Scattered-wave-packet formalism with applications to barrier scattering and quantum transistors

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Computational physics

Background:

• Simulating quantum systems interacting with their environment (reservoirs) through open boundaries is computationally intensive.
• Existing methods for open boundary conditions often require significant computational resources.
• Accurate modeling of time-dependent quantum phenomena is crucial for understanding quantum devices.

Purpose of the Study:

• To introduce and apply a novel scattered wave formalism for quantum systems with open boundaries.
• To demonstrate the efficiency and accuracy of this formalism for barrier scattering and quantum transistors.
• To explore its utility in studying time-dependent quantum dynamical processes.

Main Methods:

• Developed a scattered wave formalism by dividing the total wave function into incident and scattered components.
• Implemented Markovian outgoing wave boundary conditions using ratio or polynomial methods.
• Applied the formalism to one- and two-dimensional barrier scattering and quantum field-effect transistors, integrating modified time-dependent Schrödinger equations.

Main Results:

• Accurate time-dependent transmission probabilities were obtained for barrier scattering problems.
• Time-dependent transport in quantum transistors was successfully simulated for wave packet propagation.
• The scattered wave formalism demonstrated significant reductions in computational effort compared to other open boundary methods.

Conclusions:

• The scattered wave formalism provides an efficient and accurate approach for quantum dynamical simulations.
• This method is broadly applicable to various quantum systems, including barrier scattering and quantum transistors.
• The formalism offers a computationally advantageous alternative for studying quantum systems with open boundaries.