# Analysis of a Simple Equation for the Ground State of the Bose Gas II: Monotonicity, Convexity, and Condensate Fraction

## Abstract

### Keywords

### MSC codes

## Get full access to this article

View all available purchase options and get full access to this article.

## References

*Complete Bose--Einstein condensation in the Gross--Pitaevskii regime*, Comm. Math. Phys., 359 (2017), pp. 975--1026.

*On the theory of superfluidity*, Izv. Akad. Nauk Ser. Fiz., 11 (1947), pp. 23--32.

*Particle distribution tail and related energy formula*, Phys. Rev. A (3), 79 (2009), 053640.

*Simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy*, Phys. Rev. A (3), 103 (2021), 053309.

*Analysis of a simple equation for the ground state energy of the Bose gas*, Pure Appl. Anal., 2 (2020), pp. 659--684.

*Ground-state energy of a hard-sphere gas*, Phys. Rev. (2), 106 (1957), pp. 20--26.

*Benjamin Schlein, and Horng-Tzer Yau*, Ground-state energy of a low-density Bose gas: A second-order upper bound, Phys. Rev. A (3), 78 (2008), no. 5, 053627.

*The energy of dilute Bose gases*, Ann. of Math. (2), 192 (2020), pp. 893--976.

*The ground state energy of the weakly interacting Bose gas at high density*, J. Stat. Phys., 135 (2009), pp. 915--934.

*Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets*, J. Stat. Phys., 53 (1988), pp. 1019--1030.

*Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties*, Phys. Rev. (2), 106 (1957), pp. 1135--1145.

*Simplified approach to the ground-state energy of an imperfect Bose gas*, Phys. Rev. (2), 130 (1963), pp. 2518--2528.

*Simplified approach to the ground-state energy of an imperfect Bose gas. III. Application to the one-dimensional model*, Phys. Rev. (2), 134 (1964), pp. A312--A315.

*Simplified approach to the ground-state energy of an imperfect Bose gas. II. Charged Bose gas at high density*, Phys. Rev. (2), 133 (1964), pp. A899--A906.

*Proof of Bose-Einstein condensation for dilute trapped gases*, Phys. Rev. Lett., 88 (2002), 170409.

*The Mathematics of the Bose Gas and its Condensation*, Oberwolfach Semin. 34, Birkhauser, Basel, Switzerland, 2005.

*Ground state energy of the low density Bose gas*, Phys. Rev. Lett., 80 (1998), pp. 2504--2507.

*Efimov physics: A review*, Rep. Progr. Phys., 80 (2017), 056001.

*Feynman integrals and the Schrödinger equation*, J. Math. Phys., 5 (1964), pp. 332--343.

*Convolution operators and $l(p,q)$ spaces*, Duke Math. J., 30 (1963), pp. 129--142.

*Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness*, 2nd ed., Academic Press, New York, 1975.

*The excitation spectrum for weakly interacting bosons*, Comm. Math. Physics, 306 (2011), pp. 565--578.

*Energetics of a strongly correlated fermi gas*, Ann. Physics, 323 (2008), pp. 2952--2970.

*Generalized virial theorem and pressure relation for a strongly correlated Fermi gas*, Ann. Physics, 323 (2008), pp. 2987--2990.

*Large momentum part of a strongly correlated Fermi gas*, Ann. Physics, 323 (2008), pp. 2971--2986.

*The second order upper bound for the ground energy of a Bose gas*, J. Stat. Phys., 136 (2009), pp. 453--503.

## Information & Authors

### Information

#### Published In

#### Copyright

#### History

**Submitted**: 30 October 2020

**Accepted**: 19 April 2021

**Published online**: 23 September 2021

#### Keywords

#### MSC codes

### Authors

#### Funding Information

## Metrics & Citations

### Metrics

### Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

#### Cited By

- The Simplified Approach to the Bose Gas Without Translation InvarianceJournal of Statistical Physics, Vol. 191, No. 7 | 17 July 2024
- A Second Order Upper Bound for the Ground State Energy of a Hard-Sphere Gas in the Gross–Pitaevskii RegimeCommunications in Mathematical Physics, Vol. 399, No. 1 | 5 December 2022
- The Condensed Fraction of a Homogeneous Dilute Bose Gas Within the Improved Hartree–Fock ApproximationJournal of Statistical Physics, Vol. 188, No. 2 | 8 June 2022
- On the Convolution Inequality f ≥ f ⋆ fInternational Mathematics Research Notices, Vol. 2021, No. 24 | 4 January 2021

## View Options

### Get Access

**Access via your Institution**- Questions about how to access this content? Contact SIAM at
**[email protected]**.