RQC Seminar

78th RQC Seminar

• Speaker

  Mr. Isaac Layton
  ( Dept of Physics ＆ Astronomy
  Faculty of Maths ＆ Physical Sciences, University of College Longon, UK )

• Date

  16:00-17:00, August 22, 2023 (Tuesday)

• Venue

  Hybrid(ZOOM・ Wako Main Research 3F 345-347 Seminar Room C01）

• Title

  A new approach to semi-classical limits

• Inquiries

  rqc_info[at]ml.riken.jp

Abstract
The standard notion of a classical limit, represented schematically by ℏ→ 0, provides a method of approximating a quantum system by a classical one. However, many systems of interest operate in a semi−classical regime, where both classical and quantum features are important. Does there exist a notion of a semi−classical limit, i.e. a limit of a quantum system in which one subsystem behaves classically, while the rest remains quantum? In this talk I will discuss why the standard classical limit fails when applied to subsystems, and show how one may resolve this by explicitly modelling the decoherence of a subsystem by its environment. Denoting the decoherence time τ, I will show that a double scaling limit in which ℏ→ 0 and τ→ 0 such that the ratio E=ℏ/τ remains fixed leads to an irreversible open−system evolution with well−defined classical and quantum subsystems. The resulting dynamics are completely positive, linear and trace−preserving, and are equivalent to the standard classical limit when applied to a single quantum system in the limit E→ 0. When E is non−zero, interactions between the effective classical and quantum systems are accompanied by diffusion in phase space and Hilbert space, with the quantum state remaining pure conditioned on the classical trajectory. The main technical result is showing that, for arbitrary Hamiltonians, the generators of partial versions of the Wigner, Husimi and Glauber−Sudarshan quasiprobability distributions may all be mapped in the above double scaling limit to the same completely−positive generator.