3D Discrete Dislocation Dynamics Investigations of Fatigue Crack Initiation and Propagation

International audienc

Clear band formation simulated by dislocation dynamics

Dislocation Dynamics simulations of dislocations gliding across a random populations of Frank loops are presented. Specific local rules are developed to reproduce elementary interaction mechanisms obtained in Molecular Dynamics simulations. It is shown that absorption of Frank loops as helical turns on screw dislocations governs the process of clear band formation, because: (1) it transforms the loops into jogs on dislocations, (2) when the dislocations unpin, the jogs are transported along the dislocation lines, leading to a progressive clearing of the band and (3) the dislocations are re-emitted in a glide plane different from the initial one, allowing for a broadening of the band. It is also shown that a pile-up of dislocations is needed to form a clear band of finite thickness.У термінах дислокаційної динаміки представлено моделювання дислокацій, що перетинають розташовану випадковим чином сукупність петель Франка. Розроблені локальні правила для відтворення елементарних механізмів взаємодії, що отримані при моделюванні методом молекулярної динаміки. Показано, що поглинання петель Франка у вигляді гелікоїдальних витків на гвинтових дислокаціях визначає процес утворення вільних зон, оскільки: 1) воно перетворює петлі у східці на дислокаціях, 2) у випадку відкріплення дислокації східці переносяться вздовж ліній дислокацій і 3) дислокації знову надходять у площину ковзання, яка відрізняється від вихідної, забезпечуючи тим самим розширення вільної зони. Крім того, показано, що скупчення дислокацій необхідне для утворення вільної зони з кінцевою товщиною.В терминах дислокационной динамики представлено моделирование дислокаций, пересекающих расположенную случайным образом совокупность петель Франка. Разработаны локальные правила для воспроизведения элементарных механизмов взаимодействия, полученных при моделировании методом молекулярной динамики. Показано, что поглощение петель Франка в виде геликоидальных витков на винтовых дислокациях определяет процесс образования свободных зон, поскольку: 1) оно преобразует петли в ступеньки на дислокациях, 2) в случае открепления дислокации ступеньки переносятся вдоль линий дислокаций и 3) дислокации вновь поступают в плоскость скольжения, отличающуюся от исходной, обеспечивая тем самым расширение свободной зоны. Кроме того, показано, что скопление дислокаций необходимо для образования свободной зоны с конечной толщиной

Separability and Fourier representations of density matrices

Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d)$ is a basis for $d\times d$ matrices. If $N=d_{1}\times d_{2}\times...\times d_{b}$ and H^{[ N]}=\bigotimes H^{% [ d_{k}]}, we give a sufficient condition for separability of a density matrix $\rho$ relative to the $H^{[ d_{k}]}$ in terms of the $L_{1}$ norm of the spin coefficients of $\rho >.$ Since the spin representation depends on the form of the tensor product, the theory applies to both full and partial separability on a given space $H^{[ N]}$% . It follows from this result that for a prescribed form of separability, there is always a neighborhood of the normalized identity in which every density matrix is separable. We also show that for every prime $p$ and $n>1$ the generalized Werner density matrix $W^{[ p^{n}]}(s)$ is fully separable if and only if $s\leq (1+p^{n-1}) ^{-1}$

q- Deformed Boson Expansions

A deformed boson mapping of the Marumori type is derived for an underlying $su(2)$ algebra. As an example, we bosonize a pairing hamiltonian in a two level space, for which an exact treatment is possible. Comparisons are then made between the exact result, our q- deformed boson expansion and the usual non - deformed expansion.Comment: 8 pages plus 2 figures (available upon request

Asymmetric universal entangling machine

We give a definition of asymmetric universal entangling machine which entangles a system in an unknown state to a specially prepared ancilla. The machine produces a fixed state-independent amount of entanglement in exchange to a fixed degradation of the system state fidelity. We describe explicitly such a machine for any quantum system having $d$ levels and prove its optimality. We show that a $d^2$-dimensional ancilla is sufficient for reaching optimality. The introduced machine is a generalization to a number of widely investigated universal quantum devices such as the symmetric and asymmetric quantum cloners, the symmetric quantum entangler, the quantum information distributor and the universal-NOT gate.Comment: 28 pages, 3 figure

Search for exchange-antisymmetric two-photon states

Atomic two-photon J=0 $\leftrightarrow$J'=1 transitions are forbidden for photons of the same energy. This selection rule is related to the fact that photons obey Bose-Einstein statistics. We have searched for small violations of this selection rule by studying transitions in atomic Ba. We set a limit on the probability $v$ that photons are in exchange-antisymmetric states: $v<1.2\cdot10^{-7}$.Comment: 5 pages, 4 figures, ReVTeX and .eps. Submitted to Phys. Rev. Lett. Revised version 9/25/9

A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.Comment: 20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two more references adde

Anyonic behavior of quantum group gases

We first introduce and discuss the formalism of $SU_q(N)$-bosons and fermions and consider the simplest Hamiltonian involving these operators. We then calculate the grand partition function for these models and study the high temperature (low density) case of the corresponding gases for $N=2$. We show that quantum group gases exhibit anyonic behavior in $D=2$ and $D=3$ spatial dimensions. In particular, for a $SU_q(2)$ boson gas at $D=2$ the parameter $q$ interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter.Comment: LaTeX file, 19 pages, two figures ,uses epsf.st

Contribution to understanding the mathematical structure of quantum mechanics

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, commutation and uncertainty relations, probability density current, momentum operator, rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of the delta-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems and the postulates of quantum mechanics are also discussed.Comment: 21 page

Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are : new algebras for infinite statistics, q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ``doubly-infinite'' statistics, many representations of orthostatistics, Hubbard statistics and its variations.Comment: This is a revised version of the earlier preprint: mp_arc 94-43. Published versio