The binding of polarons, or its absence, is an old and subtle topic. Here we prove two things rigorously. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2α, where U is the electronic Coulomb repulsion and α is the polaron coupling constant. Second, if U is large enough, there is no multipolaron binding of any kind. Considering the known fact that there is binding for some U>2α, these conclusions are not obvious and their proof has been an open problem for some time.The binding of polarons, or its absence, is an old and subtle topic. Here we prove two things rigorously. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2α, where U is the electronic Coulomb repulsion and α is the polaron coupling constant. Second, if U is large enough, there is no multipolaron binding of any kind. Considering the known fact that there is binding for some U>2α, these conclusions are not obvious and their proof has been an open problem for some time.

arXiv:1004.1196Physical Review LettersMay 27, 201028 citations

Perspectives of Polarons

WORLD SCIENTIFIC eBooksJan 1, 19960 citations

APPROACH TO THE POLARON AND RELATED SYSTEMS

Janusz Adamowski, B. Gerlach, Hajo Leschke

Jan 1, 19840 citations

BINDING, STABILITY, AND NON-BINDING OF MULTI-POLARON SYSTEMS

Rupert L. Frank, Élliott H. Lieb, Robert Seiringer +1 more

The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2α, where U is the electronic Coulomb repulsion and αis the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large α. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2α, where U is the electronic Coulomb repulsion and αis the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large α. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.

arXiv:1010.0737Mathematical Results in Quantum Mechanics (QMath)May 1, 20115 citations

Analytical approach to the Bose polaron via a q -deformed Lie algebra

Enderalp Yakaboylu

We present an approach to the Bose polaron based on the notion of quantum groups, also known as $q$ -deformed Lie algebras. In this approach, a mobile impurity can be depicted as a deformation of the Lie algebra of the bosonic creation and annihilation operators of the bath, in which the impurity is immersed. Accordingly, the Bose polaron can be described as a bath of noninteracting $q$ -deformed bosons, which allows us to provide an analytical formulation of the Bose polaron at arbitrary couplings. We derive its ground state energy in the phonon branch of the Bogoliubov dispersion and demonstrate that the previously observed transition from a repulsive to an attractive polaron occurs at the vicinity where the quantum group symmetry is broken. Furthermore, our approach has the potential to open up avenues in polaron physics by connecting it with seemingly unrelated research topics where quantum groups play an essential role, such as anyons.We present an approach to the Bose polaron based on the notion of quantum groups, also known as $q$-deformed Lie algebras. In this approach, a mobile impurity can be depicted as a deformation of the Lie algebra of the bosonic creation and annihilation operators of the bath, in which the impurity is immersed. Accordingly, the Bose polaron can be described as a bath of noninteracting $q$-deformed bosons, which allows us to provide an analytical formulation of the Bose polaron at arbitrary couplings. We derive its ground state energy in the phonon branch of the Bogoliubov dispersion and demonstrate that the previously observed transition from a repulsive to an attractive polaron occurs at the vicinity where the quantum group symmetry is broken. Furthermore, our approach has the potential to open up avenues in polaron physics by connecting it with seemingly unrelated research topics where quantum groups play an essential role, such as anyons.

arXiv:2203.14340Physical Review ASep 28, 202210 citations

Extending Polaron Concepts

David Emin

Nov 1, 20120 citations

We present an approach to the Bose polaron based on the notion of quantum groups, also known as

q

-deformed Lie algebras. In this approach, a mobile impurity can be depicted as a deformation of the Lie algebra of the bosonic creation and annihilation operators of the bath, in which the impurity is immersed. Accordingly, the Bose polaron can be described as a bath of noninteracting

q

-deformed bosons, which allows us to provide an analytical formulation of the Bose polaron at arbitrary couplings. We derive its ground state energy in the phonon branch of the Bogoliubov dispersion and demonstrate that the previously observed transition from a repulsive to an attractive polaron occurs at the vicinity where the quantum group symmetry is broken. Furthermore, our approach has the potential to open up avenues in polaron physics by connecting it with seemingly unrelated research topics where quantum groups play an essential role, such as anyons.