Semiclassical description of a system of fermions in a rotating field

The derivation of effective macroscopic theories approximating microscopic systems of interacting particles is a major question in non-equilibrium statistical mechanics. In these notes we present an approximation of systems made by many fermions interacting via inverse power law potentials in the mean-field and semiclassical regimes, reviewing the material presented at the 11th summer school "Methods and Models of Kinetic Theory" held in Pesaro in June 2022. More precisely, we focus on weakly interacting fermions whose collective effect can be approximated by an averaged potential in convolution form, and review recent mean-field techniques based on second quantization approaches. As a first step we obtain a reduced description given by the time-dependent Hartree-Fock equation. As a second step we look at longer time scales where a semiclassical description starts to be relevant and approximate the many-body dynamics with the Vlasov equation, which describes the evolution of the effective probability density of particles on the one particle phase space.The derivation of effective macroscopic theories approximating microscopic systems of interacting particles is a major question in non-equilibrium statistical mechanics. In these notes we present an approximation of systems made by many fermions interacting via inverse power law potentials in the mean-field and semiclassical regimes, reviewing the material presented at the 11th summer school "Methods and Models of Kinetic Theory" held in Pesaro in June 2022. More precisely, we focus on weakly interacting fermions whose collective effect can be approximated by an averaged potential in convolution form, and review recent mean-field techniques based on second quantization approaches. As a first step we obtain a reduced description given by the time-dependent Hartree-Fock equation. As a second step we look at longer time scales where a semiclassical description starts to be relevant and approximate the many-body dynamics with the Vlasov equation, which describes the evolution of the effective probability density of particles on the one particle phase space.

arXiv:2307.07762Jul 15, 20231 citation

Semiclassical approach to dynamics of interacting fermions

Shainen M. Davidson, Dries Sels, Anatoli Polkovnikov

arXiv:1604.08664Annals of PhysicsJul 12, 201736 citations

Open Quantum Systems Driven by Chirped Pulses: Quantized versus Semiclassical Fields and the Validity of the Rotating-Wave Approximation

Justin Zhengjie Tan, Frank Großmann, Yiying Yan +2 more

Population transfer via chirped rapid adiabatic passage is studied using open quantum and semiclassical models, with and without the rotating-wave approximation. A time-dependent variational approach based on the multiple-Davydov D $_2$ trial state is employed to simulate the quantum models with an arbitrary finite mean photon number. We examine the accuracy of both the semiclassical field description and the rotating-wave approximation. Robust population transfer is identified over a wide parameter regime controlled by the laser spectral chirp and is found to be insensitive to the spin--phonon coupling strength, Gaussian pulse area, and energy gap of the two-level system.Population transfer via chirped rapid adiabatic passage is studied using open quantum and semiclassical models, with and without the rotating-wave approximation. A time-dependent variational approach based on the multiple-Davydov D$_2$ trial state is employed to simulate the quantum models with an arbitrary finite mean photon number. We examine the accuracy of both the semiclassical field description and the rotating-wave approximation. Robust population transfer is identified over a wide parameter regime controlled by the laser spectral chirp and is found to be insensitive to the spin--phonon coupling strength, Gaussian pulse area, and energy gap of the two-level system.

quant-pharXiv:2607.00583The Journal of Physical Chemistry LettersJul 2, 20261 citation

_2

trial state is employed to simulate the quantum models with an arbitrary finite mean photon number. We examine the accuracy of both the semiclassical field description and the rotating-wave approximation. Robust population transfer is identified over a wide parameter regime controlled by the laser spectral chirp and is found to be insensitive to the spin--phonon coupling strength, Gaussian pulse area, and energy gap of the two-level system.