Dissipation in quantum mechanics

In summary, potential in classical mechanics is only defined for conservative forces, while dissipative forces like friction do not have potential. In quantum mechanics, the Schrödinger equation deals with problems involving potential. To address dissipative forces in quantum mechanics, there are several methods that can be used. One popular method is to treat the system as an open system described by a mixed density matrix instead of a pure state. Another approach is to consider the dissipative system as part of a larger, non-dissipative system. A more abstract method is using Weyl quantisation.
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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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FAQ: Dissipation in quantum mechanics

What is dissipation in quantum mechanics?

Dissipation in quantum mechanics refers to the process of energy loss or decay in a quantum system. This can occur due to interactions with other systems or the environment, leading to a decrease in the system's coherence and purity.

How does dissipation affect quantum systems?

Dissipation can cause a quantum system to lose its coherence and become entangled with its environment, leading to decoherence and a loss of quantum properties such as superposition and entanglement. It can also limit the lifetime of quantum states and hinder the performance of quantum technologies.

What are some examples of dissipation in quantum systems?

Some examples of dissipation in quantum systems include photon loss in quantum communication, energy dissipation in quantum computing, and spin relaxation in nuclear magnetic resonance (NMR) spectroscopy.

Can dissipation be controlled in quantum systems?

Yes, there are methods for controlling and minimizing dissipation in quantum systems, such as using error correction codes, quantum error correction techniques, and quantum feedback control. However, complete elimination of dissipation is not possible due to the fundamental laws of thermodynamics.

What are the implications of dissipation for quantum technologies?

Dissipation can pose a significant challenge for the development and scalability of quantum technologies. It can limit the accuracy and reliability of quantum operations, and the presence of dissipation can also make it difficult to maintain quantum states for a long time, hindering the potential applications of quantum technologies.

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