Related papers: The two classes of hybrid classical-quantum dynamics

The two classes of hybrid classical-quantum dynamics

URL: http://arxiv.org/abs/2203.01332v1
Date: Wed, 2 Mar 2022 19:00:01 GMT
Title: The two classes of hybrid classical-quantum dynamics
Authors: Jonathan Oppenheim, Carlo Sparaciari, Barbara \v{S}oda, Zachary Weller-Davies
Abstract summary: Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space. We prove that if the dynamics is memoryless, there are two classes of these dynamics. We find the most general form of each class of classical-quantum master equation.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law must be a completely positive and norm preserving map. We prove that if the dynamics is memoryless, there are two classes of these dynamics, one which features finite sized jumps in the classical phase space and one which is continuous. We find the most general form of each class of classical-quantum master equation. This is achieved by applying the complete positivity conditions using a generalized Cauchy-Schwartz inequality applicable to classical-quantum systems. The key technical result is a generalisation of the Pawula theorem.

Related papers

From integrability to chaos: the quantum-classical correspondence in a triple well bosonic model [0.0]
We investigate the semiclassical limit of a bosonic quantum many-body system exhibiting both integrable and chaotic behavior. The transition from regularity to chaos in classical dynamics is visualized through Poincar'e sections. The study systematically establishes quantum-classical correspondence for a bosonic many-body system with more than two wells.
arXiv Detail & Related papers (2023-11-22T06:31:00Z)
Differences between quantum and classical adiabatic evolution [0.0]
We show that classical adiabatic evolution is not equivalent to quantum adiabatic evolution. For general multiband systems we uncover a correction term in the non-Abelian gauge potential for classical systems.
arXiv Detail & Related papers (2023-09-15T16:14:22Z)
Learning in quantum games [41.67943127631515]
We show that the induced quantum state dynamics decompose into (i) a classical, commutative component which governs the dynamics of the system's eigenvalues. We find that the FTQL dynamics incur no more than constant regret in all quantum games.
arXiv Detail & Related papers (2023-02-05T08:23:04Z)
Path integrals for classical-quantum dynamics [0.0]
Consistent dynamics which couples classical and quantum degrees of freedom exists. We derive a general path integral representation for such dynamics in terms of a classical-quantum action. When the classical-quantum Hamiltonian is at most quadratic in the momenta we are able to derive a configuration space path integral.
arXiv Detail & Related papers (2023-01-11T19:03:26Z)
A healthier semi-classical dynamics [0.0]
We study the back-reaction of quantum systems onto classical ones. We take the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space.
arXiv Detail & Related papers (2022-08-24T18:04:14Z)
Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z)
Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
arXiv Detail & Related papers (2022-04-24T13:32:45Z)
Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
arXiv Detail & Related papers (2021-08-13T01:44:24Z)
The principle of majorization: application to random quantum circuits [68.8204255655161]
Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. We verified that all the families of circuits satisfy on average the principle of majorization. Clear differences appear in the fluctuations of the Lorenz curves associated to states.
arXiv Detail & Related papers (2021-02-19T16:07:09Z)
Objective trajectories in hybrid classical-quantum dynamics [0.0]
We introduce several toy models in which to study hybrid classical-quantum evolution. We present an unravelling approach to calculate the dynamics, and provide code to numerically simulate it.
arXiv Detail & Related papers (2020-11-11T19:00:34Z)
Emergence of classical behavior in the early universe [68.8204255655161]
Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
arXiv Detail & Related papers (2020-04-22T16:38:25Z)

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