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Remarks on time-dependent [current]-density functional theory for open quantum systems.

Joel Yuen-Zhou¹, Alán Aspuru-Guzik

¹Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA. joelyuen@mit.edu

Physical Chemistry Chemical Physics : PCCP

|June 22, 2013

Summary

This summary is machine-generated.

Time-dependent current-density functional theory for open quantum systems (OQS) formally supports Kohn-Sham schemes for dynamics, despite master equations sometimes violating density matrix properties. These theories remain crucial for studying OQS.

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Area of Science:

Quantum Mechanics
Many-Body Physics
Theoretical Chemistry

Background:

Open quantum systems (OQS) require formalisms incorporating dissipative effects.
Time-dependent current-density functional theory (TDCDFT) is a key approach for OQS dynamics.
Recent literature has questioned formal aspects of these theories.

Purpose of the Study:

To review and clarify formal aspects of TDCDFT for OQS.
To provide theoretical support for previously established conclusions.
To offer new insights and a common ground for related theories.

Main Methods:

Analysis of the master equation framework for OQS.
Evaluation of Kohn-Sham (KS) schemes within TDCDFT.
Investigation of the Lindblad master equation and stochastic Schrödinger equation.

Main Results:

A one-to-one mapping between vector potentials and current densities exists within the master equation framework.
KS schemes for OQS, including KS closed driven systems, are formally valid.
The Lindblad master equation preserves density matrix positivity; stochastic methods lack this general proof.

Conclusions:

Master equations are essential for OQS studies, even with potential limitations.
The theoretical underpinnings of TDCDFT for OQS are formally rigorous.
This work clarifies existing theories and facilitates future research in OQS.