We investigate the effects of Efimov states on the postquench dynamics of a system of three identical bosons with contact interactions in a spherically symmetric three-dimensional harmonic trap. The quench we consider is in the $s$ -wave contact interaction, and we focus on quenches from the noninteracting to strongly interacting regimes and vice versa. The calculations use the hyperspherical solutions of the three-body problem and enable us to evaluate the semianalytical results of the Ramsey and particle separation, postquench. In the case where the interactions are quenched from the noninteracting to strongly interacting regime we find convergent aperiodic solutions for both the Ramsey signal and the particle separation. In contrast, for quenches from the strongly interacting regime to the noninteracting regime both the Ramsey signal and particle separation are periodic functions. However, in this case we find that the solutions for the particle separation diverge, indicating that in such a system large oscillations may be observable.We investigate the effects of Efimov states on the postquench dynamics of a system of three identical bosons with contact interactions in a spherically symmetric three-dimensional harmonic trap. The quench we consider is in the $s$-wave contact interaction, and we focus on quenches from the noninteracting to strongly interacting regimes and vice versa. The calculations use the hyperspherical solutions of the three-body problem and enable us to evaluate the semianalytical results of the Ramsey and particle separation, postquench. In the case where the interactions are quenched from the noninteracting to strongly interacting regime we find convergent aperiodic solutions for both the Ramsey signal and the particle separation. In contrast, for quenches from the strongly interacting regime to the noninteracting regime both the Ramsey signal and particle separation are periodic functions. However, in this case we find that the solutions for the particle separation diverge, indicating that in such a system large oscillations may be observable.

arXiv:2208.05666Physical Review ADec 21, 20222 citations

Model of an unstable system with a Coulomb interaction distorted at short distances

Boris O Kerbikov

We present an exactly soluble model of an unstable system with nuclear and Coulomb interactions. The system considered consists of two pairs of particles capable of transforming into each other. The interaction in the heavy-particle channel consists of the Coulomb potential and a short-range separable potential. The off-diagonal interaction which is responsible for the transition between the two pairs of particles is also taken in a separable form. The particles in the decay channel are free. Analytic expressions are obtained for the T matrix of the pure nuclear and nuclear-Coulomb scattering lengths. The equation which describes the shift of the atomic S levels in the heavy-particle channel is analyzed.We present an exactly soluble model of an unstable system with nuclear and Coulomb interactions. The system considered consists of two pairs of particles capable of transforming into each other. The interaction in the heavy-particle channel consists of the Coulomb potential and a short-range separable potential. The off-diagonal interaction which is responsible for the transition between the two pairs of particles is also taken in a separable form. The particles in the decay channel are free. Analytic expressions are obtained for the T matrix of the pure nuclear and nuclear-Coulomb scattering lengths. The equation which describes the shift of the atomic S levels in the heavy-particle channel is analyzed.

Nov 1, 19830 citations

Theory of Many-Particle Systems. I

Paul C. Martin, Julian Schwinger

World Scientific series in 20th century physicsMay 1, 2000967 citations

Many-Particle Systems: II

H R Post

Proceedings of the Physical Society Section ADec 1, 195647 citations

On a non-separable quantum many-particle system on the half-line

Joachim Kerner, Tobias Mühlenbruch

In this paper we will report on a one-dimensional, non-separable quantum many-particle system.It consists of two (distinguishable) particles moving on the half-line R + being subjected to two different kinds of two-particle interactions: singular many-particle interactions localized at the origin and a binding-potential leading to a molecular-like state.We will formulate the model precisely, obtaining a well-defined self-adjoint operator (the Hamiltonian for our system) and elaborate on its spectral properties.In addition, we will present possible directions for future research.In this paper we will report on a one-dimensional, non-separable quantum many-particle system.It consists of two (distinguishable) particles moving on the half-line R + being subjected to two different kinds of two-particle interactions: singular many-particle interactions localized at the origin and a binding-potential leading to a molecular-like state.We will formulate the model precisely, obtaining a well-defined self-adjoint operator (the Hamiltonian for our system) and elaborate on its spectral properties.In addition, we will present possible directions for future research.

arXiv:1702.05799Nanosystems Physics Chemistry MathematicsFeb 20, 20170 citations

s

-wave contact interaction, and we focus on quenches from the noninteracting to strongly interacting regimes and vice versa. The calculations use the hyperspherical solutions of the three-body problem and enable us to evaluate the semianalytical results of the Ramsey and particle separation, postquench. In the case where the interactions are quenched from the noninteracting to strongly interacting regime we find convergent aperiodic solutions for both the Ramsey signal and the particle separation. In contrast, for quenches from the strongly interacting regime to the noninteracting regime both the Ramsey signal and particle separation are periodic functions. However, in this case we find that the solutions for the particle separation diverge, indicating that in such a system large oscillations may be observable.