Cluster development method in the quantum mechanics of many particle system

In order to investigate the many particle system by the variational principle, the cluster development method proposed by Jastrow is systematically formulated. It is a direct generalization of the Hartree method, in which two particle functions are included in the trial function to represent the correlations between particles. The energy expectation value is expanded in a series, each term of which is expressed in cluster integrals. It is found that the series converges rapidly when the correlations are marked only for small particle separations, so that this method is expected to be useful especially for the system of particles interacting through short range potentials with repulsive cores.In order to investigate the many particle system by the variational principle, the cluster development method proposed by Jastrow is systematically formulated. It is a direct generalization of the Hartree method, in which two particle functions are included in the trial function to represent the correlations between particles. The energy expectation value is expanded in a series, each term of which is expressed in cluster integrals. It is found that the series converges rapidly when the correlations are marked only for small particle separations, so that this method is expected to be useful especially for the system of particles interacting through short range potentials with repulsive cores.

Progress of Theoretical PhysicsApr 1, 1957185 citations

Quantum Mechanics of Many-Particle Systems

Ajit Kumar

Cambridge University Press eBooksOct 20, 201813 citations

Development of multicomponent coupled-cluster method for investigation of multiexcitonic interactions

Benjamin H. Ellis, Somil Aggarwal, Arindam Chakraborty

Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born-Oppenheimer electron-nuclear interactions in molecules, electron-hole interactions in electronically excited nanoparticles, and electron-positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron-electron) but also between particles of different types (electron-nuclear and electron-hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle-particle correlation in multicomponent systems is presented. This method provides a balanced treatment of many-particle correlation in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is the extension of the electronic structure CCSD formulation for multicomponent systems and is defined as $\vert Ψ_\mathrm{mcCC} \rangle = e^{T_1^\mathrm{I}+T_2^\mathrm{I}+T_1^\mathrm{II}+T_2^\mathrm{II}+T_{11}^\mathrm{I,II}+T_{12}^\mathrm{I,II}+T_{21}^\mathrm{I,II}+T_{22}^\mathrm{I,II}}\vert 0^\mathrm{I}0^\mathrm{II}\rangle$ . The applicability of the mcCC method was demonstrated by computing biexciton binding energies for multiexcitonic systems and benchmarking the results against full configuration interaction calculations. The results demonstrated that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron-hole correlation in multiexcitonic systems.Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born-Oppenheimer electron-nuclear interactions in molecules, electron-hole interactions in electronically excited nanoparticles, and electron-positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron-electron) but also between particles of different types (electron-nuclear and electron-hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle-particle correlation in multicomponent systems is presented. This method provides a balanced treatment of many-particle correlation in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is the extension of the electronic structure CCSD formulation for multicomponent systems and is defined as $\vert Ψ_\mathrm{mcCC} \rangle = e^{T_1^\mathrm{I}+T_2^\mathrm{I}+T_1^\mathrm{II}+T_2^\mathrm{II}+T_{11}^\mathrm{I,II}+T_{12}^\mathrm{I,II}+T_{21}^\mathrm{I,II}+T_{22}^\mathrm{I,II}}\vert 0^\mathrm{I}0^\mathrm{II}\rangle$. The applicability of the mcCC method was demonstrated by computing biexciton binding energies for multiexcitonic systems and benchmarking the results against full configuration interaction calculations. The results demonstrated that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron-hole correlation in multiexcitonic systems.

arXiv:1510.05762Oct 20, 20150 citations

The Quantum Mechanics of N-Particle Systems

Pure and applied physicsJan 1, 19700 citations

Quantum statistical mechanics : a Monte Carlo study of clusters

Fung-kiu Chow

Jan 1, 20000 citations

Cluster Variation Method for Finite-Temperature Systems. I: Formalism for Fermion Systems

T. Yoshikoshi, H. Yamaoka, M. Yamada

The cluster variation method, which was originally devised for quantum-mechanical many-body systems at zero temperature, is extended to treat finite-temperature systems. The new method is based on a variational principle that the partition function is the maximum of a certain functional, APF (approximate partition function). This method includes the conventional cluster variation method at zero temperature as a limiting case. A procedure is given for calculating APF by cluster expansion for fermion systems. In this procedure, use is made of single-particle energies which should be determined self-consistently. The non-orthogonality problem which comes from the presence of correlations among particles is solved by the use of linear combinations of (generalized) Jastrow wave functions. Further development of this method is briefly discussed.The cluster variation method, which was originally devised for quantum-mechanical many-body systems at zero temperature, is extended to treat finite-temperature systems. The new method is based on a variational principle that the partition function is the maximum of a certain functional, APF (approximate partition function). This method includes the conventional cluster variation method at zero temperature as a limiting case. A procedure is given for calculating APF by cluster expansion for fermion systems. In this procedure, use is made of single-particle energies which should be determined self-consistently. The non-orthogonality problem which comes from the presence of correlations among particles is solved by the use of linear combinations of (generalized) Jastrow wave functions. Further development of this method is briefly discussed.

Progress of Theoretical PhysicsNov 1, 19851 citation

\vert Ψ_\mathrm{mcCC} \rangle = e^{T_1^\mathrm{I}+T_2^\mathrm{I}+T_1^\mathrm{II}+T_2^\mathrm{II}+T_{11}^\mathrm{I,II}+T_{12}^\mathrm{I,II}+T_{21}^\mathrm{I,II}+T_{22}^\mathrm{I,II}}\vert 0^\mathrm{I}0^\mathrm{II}\rangle

. The applicability of the mcCC method was demonstrated by computing biexciton binding energies for multiexcitonic systems and benchmarking the results against full configuration interaction calculations. The results demonstrated that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron-hole correlation in multiexcitonic systems.