An illustration of canonical quantum-classical dynamics

• URL: http://arxiv.org/abs/2107.01341v1
• Date: Sat, 3 Jul 2021 04:30:02 GMT
• Title: An illustration of canonical quantum-classical dynamics
• Authors: Mustafa Amin and Mark A. Walton
• Abstract summary: We show that while pure variables evolve to violate the pure canonical relations, they always obey the hybrid canonical relations. The dynamics of hybrid variables, on the other hand, is shown to require a fully specified and consistent hybrid bracket.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Using the example of the harmonic oscillator, we illustrate the use of hybrid dynamical brackets in analyzing quantum-classical interaction. We only assume that a hybrid dynamical bracket exists, is bilinear, and reduces to the pure quantum/classical bracket when acting on pure quantum/classical variables. Any hybrid bracket obeying these natural requirements will produce the same dynamics for pure classical or quantum variables, given a hybrid Hamiltonian. Backreaction is manifested in the evolution of a nonvanishing commutator between classical variables. The more massive the classical system is, the less it is affected by backreaction. Interestingly, we show that while pure variables evolve to violate the pure canonical relations, they always obey the hybrid canonical relations. The dynamics of hybrid variables, on the other hand, is shown to require a fully specified and consistent hybrid bracket, otherwise evolution cannot be defined.

Related papers

• Quantum Principle of Least Action in Dynamic Theories With Higher Derivatives [44.99833362998488]
  This form is the initial point for the construction of quantum theory. The correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit.
  arXiv  Detail & Related papers  (2024-04-15T09:29:58Z)
• Hybrid classical-quantum systems in terms of moments [0.0]
  We describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. In particular, a closed formula for the Poisson brackets between any two moments for an arbitrary number of degrees of freedom is presented.
  arXiv  Detail & Related papers  (2023-12-21T15:36:40Z)
• Observation of many-body dynamical localization [12.36065516066796]
  We present evidence for many-body dynamical localization for the Lieb-Liniger version of the many-body quantum kicked rotor. Our results shed light on the boundary between the classical, chaotic world and the realm of quantum physics.
  arXiv  Detail & Related papers  (2023-12-21T14:24:50Z)
• Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit [8.437514200532176]
  We show how mixed eigenstates vary with approaching the semiclassical limit in mixed-type many-body quantum systems. Using the Husimi function, we show that the eigenstates of the Dicke model with mixed-type classical phase space can be classified into different types.
  arXiv  Detail & Related papers  (2023-09-21T02:31:21Z)
• Hybrid quantum-classical dynamics of pure-dephasing systems [0.0]
  We consider the interaction dynamics of a classical oscillator and a quantum two-level system for different pure-dephasing Hamiltonians of the type $widehatH(q,p)=H_C(q,p)boldsymbol1+H_I(q,p)widehatsigma_z$.
  arXiv  Detail & Related papers  (2023-03-08T12:22:00Z)
• Hybrid completely positive Markovian quantum-classical dynamics [0.0]
  derivation of hybrid quantum-classical dynamics is given in terms of Markovian master equations. Goal is a brief introduction to state-of-the-art of hybrid dynamics.
  arXiv  Detail & Related papers  (2023-02-26T22:10:38Z)
• The role of fluctuations in quantum and classical time crystals [58.720142291102135]
  We study the role of fluctuations on the stability of the system and find no distinction between quantum and classical DTCs. This allows us to probe the fluctuations in an experiment using two strongly coupled parametric resonators subject to classical noise.
  arXiv  Detail & Related papers  (2022-03-10T19:00:01Z)
• Koopman wavefunctions and classical states in hybrid quantum-classical dynamics [0.0]
  We deal with the reversible dynamics of coupled quantum and classical systems. We exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics.
  arXiv  Detail & Related papers  (2021-08-03T13:19:38Z)
• Sets of Marginals and Pearson-Correlation-based CHSH Inequalities for a Two-Qubit System [22.1737984719789]
  We characterize a set of jointly classicable variables of a graphical model. A crucial feature of this inequality is its nonlinearity, which poses difficulties in the proof.
  arXiv  Detail & Related papers  (2021-07-05T06:52:49Z)
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain [21.24186888129542]
  We study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves.
  arXiv  Detail & Related papers  (2020-10-14T16:46:11Z)
• Quantum-Classical Dynamical Brackets [0.0]
  We study the problem of constructing a general hybrid quantum-classical bracket from a partial classical limit of a full quantum bracket. We show that such a bracket is the commutator of that product. In the proposed scheme, quantum backreaction appears as quantum-dependent terms in the classical equations of motion.
  arXiv  Detail & Related papers  (2020-09-21T02:07:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.