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Semiclassical approach to dynamics of interacting fermions

Shainen M. Davidson, Dries Sels, Anatoli Polkovnikov

arXiv:1604.08664Annals of PhysicsJul 12, 201736 citations

Gaussian phase-space representation of fermion dynamics: Beyond the time-dependent Hartree-Fock approximation

Saar Rahav, Shaul Mukamel

A Gaussian operator representation for the many-body density matrix of fermionic systems, developed by Corney and Drummond [Phys. Rev. Lett. 93, 260401 (2004)], is used to derive approximate decoupling schemes for their dynamics. In this approach the reduced single electron density-matrix elements serve as stochastic variables which satisfy an exact Fokker-Planck equation. The number of variables scales as $\ensuremath{\sim}{N}^{2}$ rather than $\ensuremath{\sim}\text{exp}(N)$ with the basis set size, and the time-dependent Hartree-Fock approximation (TDHF) is recovered in the ``classical'' limit. An approximate closed set of equations of motion for the one- and two-particle reduced density matrices provides a direct generalization of the TDHF.A Gaussian operator representation for the many-body density matrix of fermionic systems, developed by Corney and Drummond [Phys. Rev. Lett. 93, 260401 (2004)], is used to derive approximate decoupling schemes for their dynamics. In this approach the reduced single electron density-matrix elements serve as stochastic variables which satisfy an exact Fokker-Planck equation. The number of variables scales as $\ensuremath{\sim}{N}^{2}$ rather than $\ensuremath{\sim}\text{exp}(N)$ with the basis set size, and the time-dependent Hartree-Fock approximation (TDHF) is recovered in the ``classical'' limit. An approximate closed set of equations of motion for the one- and two-particle reduced density matrices provides a direct generalization of the TDHF.

arXiv:0902.3227Physical Review BApr 10, 200910 citations

Quantum dynamics of a bosonic mode and a two-level system interacting with several reservoirs

Narges Cheraghpour, Fardin Kheirandish

Abstract In the framework of a novel dissipative scheme, we have investigated the quantum dynamics of an oscillating system interacting with two reservoirs with different temperatures trough different time-dependent coupling functions. The reduced density matrix, quantum optical characteristic functions, and (quasi) distribution functions like Husimi, Glauber–Sudarshan and Wigner functions on the phase space of the oscillator are obtained. The problem has been generalized to the case where the oscillator is interacting with n distinctive reservoirs, and a quantum current and an effective reservoir is introduced. Finally, the quantum dynamics of a two-level system interacting with two reservoirs has been investigated, and the exact reduced density matrix is obtained.Abstract In the framework of a novel dissipative scheme, we have investigated the quantum dynamics of an oscillating system interacting with two reservoirs with different temperatures trough different time-dependent coupling functions. The reduced density matrix, quantum optical characteristic functions, and (quasi) distribution functions like Husimi, Glauber–Sudarshan and Wigner functions on the phase space of the oscillator are obtained. The problem has been generalized to the case where the oscillator is interacting with n distinctive reservoirs, and a quantum current and an effective reservoir is introduced. Finally, the quantum dynamics of a two-level system interacting with two reservoirs has been investigated, and the exact reduced density matrix is obtained.

arXiv:2504.13303Laser PhysicsMay 1, 20250 citations

Stochastic simulations of fermionic dynamics with phase-space representations

Magnus Ögren, Karen V. Kheruntsyan, Joel Frederick Corney

arXiv:1008.0970Computer Physics CommunicationsOct 29, 201010 citations

Time-dependent fluctuating local field approach for the description of correlated fermions dynamics

L. D. Silakov, Yana S. Lyakhova, Alexey N. Rubtsov

Physical review. B./Physical review. BMay 26, 20260 citations

Time-dependent density-matrix functional in Liouville space and the optical response of many-electron systems

Vladimir Chernyak, Shaul Mukamel

A time-dependent functional approach is developed for calculating the dynamical optical response and ground-state properties of nonrelativistic fermion systems. The functional (effective action) uses the particle-hole components of the reduced single-electron density matrix as variables and is constructed using the natural orbitals as a reference. It is defined on pairs of trajectories that constitute a Liouville space path in the phase space of the classical analog of the quantum system. A perturbative ``semiclassical'' calculation of the effective Liouville-space action is used to incorporate correlation effects in the linear optical response.A time-dependent functional approach is developed for calculating the dynamical optical response and ground-state properties of nonrelativistic fermion systems. The functional (effective action) uses the particle-hole components of the reduced single-electron density matrix as variables and is constructed using the natural orbitals as a reference. It is defined on pairs of trajectories that constitute a Liouville space path in the phase space of the classical analog of the quantum system. A perturbative ``semiclassical'' calculation of the effective Liouville-space action is used to incorporate correlation effects in the linear optical response.

Physical Review ANov 1, 199513 citations

Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions

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Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions

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