Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations
- URL: http://arxiv.org/abs/2302.14047v2
- Date: Fri, 7 Apr 2023 00:01:57 GMT
- Title: Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations
- Authors: Alexander McDonald, Aashish A. Clerk
- Abstract summary: We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
- Score: 77.34726150561087
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The connections between standard theoretical tools used to study open quantum
systems can sometimes seem opaque. Whether it is a Lindblad master equation,
the equation of motion for the Wigner function or a dissipative Keldysh action,
features evident in one formalism are often masked in another. Here, we
reformulate the technique of third quantization in a way that explicitly
connects all three methods. We first show that our formulation reveals a
fundamental dissipative symmetry present in all quadratic bosonic or fermionic
Lindbladians. This symmetry can then be used to easily diagonalize these
models, and provides a intuitive way to demonstrate the separation of
dissipation and fluctations in linear systems. For bosons, we then show that
the Wigner function and the characteristic function can be thought of as
''wavefunctions'' of the density matrix in the eigenbasis of the
third-quantized superoperators we introduce. The field-theory representation of
the time-evolution operator in this basis is then the Keldysh path integral. To
highlight the utility of our approach, we apply our version of third
quantization to a dissipative non-linear oscillator, and use it to obtain new
exact results.
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