phase transition taking place at T_C1=475 K giving evidence in strong lattice anharmonicity and a large dynamical disorder of Bi cations above T_C1. Step-like dielectric anomaly observed at T_C1 in THz permittivity reminds antiferroelectric phase transition. Nevertheless, the low-temperature dielectric studies did not reveal any antiferroelectric or ferroelectric hysteresis loop. Our experimental results support theoretical paper of P. Baettig et al. (J. Am. Chem. Soc. 129, 9854 (2007)) claiming that BiMnO3 is not multiferroic, but only antipolar ferromagnet.Comment: accepted to JA

Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

Absence of Two-Dimensional Bragg Glasses

The stability to dislocations of the elastic phase, or ``Bragg glass'', of a randomly pinned elastic medium in two dimensions is studied using the minimum-cost-flow algorithm for a disordered fully-packed loop model. The elastic phase is found to be unstable to dislocations due to the quenched disorder. The energetics of dislocations are discussed within the framework of renormalization group predictions as well as in terms of a domain wall picture.Comment: 5 pages, REVTEX, 3 figures included. Further information can be obtained from [email protected]

Absence of Singularity in Loop Quantum Cosmology

It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstation comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.Comment: 4 pages, 1 figur