Hybrid classical-quantum systems in terms of moments
- URL: http://arxiv.org/abs/2312.13946v2
- Date: Tue, 5 Mar 2024 17:11:28 GMT
- Title: Hybrid classical-quantum systems in terms of moments
- Authors: David Brizuela and Sara F. Uria
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a consistent formalism to describe the dynamics of hybrid systems
with mixed classical and quantum degrees of freedom. The probability function
of the system, which, in general, will be a combination of the classical
distribution function and the quantum density matrix, is described in terms of
its corresponding moments. We then define a hybrid Poisson bracket, such that
the dynamics of the moments is ruled by an effective Hamiltonian. In
particular, a closed formula for the Poisson brackets between any two moments
for an arbitrary number of degrees of freedom is presented, which corrects
previous expressions derived in the literature for the purely quantum case.
This formula is of special relevance for practical applications of the
formalism. Finally, we study the dynamics of a particular hybrid system given
by two coupled oscillators, one being quantum and the other classical. Due to
the coupling, specific quantum and classical properties are transferred between
different sectors. In particular, the quantum sector is allowed to violate the
uncertainty relation, though we explicitly show that there exists a minimum
positive bound of the total uncertainty of the hybrid system.
Related papers
- Study of quantum phase transition and entanglement in coupled top systems with standard and nonstandard symmetries under Floquet formalism [15.699822139827916]
We study an effective time-independent Hamiltonian of a coupled kicked-top (CKT) system derived using the Van Vleck-based perturbation theory at the high-frequency driving limit under Floquet formalism.
We study classical and quantum versions of this coupled top system for torsion-free and nonzero torsion cases.
arXiv Detail & Related papers (2024-09-13T06:36:41Z) - Markovian dynamics for a quantum/classical system and quantum trajectories [0.0]
We develop a general approach to the dynamics of quantum/classical systems.
An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative.
arXiv Detail & Related papers (2024-03-24T08:26:54Z) - Effective nonlinear Ehrenfest hybrid quantum-classical dynamics [0.0]
We analyze the case of Ehrenfest dynamics on systems defined by a probability density.
We identify the relations of the non-linearity of the dynamics with the obstructions to define a consistent dynamics for the first quantum moment.
arXiv Detail & Related papers (2023-08-28T09:25:36Z) - Hybrid quantum-classical systems: Quasi-free Markovian dynamics [0.0]
In the case of a quantum-classical hybrid system, the problem of characterizing the most general dynamical semigroup is solved under the restriction of being quasi-free.
We show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator valued measure and instrument.
A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behaviour of the quantum one.
arXiv Detail & Related papers (2023-07-05T19:26:09Z) - 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) - Quantum Instability [30.674987397533997]
We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system.
An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
arXiv Detail & Related papers (2022-08-05T19:53:46Z) - 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) - 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) - 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)
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.