Resolving the Classical-Quantum Limit: A New Approach by Layton and Oppenheim

Physicists Isaac Layton and Jonathan Oppenheim from University College London have proposed a solution to the problem of the classical-quantum limit, a concept that describes the transition from quantum to classical physics. The classical-quantum limit fails when applied to subsystems, but the researchers suggest this can be resolved by modeling the decoherence of a subsystem by its environment. By taking the decoherence time to zero, the subsystem becomes classical. This work could have implications for studying effective classical-quantum dynamics and potential applications in quantum control, quantum measurement, and quantum gravity.

What is the Classical-Quantum Limit?

The classical-quantum limit is a concept in physics that describes the transition from quantum to classical physics. This limit is typically justified in a variety of ways, with the most famous being the consideration of action large compared to the reduced Planck constant. This leads to the statement that the classical limit is taking the Planck constant to zero. This concept is important as it provides a theoretical tool for simplifying the analysis of quantum systems that are too complex to study directly.

The classical limit allows one to replace a quantum system with an entirely classical description. However, many systems of interest operate in a regime where both classical and quantum features are important. This leads to the question: Can we take a limit of a quantum system such that one subsystem behaves classically while the rest remain quantum? A limit of this kind would have a wide variety of applications, from providing first-principles derivations of quantum control and measurement setups to describing systems at the classical-quantum boundary.

What is the Problem with the Classical-Quantum Limit?

The problem with the classical-quantum limit is that it fails when applied to subsystems. This is because the standard classical limit fails to describe an effective classical subsystem. In this case, the resulting dynamics is known as the quantum-classical Liouville equation and does not lead to well-defined classical evolution on the subsystem in question.

The first example of a limit procedure leading to consistent dynamics was provided in the pioneering work of Diósi, who considered two particles each having a different Planck constant. While this allowed one of the first examples of consistent classical-quantum dynamics to be derived, it came at the expense of requiring a number of unphysical considerations including modified quantum mechanical evolution laws and ad hoc sources of classical noise.

How Can the Classical-Quantum Limit be Resolved?

The classical-quantum limit can be resolved by explicitly modeling the decoherence of a subsystem by its environment. Decoherence is a process that removes the entanglement generated between subsystems, which is a key feature of quantum mechanics. By taking the decoherence time to zero, one can ensure that this subsystem is classical.

In this work, Isaac Layton and Jonathan Oppenheim from the Department of Physics and Astronomy at University College London demonstrate that a physically motivated and consistent limit procedure exists starting from standard unitary quantum mechanics in a closed system. They show that a double scaling limit in which the Planck constant and the decoherence time both approach zero, while their ratio remains fixed, leads to an irreversible open-system evolution with well-defined classical and quantum subsystems.

What are the Implications of this Work?

This work has a wide range of implications. It provides a regime in which one can study effective and consistent classical-quantum dynamics. This could be useful in a variety of applications, from quantum control and measurement setups to systems at the classical-quantum boundary.

Furthermore, it could be interesting if recently proposed models of classical-quantum theories of gravity could arise as effective descriptions of quantum gravity. This work also formalizes approaches in quantum chemistry where the nuclear degrees of freedom are treated as classical and the electronic degrees of freedom are treated quantum mechanically.

Conclusion

In conclusion, the work of Isaac Layton and Jonathan Oppenheim provides a new perspective on the classical-quantum limit. They show that by explicitly modeling the decoherence of a subsystem by its environment, one can resolve the issues associated with the classical-quantum limit. This work opens up new possibilities for studying effective and consistent classical-quantum dynamics and has potential applications in a variety of fields, including quantum control, quantum measurement, and quantum gravity.