An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency

The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality. Motivated by the form of sharp interface problems, we formulate such an alternative equation and compare the properties of the models for the evolution of phase interfaces in solids, which consist of the elasticity equations and the Allen-Cahn equation or the alternative equation. We find that numerical simulations of phase interfaces with small interface energy based on the alternative model are more effective then simulations based on the Allen-Cahn model.Comment: arXiv admin note: text overlap with arXiv:1505.0544

Continuous macroscopic limit of a discrete stochastic model for interaction of living cells

In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded volume is derived, describing cells moving in a medium and reacting to each other through both direct contact and long range chemotaxis. The continuous macroscopic model is obtained as a Fokker-Planck equation describing evolution of the cell probability density function. All coefficients of the general macroscopic model are derived from parameters of the CPM and a very good agreement is demonstrated between CPM Monte Carlo simulations and numerical solution of the macroscopic model. It is also shown that in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. General multiscale approach is demonstrated by simulating spongy bone formation from loosely packed mesenchyme via the intramembranous route suggesting that self-organizing physical mechanisms can account for this developmental process.Comment: 4 pages, 3 figure

Change of decoherence scenario and appearance of localization due to reservoir anharmonicity

Although coupling to a super-Ohmic bosonic reservoir leads only to partial dephasing on short time scales, exponential decay of coherence appears in the Markovian limit (for long times) if anharmonicity of the reservoir is taken into account. This effect not only qualitatively changes the decoherence scenario but also leads to localization processes in which superpositions of spatially separated states dephase with a rate that depends on the distance between the localized states. As an example of the latter process, we study the decay of coherence of an electron state delocalized over two semiconductor quantum dots due to anharmonicity of phonon modes.Comment: 4 pages, 1 figure; moderate changes; auxiliary material added; to appear in Phys. Rev. Let

Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians

The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems under study include the shallow water equation and Dym type equation. The classes of solutions are described in terms of theta-functions and their singular limits by using new parameterizations. A qualitative description of real valued solutions is provided

Entanglement in SO(3)-invariant bipartite quantum systems

The structure of the state spaces of bipartite (N tensor N) quantum systems which are invariant under product representations of the group SO(3) of three-dimensional proper rotations is analyzed. The subsystems represent particles of arbitrary spin j which transform according to an irreducible representation of the rotation group. A positive map theta is introduced which describes the time reversal symmetry of the local states and which is unitarily equivalent to the transposition of matrices. It is shown that the partial time reversal transformation theta_2 = (I tensor theta) acting on the composite system can be expressed in terms of the invariant 6-j symbols introduced by Wigner into the quantum theory of angular momentum. This fact enables a complete geometrical construction of the manifold of states with positive partial transposition and of the sets of separable and entangled states of (4 tensor 4) systems. The separable states are shown to form a three-dimensional prism and a three-dimensional manifold of bound entangled states is identified. A positive maps is obtained which yields, together with the time reversal, a necessary and sufficient condition for the separability of states of (4 tensor 4) systems. The relations to the reduction criterion and to the recently proposed cross norm criterion for separability are discussed.Comment: 15 pages, 3 figure

Security bound of two-bases quantum key-distribution protocols using qudits

We investigate the security bounds of quantum cryptographic protocols using $d$-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the BB84 quantum key distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.Comment: 12 pages, 2 figures, to appear in Phys. Rev.

Preparation of Knill-Laflamme-Milburn states using tunable controlled phase gate

A specific class of partially entangled states known as Knill-Laflamme-Milburn states (or KLM states) has been proved to be useful in relation to quantum information processing [Knill et al., Nature 409, 46 (2001)]. Although the usage of such states is widely investigated, considerably less effort has been invested into experimentally accessible preparation schemes. This paper discusses the possibility to employ a tunable controlled phase gate to generate an arbitrary Knill-Laflamme-Milburn state. In the first part, the idea of using the controlled phase gate is explained on the case of two-qubit KLM states. Optimization of the proposed scheme is then discussed for the framework of linear optics. Subsequent generalization of the scheme to arbitrary n-qubit KLM state is derived in the second part of this paper.Comment: 5 pages, 4 figures, accepted in Journal of Physics

Theory of 'which path' dephasing in single electron interference due to trace in conductive environment

A single-electron two-path interference (Young) experiment is considered theoretically. The decoherence of an electron wave packet due to the 'which path' trace left in the conducting (metallic) plate placed under the electron trajectories is calculated using the many-body quantum description of the electron gas reservoir.Comment: 11 pages, 5 figures, moderate changes, 1 new figure, updated reference

Global smooth solutions and exponential stability for a nonlinear beam

Published versio

Many--Particle Correlations in Relativistic Nuclear Collisions

Many--particle correlations due to Bose-Einstein interference are studied in ultrarelativistic heavy--ion collisions. We calculate the higher order correlation functions from the 2--particle correlation function by assuming that the source is emitting particles incoherently. In particular parametrizations of and relations between longitudinal, sidewards, outwards and invariant radii and corresponding momenta are discussed. The results are especially useful in low statistics measurements of higher order correlation functions. We evaluate the three--pion correlation function recently measured by NA44 and predict the 2--pion--2--kaon correlation function. Finally, many particle Coulomb corrections are discussed.Comment: 5 corrected misprints, 14 pages, revtex, epsfig, 6 figures included, manuscript also available at http://www.nbi.dk/~vischer/publications.htm