Continuum mechanics for quantum many-body systems

D. J. Thouless, H. S. W. Massey, R. W. Hellwarth

Jianmin Tao, Gao Xianlong, Giovanni Vignale +1 more

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally comoving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.

Lucas Happ, Pascal Naidon

Three-body resonances are ubiquitous in quantum few-body physics and are characterized by a finite lifetime before decaying into continuum states of their composing subsystems. In this work we present a theoretical study on the possibility to stabilize three-body resonances to so-called bound states in a continuum: resonances with vanishing width that do not decay. Within a two-channel approach we unveil the underlying mechanism and show how the lifetime can be made infinitely long by a continuous tuning of system parameters. The validity of our theory is illustrated in two different examples: a mass-imbalanced system in one dimension and a system of three identical bosons in three dimensions, relevant to Efimov physics. Crucially, for the latter we find that one of the parameters that can be tuned to achieve a three-body bound state in a continuum is an external magnetic field, a common tunable variable in cold-atom experiments. Due to the generality of this stabilization effect, it is expected to be applicable to a wide range of unstable few-body systems, opening new perspectives for fundamental studies as well as technical applications.

Luca Salasnich

Sandra Kühn, Marten Richter

We present a theoretical factorization scheme for interactions between many-body systems with localized discrete and delocalized quasicontinuous states. The projection operator technique combines a conventional correlation expansion with an exact diagonalization scheme. Our approach is capable of treating the continuum dynamically and to apply non-Markovian treatments beyond the Markovian approximation typically used in Lindblad formalism. Therefore it can be an important tool to describe a variety of systems as well as interaction mechanisms.