1,796 research outputs found
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
Hydrodynamical analysis of single inclusive spectra and Bose-Einstein correlations for at 160 AGeV
We present the first analysis of preliminary data for at 160
using 3+1-dimensional relativistic hydrodynamics. We find excellent agreement
with the rapidity spectra of negative hadrons and the correlation measurements.
The data indicates a large amount of stopping; of the invariant energy
of the collision is thermalized and of the baryons are contained in the
central fireball. Within our model this implies that a quark-gluon-plasma of
lifetime 3.4 was formed.Comment: 13 pages, 5 Postscript figures (attached to this file as compressed
and uuencoded Postscript file
Efficient bipartite quantum state purification in arbitrary dimensional Hilbert spaces
A new purification scheme is proposed which applies to arbitrary dimensional
bipartite quantum systems. It is based on the repeated application of a special
class of nonlinear quantum maps and a single, local unitary operation. This
special class of nonlinear quantum maps is generated in a natural way by a
hermitian generalized XOR-gate. The proposed purification scheme offers two
major advantages, namely it does not require local depolarization operations at
each step of the purification procedure and it purifies more efficiently than
other know purification schemes.Comment: This manuscript is based on results of our previous manuscript
'Generalized quantum XOR-gate for quantum teleportation and state
purification in arbitrary dimensional Hilbert spaces
On Soliton-type Solutions of Equations Associated with N-component Systems
The algebraic geometric approach to -component systems of nonlinear
integrable PDE's is used to obtain and analyze explicit solutions of the
coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to
anti-kink transitions and multi-peaked soliton solutions is carried out.
Transformations are used to connect these solutions to several other equations
that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure
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
Sequential Quantum Cloning
Not all unitary operations upon a set of qubits can be implemented by
sequential interactions between each qubit and an ancillary system. We analyze
the specific case of sequential quantum cloning 1->M and prove that the minimal
dimension D of the ancilla grows linearly with the number of clones M. In
particular, we obtain D = 2M for symmetric universal quantum cloning and D =
M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for
the required ancilla-qubit interactions in each step of the sequential
procedure for both cases.Comment: 4 pages, no figures. New version with changes. Accepted in Physical
Review Letter
Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift
Recently, Yu, Brown, and Chuang [Phys. Rev. A {\bf 71}, 032341 (2005)]
investigated the entanglement attainable from unitary transformed thermal
states in liquid-state nuclear magnetic resonance (NMR). Their research gave an
insight into the role of the entanglement in a liquid-state NMR quantum
computer. Moreover, they attempted to reveal the role of mixed-state
entanglement in quantum computing. However, they assumed that the Zeeman energy
of each nuclear spin which corresponds to a qubit takes a common value for all;
there is no chemical shift. In this paper, we research a model with the
chemical shifts and analytically derive the physical parameter region where
unitary transformed thermal states are entangled, by the positive partial
transposition (PPT) criterion with respect to any bipartition. We examine the
effect of the chemical shifts on the boundary between the separability and the
nonseparability, and find it is negligible.Comment: 9 pages, 1 figures. There were mistakes in the previous version. The
main results don't change, but our motivation has to be reconsidere
Interface motion by interface diffusion driven by bulk energy: Justification of a diffusive interface model
We construct an asymptotic solution of a system consisting of the partial differential equations of linear elasticity theory coupled with a degenerate parabolic equation, and show that when a regularity parameter tends to zero, this solution converges to a solution of a sharp interface model, which describes the phase interface in an elastically deformable solid moving by interface diffusion. Therefore, the coupled system can be used as diffusive interface model. Differently from diffusive interface models based on the Cahn-Hilliard equation, the interface diffusion is solely driven by the bulk energy, hence the Laplacian of the curvature is not part of the driving force. Also, no rescaling of the parabolic equation is necessary. Since the asymptotic solution does not solve the system exactly, the proof is formal
Solutions to a model with Neumann boundary conditions for phase transitions driven by configurational forces
We study an initial boundary value problem of a model describing the evolution in time of diffusive phase interfaces in solid materials, in which martensitic phase transformations driven by configurational forces take place. The model was proposed earlier by the authors and consists of the partial differential equations of linear elasticity coupled to a nonlinear, degenerate parabolic equation of second order for an order parameter. In a previous paper global existence of weak solutions in one space dimension was proved under Dirichlet boundary conditions for the order parameter. Here we show that global solutions also exist for Neumann boundary conditions. Again, the method of proof is only valid in one space dimension
Preparation of entangled states of two photons in several spatial modes
We describe a protocol capable of preparing an arbitrary state of two photons
in several spatial modes using pairs of photons generated by spontaneous
parametric down-conversion, linear optical elements and single-photon detectors
or post-selection. The protocol involves unitary and non-unitary
transformations realizable by beam splitters and phase shifters. Non-unitary
transformations are implemented by attenuation filters. The protocol contains
several optimization capabilities with the goal of improving overall
probability of its success. We also show how entangled two-photon states
required for quantum computing with linear optics can be prepared using a very
simple and feasible scheme.Comment: 9 pages, 9 figures, REVTeX
- …