2009, ISBN 9783527320189, xxiii, 419

The first book dedicated to this new and powerful computational method begins with a comprehensive description of MCTDH and its theoretical background. There...

MCTDH | Quantum theory | Computational Chemistry & Molecular Modeling

MCTDH | Quantum theory | Computational Chemistry & Molecular Modeling

Book

Journal of Chemical Physics, ISSN 0021-9606, 12/2012, Volume 137, Issue 22, p. 22A301

Nonadiabatic dynamics-nuclear motion evolving on multiple potential energy surfaces-has captivated the interest of chemists for decades. Exciting advances in...

MOLECULAR-DYNAMICS | ELECTRON-TRANSFER | APPROXIMATION | SCHRODINGER-EQUATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | QUANTUM-CLASSICAL DYNAMICS | ENERGY-TRANSFER | TRANSITIONS | CONICAL INTERSECTIONS | COLLISIONS | BORN-OPPENHEIMER

MOLECULAR-DYNAMICS | ELECTRON-TRANSFER | APPROXIMATION | SCHRODINGER-EQUATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | QUANTUM-CLASSICAL DYNAMICS | ENERGY-TRANSFER | TRANSITIONS | CONICAL INTERSECTIONS | COLLISIONS | BORN-OPPENHEIMER

Journal Article

2016, Graduate Studies in Mathematics, ISBN 9781470419134, Volume 168., 326

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

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2018, Volume 505, pp. 355 - 373

In some recent papers, the so called (H,ρ)-induced dynamics of a system S whose time evolution is deduced adopting an operatorial approach, borrowed in part...

[formula omitted]-induced dynamics | Schrödinger and Heisenberg dynamics | Stressed bacterial populations | Operatorial models | (H,ρ)-induced dynamics | SURVIVAL | ALLIANCES | (H, rho)-induced dynamics | DECISION-MAKING | PHYSICS, MULTIDISCIPLINARY | Schrodinger and Heisenberg dynamics | OPERATORIAL MODEL | POPULATIONS | SYSTEMS | POLITICAL-PARTIES | Analysis | Quantum theory

[formula omitted]-induced dynamics | Schrödinger and Heisenberg dynamics | Stressed bacterial populations | Operatorial models | (H,ρ)-induced dynamics | SURVIVAL | ALLIANCES | (H, rho)-induced dynamics | DECISION-MAKING | PHYSICS, MULTIDISCIPLINARY | Schrodinger and Heisenberg dynamics | OPERATORIAL MODEL | POPULATIONS | SYSTEMS | POLITICAL-PARTIES | Analysis | Quantum theory

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 08/2005, Volume 123, Issue 8, pp. 084106 - 084106-7

We present an ab initio direct Ehrenfest dynamics scheme using a three time-step integrator. The three different time steps are implemented with nuclear...

SURFACE-HOPPING METHODS | MOLECULAR-DYNAMICS | ELECTRONIC-TRANSITIONS | SCHRODINGER-EQUATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | MULTIPHOTON IONIZATION | NONADIABATIC DYNAMICS | DENSITY-FUNCTIONAL THEORY | CHARGE-TRANSFER | TIME-DEPENDENT SYSTEMS | OPTICAL-RESPONSE

SURFACE-HOPPING METHODS | MOLECULAR-DYNAMICS | ELECTRONIC-TRANSITIONS | SCHRODINGER-EQUATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | MULTIPHOTON IONIZATION | NONADIABATIC DYNAMICS | DENSITY-FUNCTIONAL THEORY | CHARGE-TRANSFER | TIME-DEPENDENT SYSTEMS | OPTICAL-RESPONSE

Journal Article

Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, 06/2014, Volume 47, Issue 12, pp. 1 - 12

Exposing molecules to ultrashort laser pulses creates electronic wave packets, and therefore, triggers pure electron dynamics in the excited or ionized system....

charge migration | electron dynamics | ultrafast phenomena | HOLE DYNAMICS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | MOLECULES | SPECTROSCOPY | SYSTEMS | OPTICS | DENSITY-FUNCTIONAL THEORY | VALENCE IONIZATION | DEPENDENT SCHRODINGER-EQUATION | REAL-TIME | PROPAGATOR | Foundations | Lasers | Ionization | Dynamics | Migration | Charge | Electronics | Dynamical systems

charge migration | electron dynamics | ultrafast phenomena | HOLE DYNAMICS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | MOLECULES | SPECTROSCOPY | SYSTEMS | OPTICS | DENSITY-FUNCTIONAL THEORY | VALENCE IONIZATION | DEPENDENT SCHRODINGER-EQUATION | REAL-TIME | PROPAGATOR | Foundations | Lasers | Ionization | Dynamics | Migration | Charge | Electronics | Dynamical systems

Journal Article

Physical Review Letters, ISSN 0031-9007, 09/2012, Volume 109, Issue 10, p. 100403

A Schrodinger equation may be unitarily transformed into dynamical equations in different interaction pictures which describe a common physical process, i.e.,...

PHYSICS, MULTIDISCIPLINARY

PHYSICS, MULTIDISCIPLINARY

Journal Article

NONLINEAR DYNAMICS, ISSN 0924-090X, 01/2017, Volume 87, Issue 1, pp. 83 - 92

We study a three-coupled variable-coefficient nonlinear Schrodinger equation, which describes soliton dynamics in the three-spine -helical protein with...

ENERGY | ENGINEERING, MECHANICAL | Inhomogeneous effect | MOLECULAR-SYSTEMS | TRANSPORT | MECHANICS | TEMPERATURE | Three-coupled nonlinear Schrodinger equation | DISORDER | Multi-soliton | DARK OPTICAL SOLITONS | SPATIOTEMPORAL DISPERSION | Three-spine alpha-helical protein | BRIGHT | Numerical analysis | Proteins | Dipoles | Computer simulation | Resonant interactions | Exact solutions | Schroedinger equation | Inhomogeneity | Solitary waves | Nonlinear dynamics | Vibration | Mathematical analysis | Solitons | Nonlinearity | Mathematical models

ENERGY | ENGINEERING, MECHANICAL | Inhomogeneous effect | MOLECULAR-SYSTEMS | TRANSPORT | MECHANICS | TEMPERATURE | Three-coupled nonlinear Schrodinger equation | DISORDER | Multi-soliton | DARK OPTICAL SOLITONS | SPATIOTEMPORAL DISPERSION | Three-spine alpha-helical protein | BRIGHT | Numerical analysis | Proteins | Dipoles | Computer simulation | Resonant interactions | Exact solutions | Schroedinger equation | Inhomogeneity | Solitary waves | Nonlinear dynamics | Vibration | Mathematical analysis | Solitons | Nonlinearity | Mathematical models

Journal Article

10.
Full Text
General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation

Proceedings: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 6/2012, Volume 468, Issue 2142, pp. 1716 - 1740

General high-order rogue waves in the nonlinear Schrödinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants...

Amplitude | Algebra | Solitons | Determinants | Polynomials | Coefficients | Waves | Algebraic conjugates | Mathematical expressions | Bilinear method | Rogue waves | Nonlinear Schrödinger equation | FIBER | NLS EQUATION | SOLITONS | MULTIDISCIPLINARY SCIENCES | nonlinear Schrodinger equation | rogue waves | bilinear method | PULSES | Amplitudes | Dynamics | Mathematical analysis | Nonlinearity | Schroedinger equation | Arrays

Amplitude | Algebra | Solitons | Determinants | Polynomials | Coefficients | Waves | Algebraic conjugates | Mathematical expressions | Bilinear method | Rogue waves | Nonlinear Schrödinger equation | FIBER | NLS EQUATION | SOLITONS | MULTIDISCIPLINARY SCIENCES | nonlinear Schrodinger equation | rogue waves | bilinear method | PULSES | Amplitudes | Dynamics | Mathematical analysis | Nonlinearity | Schroedinger equation | Arrays

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 10/2016, Volume 332, pp. 41 - 54

We study the dynamics of the Schrödinger equation with a fractional Laplacian (−Δ)α, and the decoherence of the solution is observed. Analytically, we obtain...

Fourier pseudo-spectral method | Decoherence | Fractional Schrödinger equation | Center of mass | Fractional momentum | MATHEMATICS, APPLIED | STATES | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | Fractional Schrodinger equation | WELL-POSEDNESS | LIMIT | PHYSICS, MATHEMATICAL | SOLITON DYNAMICS | MASS | WAVE TURBULENCE | EQUATION | EFFICIENT | Newton's laws of motion

Fourier pseudo-spectral method | Decoherence | Fractional Schrödinger equation | Center of mass | Fractional momentum | MATHEMATICS, APPLIED | STATES | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | Fractional Schrodinger equation | WELL-POSEDNESS | LIMIT | PHYSICS, MATHEMATICAL | SOLITON DYNAMICS | MASS | WAVE TURBULENCE | EQUATION | EFFICIENT | Newton's laws of motion

Journal Article

The Journal of Chemical Physics, ISSN 0021-9606, 11/2016, Volume 145, Issue 19, p. 191104

Attoscience is an emerging field where attosecond pulses or few cycle IR pulses are used to pump and probe the correlated electron-nuclear motion of molecules....

SPACE | QUANTUM MOLECULAR-DYNAMICS | SCHRODINGER-EQUATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | STATE | TIME | DENSITY-FUNCTIONAL THEORY | TOOL | Femtosecond | Polyatomic molecules | Electron states | Computer simulation | Lasers | Attosecond pulses | Mathematical models | Photoexcitation | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

SPACE | QUANTUM MOLECULAR-DYNAMICS | SCHRODINGER-EQUATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | STATE | TIME | DENSITY-FUNCTIONAL THEORY | TOOL | Femtosecond | Polyatomic molecules | Electron states | Computer simulation | Lasers | Attosecond pulses | Mathematical models | Photoexcitation | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Journal Article

13.
Full Text
Dynamics of the optical solitons for a (2+1)-dimensional nonlinear Schrödinger equation

Superlattices and Microstructures, ISSN 0749-6036, 01/2017, Volume 101, pp. 522 - 528

In this paper, a nonlinear Schrödinger equation (NLS) has been studied, which can describe the propagation and interaction of optical solitons in a material...

Optical solitons | Hermite-Gaussian vortex solitons | Nonlinear Schrödinger equation | PHYSICS, CONDENSED MATTER | Nonlinear Schrodinger equation

Optical solitons | Hermite-Gaussian vortex solitons | Nonlinear Schrödinger equation | PHYSICS, CONDENSED MATTER | Nonlinear Schrodinger equation

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 07/2018, Volume 474, Issue 2215, p. 20170688

The general n-component nonlinear Schrodinger equations are systematically investigated with the aid of the Darboux transformation method and its extension....

N-component nonlinear Schrödinger equations | Dynamics | Dark-bright mixed high-order solitons | Dark-brightmixed solitons | Wing-shaped structure of thebreathers | Darboux transformation | wing-shaped structure of the breathers | OPTICAL PULSES | dynamics | WAVES | TRANSMISSION | n-component nonlinear Schrodinger equations | Darboux transformation dark-bright mixed solitons | INVERSE SCATTERING TRANSFORM | MULTIDISCIPLINARY SCIENCES | DISPERSIVE DIELECTRIC FIBERS | dark-bright mixed high-order solitons | MODULATION

N-component nonlinear Schrödinger equations | Dynamics | Dark-bright mixed high-order solitons | Dark-brightmixed solitons | Wing-shaped structure of thebreathers | Darboux transformation | wing-shaped structure of the breathers | OPTICAL PULSES | dynamics | WAVES | TRANSMISSION | n-component nonlinear Schrodinger equations | Darboux transformation dark-bright mixed solitons | INVERSE SCATTERING TRANSFORM | MULTIDISCIPLINARY SCIENCES | DISPERSIVE DIELECTRIC FIBERS | dark-bright mixed high-order solitons | MODULATION

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2013, Volume 46, Issue 10, pp. 105202 - 19

General rogue waves in the Davey-Stewartson (DS) II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown...

WATER-WAVES | NLS EQUATION | PHYSICS, MULTIDISCIPLINARY | PACKETS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | SOLITON | Determinants | Constants | Explosions | Infinity | Dynamics | Mathematical analysis

WATER-WAVES | NLS EQUATION | PHYSICS, MULTIDISCIPLINARY | PACKETS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | SOLITON | Determinants | Constants | Explosions | Infinity | Dynamics | Mathematical analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2016, Volume 325, pp. 74 - 97

In this paper, we propose some efficient and robust numerical methods to compute the ground states and dynamics of Fractional Schrödinger Equation (FSE) with a...

Rotating Lagrangian coordinates | Gaussian-sum solver | Dynamics | Nonlocal nonlinear interaction | Ground state | Fractional Schrödinger equation | Rotation | NUMERICAL-METHODS | COULOMB | Fractional Schrodinger equation | PHYSICS, MATHEMATICAL | MATLAB TOOLBOX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTATION | GPELAB | Turbulence | Numerical Analysis | Analysis of PDEs | Mathematics

Rotating Lagrangian coordinates | Gaussian-sum solver | Dynamics | Nonlocal nonlinear interaction | Ground state | Fractional Schrödinger equation | Rotation | NUMERICAL-METHODS | COULOMB | Fractional Schrodinger equation | PHYSICS, MATHEMATICAL | MATLAB TOOLBOX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTATION | GPELAB | Turbulence | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

The Journal of Physical Chemistry B, ISSN 1520-6106, 04/2016, Volume 120, Issue 16, pp. 3854 - 3862

In this study, the proton dynamics of hydrogen bonds for two forms of crystalline aspirin was investigated by the Born–Oppenheimer molecular dynamics (BOMD)...

ACID N-OXIDE | DISSOLUTION | APPROXIMATION | AB-INITIO | CAR-PARRINELLO SIMULATION | CHEMISTRY, PHYSICAL | DIHYDRATE | TEMPERATURE NEUTRON-DIFFRACTION | POTENTIALS | VIBRATIONAL-SPECTRA | POLYMORPHIC FORMS | Protons | Aspirin - chemistry | Crystallography, X-Ray | Hydrogen Bonding | Molecular Dynamics Simulation | Molecular dynamics | Infrared spectroscopy | Usage | Schrodinger equation | Chemical properties | Hydrogen bonding

ACID N-OXIDE | DISSOLUTION | APPROXIMATION | AB-INITIO | CAR-PARRINELLO SIMULATION | CHEMISTRY, PHYSICAL | DIHYDRATE | TEMPERATURE NEUTRON-DIFFRACTION | POTENTIALS | VIBRATIONAL-SPECTRA | POLYMORPHIC FORMS | Protons | Aspirin - chemistry | Crystallography, X-Ray | Hydrogen Bonding | Molecular Dynamics Simulation | Molecular dynamics | Infrared spectroscopy | Usage | Schrodinger equation | Chemical properties | Hydrogen bonding

Journal Article