In the framework of recently developed description of the non-relativistic constrained quantum mechanics of systems of $N$ -Coulombically interacting electrons [Phys. Rev. {\bf A} 78, 032503 (2008)], we study the relation between spin and statistics in two-electron systems. We find that that the Fermi-Dirac statistics implies lowering of the spatial SO(3) symmetry of the wave-functions of electronic states to Abelian SO(2) rotational subgroup, which is accompanied by reduction of the number of spatial degrees-of-freedom from 6 to 5. We find that the relation between spin and statistics is necessarily related to the anti-symmetry of the relative phase of the spatial part of the two-electron wave-function. We find that it leads to distinct classification of the electronic states according to their relative orbital parity $(-1)^m$ and total spin $S=\{0,1\}$ . We also find that the Pauli exclusion principle is realized dynamically due to Coulombic interaction between the particles. We find that the broken rotation symmetry of the wave-functions of the electronic states can be restored dynamically, due to conservation of the Laplace-Runge-Lenz vector. We demonstrate that the proposed theoretical description is internally consistent and predictive, and we find the non-equivalence of the above mention representation to the conventional Schr\{o}dinger picture for the description of the quantum dynamics in Coulombic systems with more than one electron.In the framework of recently developed description of the non-relativistic constrained quantum mechanics of systems of $N$-Coulombically interacting electrons [Phys. Rev. {\bf A} 78, 032503 (2008)], we study the relation between spin and statistics in two-electron systems. We find that that the Fermi-Dirac statistics implies lowering of the spatial SO(3) symmetry of the wave-functions of electronic states to Abelian SO(2) rotational subgroup, which is accompanied by reduction of the number of spatial degrees-of-freedom from 6 to 5. We find that the relation between spin and statistics is necessarily related to the anti-symmetry of the relative phase of the spatial part of the two-electron wave-function. We find that it leads to distinct classification of the electronic states according to their relative orbital parity $(-1)^m$ and total spin $S=\{0,1\}$. We also find that the Pauli exclusion principle is realized dynamically due to Coulombic interaction between the particles. We find that the broken rotation symmetry of the wave-functions of the electronic states can be restored dynamically, due to conservation of the Laplace-Runge-Lenz vector. We demonstrate that the proposed theoretical description is internally consistent and predictive, and we find the non-equivalence of the above mention representation to the conventional Schr\{o}dinger picture for the description of the quantum dynamics in Coulombic systems with more than one electron.

Mar 31, 20090 citations

Dynamics of Electrons and Nuclei

Rubén Santamaría

Springer eBooksJan 1, 20230 citations

Linear response of independent electrons

Gabriele F. Giuliani, Giovanni Vignale

Introduction The calculation of the linear response functions of an electron liquid is a very important, but obviously extremely difficult task. Even after many years of study, and in spite of much progress, a complete solution of the problem is still lacking. In preparation to the study of this difficult problem, we consider in this chapter the main response functions of the non-interacting electron gas, namely, the density–density, spin–spin, and current–current response functions, all of which can be calculated analytically. It turns out that understanding the response of the non-interacting electron gas is an essential prerequisite for understanding the richer and more complex response of the interacting liquid. Indeed, one of the most fruitful ideas in many-body physics is that the response of an interacting system can be pictured as the response of a non-interacting system to an effective self-consistent field, which depends on global properties such as the particle density, the density matrix, the current–density etc. ‥ This is true, in particular, for every dynamical mean field theory , which can be derived from the corresponding static mean field theory (such as the HF theory) with the help of the techniques introduced in Section 4.7. In the first part of this chapter we present a detailed study of the response functions of the homogeneous non-interacting electron gas in three, two, and one dimension. Electron–impurity scattering is included only at the most elementary level, and only to demonstrate its main effect, namely, the emergence of diffusion in the dynamics of density fluctuations. In the next chapter we shall present approximations for the effective self-consistent field.Introduction The calculation of the linear response functions of an electron liquid is a very important, but obviously extremely difficult task. Even after many years of study, and in spite of much progress, a complete solution of the problem is still lacking. In preparation to the study of this difficult problem, we consider in this chapter the main response functions of the non-interacting electron gas, namely, the density–density, spin–spin, and current–current response functions, all of which can be calculated analytically. It turns out that understanding the response of the non-interacting electron gas is an essential prerequisite for understanding the richer and more complex response of the interacting liquid. Indeed, one of the most fruitful ideas in many-body physics is that the response of an interacting system can be pictured as the response of a non-interacting system to an effective self-consistent field, which depends on global properties such as the particle density, the density matrix, the current–density etc. ‥ This is true, in particular, for every dynamical mean field theory , which can be derived from the corresponding static mean field theory (such as the HF theory) with the help of the techniques introduced in Section 4.7. In the first part of this chapter we present a detailed study of the response functions of the homogeneous non-interacting electron gas in three, two, and one dimension. Electron–impurity scattering is included only at the most elementary level, and only to demonstrate its main effect, namely, the emergence of diffusion in the dynamics of density fluctuations. In the next chapter we shall present approximations for the effective self-consistent field.

Cambridge University Press eBooksMar 31, 20051 citation

Non-equilibrium quantum domain reconfiguration dynamics in a two-dimensional electronic crystal and a quantum annealer

Jaka Vodeb, Michele Diego, Yevhenii Vaskivskyi +6 more

Abstract Emergent metastability in non-equilibrium systems is a subject that touches everything from the origins of life1 to the quantum nature of the universe2. In condensed quantum matter, a good topical example is the metastability of topologically inhibited self-organization of electronic domains in a correlated electronic crystal in the aftermath of a symmetry-breaking phase transition3. Understanding the dynamics of such systems is crucial for developing new quantum technologies and exploring fundamental aspects of many-body non-equilibrium quantum mechanics. Here, a non-equilibrium state is set up by carrier injection in the quantum material (M), resulting in a domain structure, whose time-evolution is investigated by scanning tunneling microscopy. Demonstrating a new approach to modelling of emergent non-equilibrium quantum behavior, we use an array of 2008 qubits in a programmable noisy superconducting quantum simulator (NSQS) without error correction (P), in which mutual qubit interconnections correspond directly to the electronic interactions on the triangular lattice of the electronic crystal material. The success of the simulations critically depends on both the faithfulness of the model correspondence between the two systems and careful management of the decoherence pathways. Importantly, decoherence of both P and M is driven by noise with a characteristic 1/ν frequency spectrum. The simulations reveal how an emergent false vacuum state arises, describing the time evolution and temperature dependence of the observed electronic domain dynamics of M solely on the basis of microscopic electronic interactions. The parallel experiments demonstrate the potential of NSQSs for studying emergent non-equilibrium dynamics in complex many-body quantum systems.Abstract Emergent metastability in non-equilibrium systems is a subject that touches everything from the origins of life1 to the quantum nature of the universe2. In condensed quantum matter, a good topical example is the metastability of topologically inhibited self-organization of electronic domains in a correlated electronic crystal in the aftermath of a symmetry-breaking phase transition3. Understanding the dynamics of such systems is crucial for developing new quantum technologies and exploring fundamental aspects of many-body non-equilibrium quantum mechanics. Here, a non-equilibrium state is set up by carrier injection in the quantum material (M), resulting in a domain structure, whose time-evolution is investigated by scanning tunneling microscopy. Demonstrating a new approach to modelling of emergent non-equilibrium quantum behavior, we use an array of 2008 qubits in a programmable noisy superconducting quantum simulator (NSQS) without error correction (P), in which mutual qubit interconnections correspond directly to the electronic interactions on the triangular lattice of the electronic crystal material. The success of the simulations critically depends on both the faithfulness of the model correspondence between the two systems and careful management of the decoherence pathways. Importantly, decoherence of both P and M is driven by noise with a characteristic 1/ν frequency spectrum. The simulations reveal how an emergent false vacuum state arises, describing the time evolution and temperature dependence of the observed electronic domain dynamics of M solely on the basis of microscopic electronic interactions. The parallel experiments demonstrate the potential of NSQSs for studying emergent non-equilibrium dynamics in complex many-body quantum systems.

Nature CommunicationsJun 6, 20247 citations

Spin Dynamics of Electron

WORLD SCIENTIFIC eBooksApr 1, 20220 citations

In the framework of recently developed description of the non-relativistic constrained quantum mechanics of systems of

N

-Coulombically interacting electrons [Phys. Rev. {\bf A} 78, 032503 (2008)], we study the relation between spin and statistics in two-electron systems. We find that that the Fermi-Dirac statistics implies lowering of the spatial SO(3) symmetry of the wave-functions of electronic states to Abelian SO(2) rotational subgroup, which is accompanied by reduction of the number of spatial degrees-of-freedom from 6 to 5. We find that the relation between spin and statistics is necessarily related to the anti-symmetry of the relative phase of the spatial part of the two-electron wave-function. We find that it leads to distinct classification of the electronic states according to their relative orbital parity

(-1)^m

and total spin

S=\{0,1\}

. We also find that the Pauli exclusion principle is realized dynamically due to Coulombic interaction between the particles. We find that the broken rotation symmetry of the wave-functions of the electronic states can be restored dynamically, due to conservation of the Laplace-Runge-Lenz vector. We demonstrate that the proposed theoretical description is internally consistent and predictive, and we find the non-equivalence of the above mention representation to the conventional Schr\{o}dinger picture for the description of the quantum dynamics in Coulombic systems with more than one electron.