2007, Lecture notes in physics, ISBN 9783540712923, Volume 722., xiv, 445

Maxwell, Dirac and Einstein's equations are certainly among the most imp- tant equations of XXth century Physics and it is our intention in this book to 1...

Space and time | Geometry, Differential | Dirac equation | Relativity (Physics) | Maxwell equations | Mathematical physics | Einstein field equations | Mathematical Methods in Physics | Differential Geometry | Relativity and Cosmology | Physics

Space and time | Geometry, Differential | Dirac equation | Relativity (Physics) | Maxwell equations | Mathematical physics | Einstein field equations | Mathematical Methods in Physics | Differential Geometry | Relativity and Cosmology | Physics

Book

2009, Oxford mathematical monographs, ISBN 0199230722, xxiv, 785

General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the...

General relativity (Physics) | Mathematics | Physics | Einstein field equations | Gravitational fields | Cosmos | Manifold of dimensions | Motion of isolated bodies | General relativity

General relativity (Physics) | Mathematics | Physics | Einstein field equations | Gravitational fields | Cosmos | Manifold of dimensions | Motion of isolated bodies | General relativity

Book

1994, Mathematics and its applications, ISBN 079233048X, Volume 299, xix, 258

Book

2015, ISBN 1611973937, x, 429

Book

2008, ISBN 9812832513, xii, 562

Book

2010, ISBN 052151407X, xviii, 698

Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad...

Numerical calculations | General relativity (Physics) | Einstein field equations | Data processing | Relativity (Physics) | Computer programs

Numerical calculations | General relativity (Physics) | Einstein field equations | Data processing | Relativity (Physics) | Computer programs

Book

1988, ISBN 9782881246623, xi, 504

Book

2004, ISBN 9783764371302, xi, 481

Book

Computer Physics Communications, ISSN 0010-4655, 12/2013, Volume 184, Issue 12, pp. 2621 - 2633

In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation (NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics...

Gross–Pitaevskii equation | Nonlinear Schrödinger equation | Bose–Einstein condensation | Crank–Nicolson finite difference method | Absorbing boundary condition | Time-splitting spectral method | Crank-Nicolson finite difference method | Gross-Pitaevskii equation | Bose-Einstein condensation | SPLITTING SPECTRAL APPROXIMATIONS | Nonlinear Schrodinger equation | PHYSICS, MATHEMATICAL | PSEUDOSPECTRAL METHOD | QUANTUM DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE METHODS | PERFECTLY MATCHED LAYER | CENTRAL VORTEX STATES | PRESERVING SCHEME | NUMERICAL-SIMULATION | ABSORBING BOUNDARY-CONDITIONS | SEMICLASSICAL LIMIT | Energy conservation | Analysis | Methods | Nonlinear dynamics | Numerical analysis | Computer simulation | Mathematical analysis | Nonlinearity | Mathematical models | Schroedinger equation | Dispersions | Invariants | Mathematics - Numerical Analysis | Quantum Gases | Mathematical Physics | Numerical Analysis | Condensed Matter | Mathematics | Quantum Physics | Physics

Gross–Pitaevskii equation | Nonlinear Schrödinger equation | Bose–Einstein condensation | Crank–Nicolson finite difference method | Absorbing boundary condition | Time-splitting spectral method | Crank-Nicolson finite difference method | Gross-Pitaevskii equation | Bose-Einstein condensation | SPLITTING SPECTRAL APPROXIMATIONS | Nonlinear Schrodinger equation | PHYSICS, MATHEMATICAL | PSEUDOSPECTRAL METHOD | QUANTUM DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE METHODS | PERFECTLY MATCHED LAYER | CENTRAL VORTEX STATES | PRESERVING SCHEME | NUMERICAL-SIMULATION | ABSORBING BOUNDARY-CONDITIONS | SEMICLASSICAL LIMIT | Energy conservation | Analysis | Methods | Nonlinear dynamics | Numerical analysis | Computer simulation | Mathematical analysis | Nonlinearity | Mathematical models | Schroedinger equation | Dispersions | Invariants | Mathematics - Numerical Analysis | Quantum Gases | Mathematical Physics | Numerical Analysis | Condensed Matter | Mathematics | Quantum Physics | Physics

Journal Article

2000, Lecture notes in physics, ISBN 9783540670735, Volume 540, xiii, 433

This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they...

Einstein field equations

Einstein field equations

Book

Acta Mathematica, ISSN 0001-5962, 12/2010, Volume 205, Issue 2, pp. 199 - 262

We define non-pluripolar products of an arbitrary number of closed positive (1, 1)-currents on a compact Kähler manifold X. Given a big (1, 1)-cohomology class...

Mathematics, general | Mathematics | DEFINITION | MATHEMATICS | COMPLEX | ENERGY | INVARIANTS | PLURISUBHARMONIC-FUNCTIONS | INEQUALITY | VARIETIES | GENERAL TYPE | MANIFOLDS | KAHLER-EINSTEIN METRICS | Manifolds | Construction | Theorems | Monge-Ampere equation | Singularities | Mathematical analysis | Estimates

Mathematics, general | Mathematics | DEFINITION | MATHEMATICS | COMPLEX | ENERGY | INVARIANTS | PLURISUBHARMONIC-FUNCTIONS | INEQUALITY | VARIETIES | GENERAL TYPE | MANIFOLDS | KAHLER-EINSTEIN METRICS | Manifolds | Construction | Theorems | Monge-Ampere equation | Singularities | Mathematical analysis | Estimates

Journal Article

12.
Localization in periodic potentials

: from Schrödinger operators to the Gross-Pitaevskii equation

2011, London Mathematical Society lecture note series, ISBN 9781107621541, Volume 390., x, 398

This book provides a comprehensive treatment of the Gross–Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the...

Localization theory | Schrödinger equation | Gross-Pitaevskii equations | Schrodinger operator | Lattice theory | Bose-Einstein condensation

Localization theory | Schrödinger equation | Gross-Pitaevskii equations | Schrodinger operator | Lattice theory | Bose-Einstein condensation

Book

1989, ISBN 9971507455, xii, 136

Book

2008, Oxford graduate texts in mathematics, ISBN 9780199215416, Volume 16., xvi, 279

Book

2002, ISBN 9780684863481, 277

Book

New Journal of Physics, ISSN 1367-2630, 2014, Volume 16, Issue 8, pp. 85007 - 19

We examine the origin of the Newton-Schrodinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum...

Newton-Schrödinger equation | gravitational quantum physics | gravitational decoherence | nonlinear Schrödinger equation | semiclassical gravity | EARLY UNIVERSE | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | nonlinear Schrodinger equation | BLACK-HOLE | STATE-VECTOR | PARTICLE HORIZONS | STOCHASTIC GRAVITY | REDUCTION | Newton-Schrodinger equation | SCALAR FIELDS | BACK-REACTION | QUANTUM-MECHANICS | Relativism | Quantum field theory | Collapse | Nonlinear dynamics | Origins | Einstein equations | Mathematical analysis | Wave functions | Dynamical systems | Quantum theory

Newton-Schrödinger equation | gravitational quantum physics | gravitational decoherence | nonlinear Schrödinger equation | semiclassical gravity | EARLY UNIVERSE | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | nonlinear Schrodinger equation | BLACK-HOLE | STATE-VECTOR | PARTICLE HORIZONS | STOCHASTIC GRAVITY | REDUCTION | Newton-Schrodinger equation | SCALAR FIELDS | BACK-REACTION | QUANTUM-MECHANICS | Relativism | Quantum field theory | Collapse | Nonlinear dynamics | Origins | Einstein equations | Mathematical analysis | Wave functions | Dynamical systems | Quantum theory

Journal Article

2005, Lecture notes in physics, ISBN 3540257799, Volume 673., xi, 151

Book

18.
Full Text
Einstein Equations Under Polarized $${\mathbb{U}}$$ U (1) Symmetry in an Elliptic Gauge

Communications in Mathematical Physics, ISSN 0010-3616, 8/2018, Volume 361, Issue 3, pp. 873 - 949

We prove local existence of solutions to the Einstein–null dust system under polarized $${\mathbb{U}}$$ U (1) symmetry in an elliptic gauge. Using in...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Employee motivation

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Employee motivation

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2016, Volume 327, pp. 252 - 269

The aim of this paper is to build and validate some explicit high-order schemes, both in space and time, for simulating the dynamics of systems of nonlinear...

Gross–Pitaevskii equation | Pseudo-spectral schemes | Adaptive time stepping | Dynamics | Bose–Einstein condensates | Time-splitting | Nonlinear Schrödinger equation | Spin-orbit | High-order discretization | IMplicit–EXplicit schemes | STATES | RUNGE-KUTTA METHODS | Nonlinear Schrodinger equation | Gross-Pitaevskii equation | IMplicit-EXplicit schemes | PHYSICS, MATHEMATICAL | SPLITTING METHODS | MATLAB TOOLBOX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Bose-Einstein condensates | COMPUTATION | EFFICIENT | GPELAB | Numerical Analysis | Analysis of PDEs | Mathematics

Gross–Pitaevskii equation | Pseudo-spectral schemes | Adaptive time stepping | Dynamics | Bose–Einstein condensates | Time-splitting | Nonlinear Schrödinger equation | Spin-orbit | High-order discretization | IMplicit–EXplicit schemes | STATES | RUNGE-KUTTA METHODS | Nonlinear Schrodinger equation | Gross-Pitaevskii equation | IMplicit-EXplicit schemes | PHYSICS, MATHEMATICAL | SPLITTING METHODS | MATLAB TOOLBOX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Bose-Einstein condensates | COMPUTATION | EFFICIENT | GPELAB | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article