The dynamics of a particle interacting with a random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain field-averaged correlation functions for quantum-mechanical probabilities and the distribution function for the probabilities of final states (which can be considered as random variables in the presence of a random field) are calculated. The calculated correlators are used to discuss the dependence of the final state on the initial state. One of the main results of this work is that, although the off-diagonal elements of the density matrix disappear with time, a particle in the system is localized incompletely (wave-packet reduction does not occur), and the distribution function for the probability of finding particle in one of the wells is a constant at infinite time.The dynamics of a particle interacting with a random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain field-averaged correlation functions for quantum-mechanical probabilities and the distribution function for the probabilities of final states (which can be considered as random variables in the presence of a random field) are calculated. The calculated correlators are used to discuss the dependence of the final state on the initial state. One of the main results of this work is that, although the off-diagonal elements of the density matrix disappear with time, a particle in the system is localized incompletely (wave-packet reduction does not occur), and the distribution function for the probability of finding particle in one of the wells is a constant at infinite time.

arXiv:quant-ph/0412026Journal of Experimental and Theoretical Physics LettersMay 1, 200214 citations

Approximation method for calculation of strongly correlated systems of electrons

Huai‐Yu Wang

The physical origin of the feature of strong correlation between electrons is mainly ascribed to doubly occupied atomic orbitals. Two-particle wave functions are believed necessary to describe strongly correlated systems. We emphasize that the on-site Coulomb interaction, which is important for strong correlation, should appear in equations as a natural term. Hartree-Fock-like self-consistent equations are derived with wave functions including two-particle wave functions for such systems. In the self-consistent equations, a strong correlation term is separated from the mean field. To our knowledge, this is the first attempt to formulate self-consistent equations in which the strong correlation effect is directly embodied. Some features of the equations are discussed. Koopmans' theorem and Brillouin's theorem are applied to the equations. The former is valid for singly occupied orbitals, and the latter is entirely available. By separating an angular correlation factor which is believed important for a strong correlation effect, an approximate form of a two-particle wave function is suggested. This kind of wave function causes the six multiple integrals to degrade to triple integrals. Under such forms of two-particle wave functions, corresponding Roothaan equations are established. Through these steps, it is believed that the equations become solvable within present computational limits.The physical origin of the feature of strong correlation between electrons is mainly ascribed to doubly occupied atomic orbitals. Two-particle wave functions are believed necessary to describe strongly correlated systems. We emphasize that the on-site Coulomb interaction, which is important for strong correlation, should appear in equations as a natural term. Hartree-Fock-like self-consistent equations are derived with wave functions including two-particle wave functions for such systems. In the self-consistent equations, a strong correlation term is separated from the mean field. To our knowledge, this is the first attempt to formulate self-consistent equations in which the strong correlation effect is directly embodied. Some features of the equations are discussed. Koopmans' theorem and Brillouin's theorem are applied to the equations. The former is valid for singly occupied orbitals, and the latter is entirely available. By separating an angular correlation factor which is believed important for a strong correlation effect, an approximate form of a two-particle wave function is suggested. This kind of wave function causes the six multiple integrals to degrade to triple integrals. Under such forms of two-particle wave functions, corresponding Roothaan equations are established. Through these steps, it is believed that the equations become solvable within present computational limits.

Physical review. B, Condensed matterNov 15, 20003 citations

Correlation functions in integrable quantum field theory

Benjamin Doyon

Jan 1, 20043 citations

Deduction of the two-particle potential function of liquid- He4 system from scattering data

P. C. W. Fung, C. C. Lam

In treating a many-body system, the concept of correlation has been used by various authors to calculate the interacting ground state. In particular, in the Wong-Fung theory, the interacting ground state is expressed in terms of the correlation operators and the noninteracting ground state. Including pair ( ${u}_{2}$ ) and three-particle ( ${u}_{3}$ ) correlations, the wave function can be written as explicit algebraic functions of ${u}_{2}$ and ${u}_{3}$ and the noninteracting wave function [K. W. Wong et al., Phys. Rev. A. 22, 1272 (1980)]. On the other hand, the authors of the present paper have recently developed a $U$ -matrix theory [Phys. Rev. A. 27, 1760 (1983)] to study general quantum-mechanical problems. For a time-independent problem, we can use this theory to find an analytic solution for the interacting wave function in terms of the potential functions of the system. A bridge between the correlation functions and the potential functions is built by identifying the interacting wave functions of the stated two theories to be the same quantity. Using the above idea, we are able to express the two-particle potential function ${v}_{2}$ as a simple function of the pair correlation ${u}_{2}$ and a "switching integral" $I$ , which determines how the interaction Hamiltonian is switched on, to the lowest order to approximation. Instead of using a model for ${u}_{2}$ , we obtain the explicit form of ${u}_{2}$ through the neutron scattering data of Henshaw and the concept of radial distribution function ${g}_{2}$ . It is interesting to note that this ${u}_{2}$ is not divergent at any point and is Fourier transformable. Then we proceed to deduce the resulting two-particle potential function. The deduced two-particle potential is shown to be similar in form to the Lenard-Jones potential, with the same depth, a smaller hard-core radius, and a softer core.In treating a many-body system, the concept of correlation has been used by various authors to calculate the interacting ground state. In particular, in the Wong-Fung theory, the interacting ground state is expressed in terms of the correlation operators and the noninteracting ground state. Including pair (${u}_{2}$) and three-particle (${u}_{3}$) correlations, the wave function can be written as explicit algebraic functions of ${u}_{2}$ and ${u}_{3}$ and the noninteracting wave function [K. W. Wong et al., Phys. Rev. A. 22, 1272 (1980)]. On the other hand, the authors of the present paper have recently developed a $U$-matrix theory [Phys. Rev. A. 27, 1760 (1983)] to study general quantum-mechanical problems. For a time-independent problem, we can use this theory to find an analytic solution for the interacting wave function in terms of the potential functions of the system. A bridge between the correlation functions and the potential functions is built by identifying the interacting wave functions of the stated two theories to be the same quantity. Using the above idea, we are able to express the two-particle potential function ${v}_{2}$ as a simple function of the pair correlation ${u}_{2}$ and a "switching integral" $I$, which determines how the interaction Hamiltonian is switched on, to the lowest order to approximation. Instead of using a model for ${u}_{2}$, we obtain the explicit form of ${u}_{2}$ through the neutron scattering data of Henshaw and the concept of radial distribution function ${g}_{2}$. It is interesting to note that this ${u}_{2}$ is not divergent at any point and is Fourier transformable. Then we proceed to deduce the resulting two-particle potential function. The deduced two-particle potential is shown to be similar in form to the Lenard-Jones potential, with the same depth, a smaller hard-core radius, and a softer core.

Physical Review ASep 1, 19843 citations

Spin correlations in two-particle quantum systems

V.L. Lyboshitz, M.I. Podgoretsky

Physics of Atomic NucleiJan 1, 19972 citations

{u}_{2}

) and three-particle (

{u}_{3}

) correlations, the wave function can be written as explicit algebraic functions of

{u}_{2}

and

{u}_{3}

and the noninteracting wave function [K. W. Wong et al., Phys. Rev. A. 22, 1272 (1980)]. On the other hand, the authors of the present paper have recently developed a

U

-matrix theory [Phys. Rev. A. 27, 1760 (1983)] to study general quantum-mechanical problems. For a time-independent problem, we can use this theory to find an analytic solution for the interacting wave function in terms of the potential functions of the system. A bridge between the correlation functions and the potential functions is built by identifying the interacting wave functions of the stated two theories to be the same quantity. Using the above idea, we are able to express the two-particle potential function

{v}_{2}

as a simple function of the pair correlation

{u}_{2}

and a "switching integral"

I

, which determines how the interaction Hamiltonian is switched on, to the lowest order to approximation. Instead of using a model for

{u}_{2}

, we obtain the explicit form of

{u}_{2}

through the neutron scattering data of Henshaw and the concept of radial distribution function

{g}_{2}

. It is interesting to note that this

{u}_{2}

is not divergent at any point and is Fourier transformable. Then we proceed to deduce the resulting two-particle potential function. The deduced two-particle potential is shown to be similar in form to the Lenard-Jones potential, with the same depth, a smaller hard-core radius, and a softer core.