Non-stochastic matrix Schrödinger equation for open systems.

Area of Science:

• Quantum mechanics
• Quantum information theory
• Theoretical chemistry

Background:

• The Schrödinger equation describes quantum system evolution.
• Quantum systems interacting with environments require specialized methods like quantum master equations.
• Existing methods can face challenges with stability and energy conservation for mixed states.

Purpose of the Study:

• To extend the Schrödinger equation for open quantum systems.
• To develop a method that ensures the stability and accuracy of quantum state evolution.
• To address limitations in current theoretical frameworks for system-environment interactions.

Main Methods:

• Formulating an extended Schrödinger equation using a matrix of auxiliary wavefunctions.
• Defining a compatibility condition to link auxiliary wavefunctions to the system density matrix.
• Ensuring the reconstructed density matrix satisfies quantum master equations.

Main Results:

• The proposed method describes quantum dynamics via auxiliary wavefunction matrices.
• A compatibility condition guarantees the reconstructed density matrix adheres to quantum master equations.
• The non-stochastic evolution preserves the positive-definiteness of the system density matrix.
• The formalism is applicable to both Markovian and non-Markovian system-bath interactions.
• It resolves the energy loss problem in time-dependent variational principles for mixed states.

Conclusions:

• The novel formalism provides a stable and accurate description of open quantum systems.
• This approach offers a unified framework for Markovian and non-Markovian dynamics.
• It overcomes a significant challenge in applying variational principles to mixed quantum states.