We construct a variational wave function for inhomogeneous weakly interacting Bose--Einstein condensates beyond the mean-field approximation by incorporating $3/2$ -body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the $3/2$ -body correlations give a contribution comparable to the mean- field energy toward lowering the ground-state energy.We construct a variational wave function for inhomogeneous weakly interacting Bose--Einstein condensates beyond the mean-field approximation by incorporating $3/2$-body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the $3/2$-body correlations give a contribution comparable to the mean- field energy toward lowering the ground-state energy.

arXiv:1810.12073Journal of the Physical Society of JapanNov 29, 20181 citation

Theory of many-body wave functions with correlations

Hermann G. Kümmel

Nuclear Physics ANov 1, 197168 citations

Wave equation for dissipative systems derived from a quantized many-body problem

Mohsen Razavy

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

Canadian Journal of PhysicsJul 1, 19807 citations

Two-body correlations in quantum many-body systems: A confrontation between different techniques

R. F. Bishop

Jan 1, 19951 citation

Cluster Expansions for Correlated Wave Functions of Finite Systems

João da Providênica, Carl M. Shakin

A theory of correlated wave functions for finite systems is developed which systematically neglects the contribution from three-body cluster terms. The approximation made leads to a derivation of a Bethe-Goldstone equation for finite systems which includes modified occupation probabilities and self-consistent potentials for occupied states. The absence of potentials in unoccupied states follows from the neglect of three-body cluster terms. It is also shown that a careful treatment of the Pauli principle and occupation probabilities allows the application of variational techniques.A theory of correlated wave functions for finite systems is developed which systematically neglects the contribution from three-body cluster terms. The approximation made leads to a derivation of a Bethe-Goldstone equation for finite systems which includes modified occupation probabilities and self-consistent potentials for occupied states. The absence of potentials in unoccupied states follows from the neglect of three-body cluster terms. It is also shown that a careful treatment of the Pauli principle and occupation probabilities allows the application of variational techniques.

Physical Review CNov 1, 197120 citations

Pair-Correlation Effects in Many-Body Systems

Kristian Blom

Springer thesesJan 1, 20233 citations

We construct a variational wave function for inhomogeneous weakly interacting Bose--Einstein condensates beyond the mean-field approximation by incorporating

3/2

-body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the

3/2

-body correlations give a contribution comparable to the mean- field energy toward lowering the ground-state energy.