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The local well-posedness for Gross-Pitaevskii hierarchies
The local well-posedness Gross-Pitaevskii hierarchies
2010/11/24
We consider the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n.$ By introducing a quasi-norm in certain Sobolev type spaces of sequences of marginal d...
On the injectivity radius and tangent cones at infinity of gradient Ricci solitons
injectivity radius tangent cones infinity of gradient Ricci solitons
2011/1/18
A lower-bound estimate of injectivity radius for complete Riemannian manifolds is discussed in a pure geometric viewpoint and is applied to study tangent cones at in nity of certain gradient Ricci sol...
Power Allocation Games in Wireless Networks of Multi-antenna Terminals
Wireless Networks Multi-antenna Terminals
2010/11/24
We consider wireless networks that can be modeled by multiple access channels in which all the terminals are equipped with multiple antennas. The propagation model used to account for the effects of ...
Lieb-Robinson Bounds and Quasi-locality for the Dynamics of Many-Body Quantum Systems
Lieb-Robinson Bounds Quasi-locality Dynamics Many-Body Quantum Systems
2010/11/23
We review a recently proven Lieb-Robinson bound for general, many-body quantum systems with bounded interactions. Several basic examples are discussed as well as the connection between commutator esti...
We construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the...
Perfect transmission scattering as a PT-symmetric spectral problem
Perfect transmission scattering PT-symmetric spectral problem
2010/11/23
We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implemen...
Quantization of the free electromagnetic field implies quantization of its angular momentum
electromagnetic field angular momentum
2010/11/23
It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field i...
Approximating Mexican highways with slime mould
Pattern Formation and Solitons(nlin.PS) Adaptation and Self-Organizing Systems(nlin.AO) Physics and Society(physics.soc-ph)
2010/11/10
Plasmodium of Physarum polycephalum is a single cell visible by unaided eye. During its foraging behavior the cell spans spatially distributed sources of nutrients with a protoplasmic network. Geometr...
Compactons in Nonlinear Schrödinger Lattices with Strong Nonlinearity Management
Compactons Nonlinear Schrö dinger Lattices Nonlinearity Management
2010/11/10
The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the re...
Geodesic Flows and Neumann Systems on Stiefel Varieties. Geometry and Integrability
Geodesic Flows Neumann Systems n Stiefel Varieties Geometry and Integrability
2010/11/10
We study integrable geodesic flows on Stiefel varieties $V_{n,r}=SO(n)/SO(n-r)$ given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics. We also consider natural generalizations ...
Bak--Sneppen type models and rank-driven processes
Bak--Sneppen type models rank-driven processes
2010/11/10
We analyse a surprising connection between Bak--Sneppen type models and much simpler Markov processes, which we call rank-driven processes (RDPs).
Symmetry Groups and Exact Solutions of a (3+1)-dimensional Nonlinear Evolution Equation and Maccari’s System
symmetry group (3+1)-dimensional nonlin ear evolution equation Maccari’s system
2012/9/25
Based on the generalized symmetry group method and symbolic computation, both the Lie point groups and the non-Lie symmetry groups of a (3+1)-dimensional nonlinear evolution equation as well as the Ma...
Noncommutative (generalized) sine-Gordon/massive Thirring correspondence, integrability and solitons
Noncommutative correspondence integrability solitons
2010/11/10
Some properties of the correspondence between the non-commutative versions of the (generalized) sine-Gordon (NCGSG$_{1,2}$) and the massive Thirring (NCGMT$_{1,2}$) models are studied. Our method rel...
On rational solutions of multicomponent and matrix KP hierarchies
On rational solutions multicomponent matrix KP hierarchies
2010/11/10
We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discu...
We establish the relation between two objects: an integrable system related to Painleve II equation, and the symplectic invariants of a certain plane curve \Sigma_{TW} describing the average eigenvalu...