Dissipation in quantum mechanics

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SUMMARY

The discussion focuses on the treatment of dissipative forces in quantum mechanics, specifically addressing how these forces differ from conservative forces. The primary method discussed is modeling the system as an open system using a mixed density matrix, as outlined in the Lindblad equation. Alternative approaches include considering the dissipative system as part of a larger non-dissipative system and employing Weyl quantization for more abstract analysis. Key resources include textbooks on quantum mechanics and relevant Wikipedia articles.

PREREQUISITES
  • Understanding of the Schrödinger equation in quantum mechanics
  • Familiarity with mixed density matrices and open quantum systems
  • Knowledge of the Lindblad equation
  • Basic concepts of Weyl quantization
NEXT STEPS
  • Research the Lindblad equation for open quantum systems
  • Study mixed density matrices in quantum mechanics
  • Explore Weyl quantization techniques
  • Read textbooks on quantum mechanics, such as "Quantum Mechanics: Concepts and Applications" and "Quantum Mechanics: A Modern Development"
USEFUL FOR

Quantum physicists, researchers in quantum mechanics, and students seeking to understand the implications of dissipative forces in quantum systems.

hokhani
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In classical mechanics potential is defined for conservative forces and dissipative forces such as friction don't have potential. In quantum mechanics, Schrödinger equation which includes a potential, deals with problems. How can one treat the dissipative forces in quantum mechanics?
 
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There are several methods one may use.

The most popular method is to consider the system as an open system, described not by a pure state (wave function) but by a mixed density matrix. For more details see
http://en.wikipedia.org/wiki/Open_quantum_system
http://en.wikipedia.org/wiki/Lindblad_equation

Some basics of methods for open quantum systems can even be found in some general textbooks on QM, such as
https://www.amazon.com/dp/052187534X/?tag=pfamazon01-20
https://www.amazon.com/dp/0521869633/?tag=pfamazon01-20Another (but related) method is to consider your dissipative system as a part of a larger system, such that the larger system is a non-dissipative one. Unfortunately, the method may depend on how exactly you enlarge your original dissipative system.A completely different, more abstract method, is by using Weyl quantisation:
http://lanl.arxiv.org/abs/quant-ph/0311159
 
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