Information about the interaction of a many-electron quantum system with its environment, we show, is encoded within the one-electron density matrix (1-RDM). While the 1-RDM from an ensemble many-electron quantum system must obey the Pauli exclusion principle, the 1-RDM must obey additional constraints known as generalized Pauli conditions when it corresponds to a closed system describable by a single wave function. By examining the 1-RDM's violation of these generalized Pauli conditions, we obtain a sufficient condition at the level of a single electron for a many-electron quantum system's openness. In an application to exciton dynamics in photosynthetic light harvesting we show that the interaction of the system with the environment (quantum noise) relaxes significant constraints imposed on the exciton dynamics by the generalized Pauli conditions. This relaxation provides a geometric (kinematic) interpretation for the role of noise in enhancing exciton transport in quantum systems.Information about the interaction of a many-electron quantum system with its environment, we show, is encoded within the one-electron density matrix (1-RDM). While the 1-RDM from an ensemble many-electron quantum system must obey the Pauli exclusion principle, the 1-RDM must obey additional constraints known as generalized Pauli conditions when it corresponds to a closed system describable by a single wave function. By examining the 1-RDM's violation of these generalized Pauli conditions, we obtain a sufficient condition at the level of a single electron for a many-electron quantum system's openness. In an application to exciton dynamics in photosynthetic light harvesting we show that the interaction of the system with the environment (quantum noise) relaxes significant constraints imposed on the exciton dynamics by the generalized Pauli conditions. This relaxation provides a geometric (kinematic) interpretation for the role of noise in enhancing exciton transport in quantum systems.

Physical Review AJan 30, 201530 citations

Schrödinger-Pauli Theory of Electrons: A Complementary Perspective

Viraht Sahni

Springer tracts in modern physicsJan 1, 20220 citations

Classical Models of the Spin 1/2 System

C. Salazar-Lazaro

We proposed a Quaternionic mechanical system motivated by the Foucault pendulum as a classical model for the dynamics of the spin 1/2 system. We showed that this mechanical system contains the dynamics of the spin state of the electron under a uniform magnetic field as it is given by the Schrodinger-Pauli-Equation (SPE). We closed with a characterization of the dynamics of this generalized classical system by showing that it is equivalent with the dynamics of the Schrodinger Pauli Equation as long as the solutions to the generalized classical system are roots of the Lagrangian, that is the condition L = 0 holds.We proposed a Quaternionic mechanical system motivated by the Foucault pendulum as a classical model for the dynamics of the spin 1/2 system. We showed that this mechanical system contains the dynamics of the spin state of the electron under a uniform magnetic field as it is given by the Schrodinger-Pauli-Equation (SPE). We closed with a characterization of the dynamics of this generalized classical system by showing that it is equivalent with the dynamics of the Schrodinger Pauli Equation as long as the solutions to the generalized classical system are roots of the Lagrangian, that is the condition L = 0 holds.

Jan 1, 20120 citations

The ubiquitous Pauli matrices

Steven B. Berger

American Journal of PhysicsJan 1, 19853 citations

Dynamical interpretation of the Pauli-exclusion principle for a system of two Coulombically interacting electrons

Boyan Obreshkov

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

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.