Abstract. In this paper, a gradient flow model is presented for conducting ground state calculations in the Wigner formalism of many-body systems in the framework of density functional theory. Theoretically, an energy functional in the Wigner formalism is proposed, based on which the minimization problem is designed and analyzed for the ground state, providing a new perspective for ground state calculations of the Wigner function. Employing density functional theory, a gradient flow model is built upon the energy functional to obtain the ground state Wigner function representing the entire many-body system. Numerically, a parallelizable algorithm is developed using the operator splitting method and the Fourier spectral collocation method, whose numerical complexity of a single iteration is [Formula: see text]. Numerical experiments demonstrate the anticipated accuracy, encompassing the one-dimensional system with up to [Formula: see text] particles and the three-dimensional system with defect, showcasing the potential of our approach to large-scale simulations and computations of systems with defect. To the best of our knowledge, this is the first deterministic method for calculating the ground state Wigner function of the three-dimensional many-body system.Abstract. In this paper, a gradient flow model is presented for conducting ground state calculations in the Wigner formalism of many-body systems in the framework of density functional theory. Theoretically, an energy functional in the Wigner formalism is proposed, based on which the minimization problem is designed and analyzed for the ground state, providing a new perspective for ground state calculations of the Wigner function. Employing density functional theory, a gradient flow model is built upon the energy functional to obtain the ground state Wigner function representing the entire many-body system. Numerically, a parallelizable algorithm is developed using the operator splitting method and the Fourier spectral collocation method, whose numerical complexity of a single iteration is [Formula: see text]. Numerical experiments demonstrate the anticipated accuracy, encompassing the one-dimensional system with up to [Formula: see text] particles and the three-dimensional system with defect, showcasing the potential of our approach to large-scale simulations and computations of systems with defect. To the best of our knowledge, this is the first deterministic method for calculating the ground state Wigner function of the three-dimensional many-body system.

arXiv:2409.10851SIAM Journal on Scientific ComputingSep 12, 20250 citations

Absence of Wigner molecules in one-dimensional few-fermion systems with short-range interactions

Jingjing Wang, Wei Li, Shu Chen +3 more

We study, by means of exact-diagonalization techniques, the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density profile displays, at strong coupling, very well pronounced Wigner oscillations with a $4{k}_{\mathrm{F}}$ periodicity, the pair-correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.We study, by means of exact-diagonalization techniques, the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density profile displays, at strong coupling, very well pronounced Wigner oscillations with a $4{k}_{\mathrm{F}}$ periodicity, the pair-correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.

arXiv:1202.3284Physical Review BAug 7, 201231 citations

Wigner functions

David K. Ferry, Xavier Oriols, Josef Weinbub

Institute of Physics eBooksNov 1, 20230 citations

Numerical study of Wigner negativity in one-dimensional steady-state resonance fluorescence

Ingrid Strandberg, Yong Lu, Fernando Quijandría +1 more

In a numerical study, we investigate the steady-state generation of nonclassical states of light from a coherently driven two-level atom in a one-dimensional waveguide. Specifically, we look for states with a negative Wigner function, since such nonclassical states are a resource for quantum information processing applications, including quantum computing. We find that a waveguide terminated by a mirror at the position of the atom can provide Wigner-negative states, while an infinite waveguide yields strictly positive Wigner functions. Moreover, our paper reveals a connection between the purity of a quantum state and its Wigner negativity. We also analyze the effects of decoherence on the negativity of a state.In a numerical study, we investigate the steady-state generation of nonclassical states of light from a coherently driven two-level atom in a one-dimensional waveguide. Specifically, we look for states with a negative Wigner function, since such nonclassical states are a resource for quantum information processing applications, including quantum computing. We find that a waveguide terminated by a mirror at the position of the atom can provide Wigner-negative states, while an infinite waveguide yields strictly positive Wigner functions. Moreover, our paper reveals a connection between the purity of a quantum state and its Wigner negativity. We also analyze the effects of decoherence on the negativity of a state.

arXiv:1909.02395Physical Review ADec 4, 201921 citations

Wigner functions

David K. Ferry, Mihail Nedjalkov

Institute of Physics eBooksNov 1, 20180 citations

4{k}_{\mathrm{F}}

periodicity, the pair-correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.