# Many-body excitations in trapped Bose gas: A non-Hermitian view

@inproceedings{Grillakis2021ManybodyEI, title={Many-body excitations in trapped Bose gas: A non-Hermitian view}, author={Manoussos G. Grillakis and Dionisios Margetis and Stephen Sorokanich}, year={2021} }

We provide the analysis of a physically motivated model for a trapped dilute Bose gas with repulsive pairwise atomic interactions at zero temperature. Our goal is to describe aspects of the excited many-body quantum states by accounting for the scattering of atoms in pairs from the macroscopic state (condensate). We formally construct a many-body Hamiltonian, Happ, that is quadratic in the Boson field operators for noncondensate atoms. This Happ conserves the total number of atoms. Inspired by…

## 2 Citations

### Beyond mean field: condensate coupled with pair excitations

- Mathematics
- 2022

. We prove existence results for a system of equations describing the approximate condensate wavefunction and pair-excitation kernel of a dilute (T=0) Bose gas in a trapping potential with repulsive…

### Excitation spectrum for the Lee-Huang-Yang model for the bose gas in a periodic box

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We derive a new formula for excited many-body eigenstates of the approximate Hamiltonian of Lee, Huang, and Yang [12–14], which describes the weakly interacting bose gas in a periodic box. Our…

## References

SHOWING 1-10 OF 61 REFERENCES

### Bose-Einstein Condensation beyond Mean Field: Many-Body Bound State of Periodic Microstructure

- PhysicsMultiscale Model. Simul.
- 2012

The goal is to describe quantum-mechanically the lowest macroscopic many-body bound state consistent with a microscopic Hamiltonian that accounts for inhomogeneous particle scattering processes, and to describe the partial depletion of the condensate.

### Collective Excitations of Bose Gases in the Mean-Field Regime

- Physics
- 2014

We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov’s theory predicts that the spectrum of the…

### Evolution of the Boson gas at zero temperature: Mean-field limit and second-order correction

- Physics
- 2016

A large system of N integer-spin atoms, called Bosons, manifests one of the most coherent macroscopic quantum states known to date, the “Bose-Einstein condensate”, at extremely low temperatures. As N…

### Bose-Einstein condensation in an external potential at zero temperature: General theory

- Physics
- 1998

Bose-Einstein condensation is described in terms of the condensate wave function and the pair-excitation function, the latter being responsible for the existence of phonons. This minimal description…

### Bogoliubov Spectrum of Interacting Bose Gases

- Physics
- 2012

We study the large‐N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next…

### The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases

- Physics, Mathematics
- 2014

We study the ground state of a trapped Bose gas, starting from the full many-body Schrodinger Hamiltonian, and derive the nonlinear Schrodinger energy functional in the limit of large particle…

### ON THE INFIMUM OF THE ENERGY-MOMENTUM SPECTRUM OF A HOMOGENEOUS BOSE GAS

- Physics
- 2005

We consider second-quantized homogeneous Bose gas in a large cubic box with periodic boundary conditions at zero temperature. We discuss the energy-momentum spectrum of the Bose gas and its physical…

### Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperatures.

- PhysicsPhysical review. B, Condensed matter
- 1996

It is pointed out that the Popov approximation to the full HFB gives a gapless single-particle spectrum at all temperatures and that the problem of determining the excitation spectrum of a Bose-condensed gas is difficult because of the need to satisfy several different constraints.

### Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate

- Mathematics
- 2004

Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N 2 V (N(xi − xj)), where x = (x1, . . ., xN) denotes the positions of the particles. Let HN…