# High density limit of the Fermi polaron with infinite mass

@article{Linden2018HighDL, title={High density limit of the Fermi polaron with infinite mass}, author={Ulrich Linden and David Mitrouskas}, journal={Letters in Mathematical Physics}, year={2018}, pages={1-21} }

We analyze the ground state energy for N identical fermions in a two-dimensional box of volume $$L^2$$L2 interacting with an external point scatterer. Since the point scatterer can be considered as an impurity particle of infinite mass, this system is a limit case of the Fermi polaron. We prove that its ground state energy in the limit of high density $$N/L^2\gg 1$$N/L2≫1 is given by the polaron energy. The polaron energy is an energy estimate based on trial states up to first order in particle…

## 6 Citations

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The Fermi polaron refers to a system of free fermions interacting with an impurity particle by means of two-body contact forces. Motivated by the physicists’ approach to this system, the present…

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### A pr 2 01 9 Spectral Theory of the Fermi Polaron

- Physics
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The Fermi polaron refers to a system of free fermions interacting with an impurity particle by means of two-body contact forces. Motivated by the physicists’ approach to this system, the present…

### Energy Contribution of a Point-Interacting Impurity in a Fermi Gas

- Physics, Materials ScienceAnnales Henri Poincaré
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We give a bound on the ground-state energy of a system of N non-interacting fermions in a three-dimensional cubic box interacting with an impurity particle via point interactions. We show that the…

### Spectral Theory of the Fermi Polaron

- PhysicsAnnales Henri Poincaré
- 2019

The Fermi polaron refers to a system of free fermions interacting with an impurity particle by means of two-body contact forces. Motivated by the physicists’ approach to this system, the present…

## References

SHOWING 1-10 OF 26 REFERENCES

### Spectral Theory of the Fermi Polaron

- PhysicsAnnales Henri Poincaré
- 2019

### Highly polarized Fermi gases in two dimensions

- Physics
- 2013

We investigate the highly polarized limit of a two-dimensional (2D) Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational…

### Energy Contribution of a Point-Interacting Impurity in a Fermi Gas

- PhysicsAnnales Henri Poincaré
- 2019

We give a bound on the ground-state energy of a system of N non-interacting fermions in a three-dimensional cubic box interacting with an impurity particle via point interactions. We show that the…

### Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions

- Physics
- 2012

We study the stability problem for a non-relativistic quantum system in dimension three composed by N ≥ 2 identical fermions, with unit mass, interacting with a different particle, with mass m, via a…

### Stability of the two-dimensional Fermi polaron

- Physics
- 2017

A system composed of an ideal gas of N fermions interacting with an impurity particle in two space dimensions is considered. The interaction between impurity and fermions is given in terms of…

### Ground state of a tightly bound composite dimer immersed in a Fermi sea

- Physics
- 2009

In this paper we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity…

### Polaron-molecule transitions in a two-dimensional Fermi gas

- Physics
- 2011

We address the problem of a single "spin-down" impurity atom interacting attractively with a spin-up Fermi gas in two dimensions (2D). We consider the case where the mass of the impurity is greater…

### Polaron-to-molecule transition in a strongly imbalanced Fermi gas

- Physics
- 2009

A single down spin Fermion with an attractive, zero range interaction with a Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated quasipart icle weight vanishes beyond a…

### On Point-Like Interaction between n Fermions and Another Particle

- Mathematics
- 2011

In this note the point-like interaction of n fermions with a particle of a different nature is considered in a framework of the theory of self-adjoint extensions of symmetric operators. It introduces…

### Decay of polarons and molecules in a strongly polarized Fermi gas.

- PhysicsPhysical review letters
- 2010

It is shown here that the coupling between these two states is strongly suppressed due to a combination of phase-space effects and Fermi statistics, and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition.