# The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics

@article{Feliciangeli2021TheSC, title={The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics}, author={Dario Feliciangeli and Robert Seiringer}, journal={Archive for Rational Mechanics and Analysis}, year={2021}, volume={242}, pages={1835 - 1906} }

We investigate the Fröhlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the translational symmetry (and its breaking in the Pekar approximation) makes the analysis substantially more challenging.

## 6 Citations

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. We study the Fr¨ohlich polaron model in R 3 , and prove a lower bound on its ground state energy as a function of the total momentum. The bound is asymptotically sharp at large coupling. In…

## References

SHOWING 1-10 OF 28 REFERENCES

### Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron

- Physics, MathematicsCommunications on Pure and Applied Mathematics
- 2020

We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we…

### Exact Ground State Energy of the Strong-Coupling Polaron

- Mathematics
- 1995

Abstract: The polaron has been of interest in condensed matter theory and field theory for about half a century, especially the limit of large coupling constant, α. It was not until 1983, however,…

### The polaron at strong coupling

- Physics
- 2019

We review old and new results on the Fr\"ohlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this…

### Persistence of the spectral gap for the Landau–Pekar equations

- Mathematics, Physics
- 2020

The Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for…

### Symmetry of Bipolaron Bound States for Small Coulomb Repulsion

- Physics
- 2013

We consider the bipolaron in the Pekar–Tomasevich approximation and address the question whether the ground state is spherically symmetric or not. Numerical analysis has, so far, not completely…

### THE POLARON REVISITED

- Mathematics
- 2006

In recent years, the spectral properties of the translation invariant Nelson model has been studied. Some of the results obtained did not extend to the related polaron model for technical reasons…

### Ground state properties of multi-polaron systems

- Physics
- 2012

We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of…

### Self-adjointness and domain of the Fröhlich Hamiltonian

- Mathematics
- 2015

In the large polaron model of Herbert Frohlich, the electron-phonon interaction is a small perturbation in form sense, but a large perturbation in operator sense. This means that the form-domain of…