A note on Choquard equations in two space dimensions

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity [Formula: see text] We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

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A note on strong instability of standing waves for some semilinear wave and heat equations

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004117000226 ◽

2017 ◽

Vol 165 (1) ◽

pp. 53-68

Author(s):

T. SAANOUNI

Keyword(s):

Ground State ◽

Initial Value Problems ◽

Standing Waves ◽

Heat Equations ◽

Initial Value ◽

Strong Instability ◽

Two Space Dimensions

AbstractThe initial value problems for some semilinear wave and heat equations are investigated in two space dimensions. By proving the existence of ground state, strong instability of standing waves for the associated wave and heat equations are obtained.

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An operator splitting method for an unconditionally stable difference scheme for a linear hyperbolic equation with variable coefficients in two space dimensions

Applied Mathematics and Computation ◽

10.1016/s0096-3003(03)00595-2 ◽

2004 ◽

Vol 152 (3) ◽

pp. 799-806 ◽

Cited By ~ 20

Author(s):

R.K. Mohanty

Keyword(s):

Difference Scheme ◽

Hyperbolic Equation ◽

Operator Splitting ◽

Splitting Method ◽

Variable Coefficients ◽

Unconditionally Stable ◽

Linear Hyperbolic Equation ◽

Operator Splitting Method ◽

Two Space Dimensions

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QUANTUM COMPUTING WITH NON-ABELIAN QUASIPARTICLES

International Journal of Modern Physics B ◽

10.1142/s0217979207042859 ◽

2007 ◽

Vol 21 (08n09) ◽

pp. 1372-1378 ◽

Cited By ~ 2

Author(s):

N. E. BONESTEEL ◽

L. HORMOZI ◽

G. ZIKOS ◽

S. H. SIMON

Keyword(s):

Dimensional Space ◽

Quantum Hall ◽

Three Dimensional ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Quantum Operations ◽

Topological Quantum ◽

Dimensional Space Time ◽

Two Space Dimensions ◽

Topological Quantum Computation

In topological quantum computation quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum operations are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum operations depend only on the topology of the braids formed by these world-lines. We describe recent work showing how to find braids which can be used to perform arbitrary quantum computations using a specific kind of quasiparticle (those described by the so-called Fibonacci anyon model) which are thought to exist in the experimentally observed ν = 12/5 fractional quantum Hall state.

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