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تسجيل مستخدم جديدWavePacket: A Matlab package for numerical quantum dynamics. III: Quantum-classical simulations and surface hopping trajectories
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WavePacket is an open-source program package for numerical simulations in quantum dynamics. Building on the previous Part I [Comp. Phys. Comm. 213, 223-234 (2017)] and Part II [Comp. Phys. Comm. 228, 229-244 (2018)] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum-classical propagations to WavePacket. In those simulations classical phase-space densities are sampled by trajectories which follow (diabatic or adiabatic) potential energy surfaces. In the vicinity of (genuine or avoided) intersections of those surfaces trajectories may switch between surfaces. To model these transitions, two classes of stochastic algorithms have been implemented: (1) J. C. Tullys fewest switches surface hopping and (2) Landau-Zener based single switch surface hopping. The latter one offers the advantage of being based on adiabatic energy gaps only, thus not requiring non-adiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.0.2 which is essentially an object-oriented rewrite of previo
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WavePacket is an open-source program package for the numerical simulation of quantum-mechanical dynamics. It can be used to solve time-independent or time-dependent linear Schrodinger and Liouville-von Neumann-equations in one or more dimensions. Als
o coupled equations can be treated, which allows to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semiclassical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry.The graphical capabilities allow visualization of quantum dynamics on the fly, including Wigner phase space representations. Being easy to use and highly versatile, WavePacket is well suited for the teaching of quantum mechanics as well as for research projects in atomic, molecular and optical physics or in physical or theoretical chemistry.The present Part I deals with the description of closed quantum systems in terms of Schrodinger equations. The emphasis is on discrete variable representations for spatial discretization as well as various techniques for temporal discretization.The upcoming Part II will focus on open quantum systems and dimension reduction; it also describes the codes for optimal control of quantum dynamics.The present work introduces the MATLAB version of WavePacket 5.2.1 which is hosted at the Sourceforge platform, where extensive Wiki-documentation as well as worked-out demonstration examples can be found.
WavePacket is an open-source program package for numeric simulations in quantum dynamics. It can solve time-independent or time-dependent linear Schrodinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be
treated, which allows, e.g., to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semi-classical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. Being highly versatile and offering visualization of quantum dynamics on the fly, WavePacket is well suited for teaching or research projects in atomic, molecular and optical physics as well as in physical or theoretical chemistry. Building on the previous Part I which dealt with closed quantum systems and discrete variable representations, the present Part II focuses on the dynamics of open quantum systems, with Lindblad operators modeling dissipation and dephasing. This part also describes the WavePacket function for optimal control of quantum dynamics, building on rapid monotonically convergent iteration methods. Furthermore, two different approaches to dimension reduction implemented in WavePacket are documented here. In the first one, a balancing transformation based on the concepts of controllability and observability Gramians is used to identify states that are neither well controllable nor well observable. Those states are either truncated or averaged out. In the other approach, the H2-error for a given reduced dimensionality is minimized by H2 optimal model reduction techniques, utilizing a bilinear iterative rational Krylov algorithm.
A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach which describes the emergence of entangled states entirely
in terms of independent and deterministic Ehrenfest-like classical trajectories. For a two-level quantum system in a classical environment, this is derived by mapping the quantum system onto a path-integral representation of a spin-1/2. We demonstrate that the method correctly accounts for coherence and decoherence and thus reproduces the splitting of a wavepacket in a nonadiabatic scattering problem. This discovery opens up a new class of simulations as an alternative to stochastic surface-hopping, coupled-trajectory or semiclassical approaches.
Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed
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