aqora

An interpretation of quantum foundations based on density functional theory and polymer self-consistent field theory

Russell B. Thompson

Abstract The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum time-dependent density functional theory. This allows the theorems of density functional theory to relate non-relativistic quantum mechanics to a classical statistical mechanical derivation of polymer self-consistent field theory for ring polymers in a 4 dimensional thermal-space. One dynamic postulate is added to two static postulates which allows for a description of quantum physics from a 5 dimensional thermal-space-time ensemble perspective. A connection with aspects of classical field theory can be made in the classical limit.Abstract The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum time-dependent density functional theory. This allows the theorems of density functional theory to relate non-relativistic quantum mechanics to a classical statistical mechanical derivation of polymer self-consistent field theory for ring polymers in a 4 dimensional thermal-space. One dynamic postulate is added to two static postulates which allows for a description of quantum physics from a 5 dimensional thermal-space-time ensemble perspective. A connection with aspects of classical field theory can be made in the classical limit.

arXiv:2111.14236Quantum Studies Mathematics and FoundationsJul 19, 20228 citations

Foundations of Density Functional Theory

Eugene S. Kryachko, Eduardo V. Ludeña

Springer eBooksJan 1, 19902 citations

A Quantum-Classical Isomorphic Interpretation of Quantum Foundations Based on Density Functional Theory and Polymer Self-Consistent Field Theory

R. B. Thompson

Bulletin of the American Physical SocietyMar 19, 20210 citations

New Perspectives on the Fundamental Theorem of Density Functional Theory

Viraht Sahni, Xiao‐Yin Pan

Bulletin of the American Physical SocietyMar 12, 20080 citations

Self-consistent Green's function embedding for advanced electronic structure methods based on a dynamical mean-field concept

Wael Chibani, Xinguo Ren, Matthias Scheffler +1 more

We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here a unit cell or a supercell) with advanced electronic structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self-consistent manner. Our scheme is based on the concept of dynamical mean-field theory formulated in terms of Green's functions. Our real-space dynamical mean-field embedding scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green's functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., computational supercell) size.We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here a unit cell or a supercell) with advanced electronic structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self-consistent manner. Our scheme is based on the concept of dynamical mean-field theory formulated in terms of Green's functions. Our real-space dynamical mean-field embedding scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green's functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., computational supercell) size.

arXiv:1506.03680Physical review. B./Physical review. BApr 6, 201647 citations

Modern Density Functional Theory

Viraht Sahni

Springer tracts in modern physicsJan 1, 202247 citations

The Self-Consistent Field Concept in Density Functional Theory

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