---
_id: '238'
abstract:
- lang: eng
text: For given positive integers a, b, q we investigate the density of solutions
(x, y) ∈ Z2 to congruences ax + by2 ≡ 0 mod q.
acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council"
author:
- first_name: Stephan
full_name: Baier, Stephan
last_name: Baier
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: Baier S, Browning TD. Inhomogeneous quadratic congruences. Functiones et
Approximatio, Commentarii Mathematici. 2012;47(2):267-286. doi:10.7169/facm/2012.47.2.9
apa: Baier, S., & Browning, T. D. (2012). Inhomogeneous quadratic congruences.
Functiones et Approximatio, Commentarii Mathematici. Adam Mickiewicz University
Press. https://doi.org/10.7169/facm/2012.47.2.9
chicago: Baier, Stephan, and Timothy D Browning. “Inhomogeneous Quadratic Congruences.”
Functiones et Approximatio, Commentarii Mathematici. Adam Mickiewicz University
Press, 2012. https://doi.org/10.7169/facm/2012.47.2.9.
ieee: S. Baier and T. D. Browning, “Inhomogeneous quadratic congruences,” Functiones
et Approximatio, Commentarii Mathematici, vol. 47, no. 2. Adam Mickiewicz
University Press, pp. 267–286, 2012.
ista: Baier S, Browning TD. 2012. Inhomogeneous quadratic congruences. Functiones
et Approximatio, Commentarii Mathematici. 47(2), 267–286.
mla: Baier, Stephan, and Timothy D. Browning. “Inhomogeneous Quadratic Congruences.”
Functiones et Approximatio, Commentarii Mathematici, vol. 47, no. 2, Adam
Mickiewicz University Press, 2012, pp. 267–86, doi:10.7169/facm/2012.47.2.9.
short: S. Baier, T.D. Browning, Functiones et Approximatio, Commentarii Mathematici
47 (2012) 267–286.
date_created: 2018-12-11T11:45:22Z
date_published: 2012-12-20T00:00:00Z
date_updated: 2021-01-12T06:57:08Z
day: '20'
doi: 10.7169/facm/2012.47.2.9
extern: 1
intvolume: ' 47'
issue: '2'
month: '12'
page: 267 - 286
publication: Functiones et Approximatio, Commentarii Mathematici
publication_status: published
publisher: Adam Mickiewicz University Press
publist_id: '7666'
quality_controlled: 0
status: public
title: Inhomogeneous quadratic congruences
type: journal_article
volume: 47
year: '2012'
...
---
_id: '2399'
abstract:
- lang: eng
text: |
Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures.
alternative_title:
- Lecture Notes in Mathematics
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Seiringer R. Cold quantum gases and bose einstein condensation. In: Rivasseau
V, Seiringer R, Solovej J, Spencer T, eds. Quantum Many Body Systems. Vol
2051. Springer; 2012:55-92. doi:10.1007/978-3-642-29511-9_2'
apa: Seiringer, R. (2012). Cold quantum gases and bose einstein condensation. In
V. Rivasseau, R. Seiringer, J. Solovej, & T. Spencer (Eds.), Quantum Many
Body Systems (Vol. 2051, pp. 55–92). Springer. https://doi.org/10.1007/978-3-642-29511-9_2
chicago: Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.”
In Quantum Many Body Systems, edited by Vincent Rivasseau, Robert Seiringer,
Jan Solovej, and Thomas Spencer, 2051:55–92. Springer, 2012. https://doi.org/10.1007/978-3-642-29511-9_2.
ieee: R. Seiringer, “Cold quantum gases and bose einstein condensation,” in Quantum
Many Body Systems, vol. 2051, V. Rivasseau, R. Seiringer, J. Solovej, and
T. Spencer, Eds. Springer, 2012, pp. 55–92.
ista: 'Seiringer R. 2012.Cold quantum gases and bose einstein condensation. In:
Quantum Many Body Systems. Lecture Notes in Mathematics, vol. 2051, 55–92.'
mla: Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” Quantum
Many Body Systems, edited by Vincent Rivasseau et al., vol. 2051, Springer,
2012, pp. 55–92, doi:10.1007/978-3-642-29511-9_2.
short: R. Seiringer, in:, V. Rivasseau, R. Seiringer, J. Solovej, T. Spencer (Eds.),
Quantum Many Body Systems, Springer, 2012, pp. 55–92.
date_created: 2018-12-11T11:57:26Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:14Z
day: '01'
doi: 10.1007/978-3-642-29511-9_2
editor:
- first_name: Vincent
full_name: Rivasseau, Vincent
last_name: Rivasseau
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
- first_name: Thomas
full_name: Spencer, Thomas
last_name: Spencer
extern: 1
intvolume: ' 2051'
month: '01'
page: 55 - 92
publication: Quantum Many Body Systems
publication_status: published
publisher: Springer
publist_id: '4526'
quality_controlled: 0
status: public
title: Cold quantum gases and bose einstein condensation
type: book_chapter
volume: 2051
year: '2012'
...
---
_id: '2394'
abstract:
- lang: eng
text: We study the BCS gap equation for a Fermi gas with unequal population of spin-up
and spin-down states. For cosh (δ μ/T) ≤ 2, with T the temperature and δμ the
chemical potential difference, the question of existence of non-trivial solutions
can be reduced to spectral properties of a linear operator, similar to the unpolarized
case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer,
R., J., Geom. Anal.17, 559-567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E.,
Seiringer, R., and Solovej, J. P., Commun., Math. Phys.281, 349-367 (2008)10.1007/s00220-008-0489-2;
and Hainzl, C. and Seiringer, R., Phys. Rev. B77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517.
For cosh (δ μ/T) > 2 the phase diagram is more complicated, however. We derive
upper and lower bounds for the critical temperature, and study their behavior
in the small coupling limit.
author:
- first_name: Abraham
full_name: Freiji, Abraham
last_name: Freiji
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Freiji A, Hainzl C, Seiringer R. The gap equation for spin-polarized fermions.
Journal of Mathematical Physics. 2012;53(1). doi:10.1063/1.3670747
apa: Freiji, A., Hainzl, C., & Seiringer, R. (2012). The gap equation for spin-polarized
fermions. Journal of Mathematical Physics. American Institute of Physics.
https://doi.org/10.1063/1.3670747
chicago: Freiji, Abraham, Christian Hainzl, and Robert Seiringer. “The Gap Equation
for Spin-Polarized Fermions.” Journal of Mathematical Physics. American
Institute of Physics, 2012. https://doi.org/10.1063/1.3670747.
ieee: A. Freiji, C. Hainzl, and R. Seiringer, “The gap equation for spin-polarized
fermions,” Journal of Mathematical Physics, vol. 53, no. 1. American Institute
of Physics, 2012.
ista: Freiji A, Hainzl C, Seiringer R. 2012. The gap equation for spin-polarized
fermions. Journal of Mathematical Physics. 53(1).
mla: Freiji, Abraham, et al. “The Gap Equation for Spin-Polarized Fermions.” Journal
of Mathematical Physics, vol. 53, no. 1, American Institute of Physics, 2012,
doi:10.1063/1.3670747.
short: A. Freiji, C. Hainzl, R. Seiringer, Journal of Mathematical Physics 53 (2012).
date_created: 2018-12-11T11:57:25Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:13Z
day: '01'
doi: 10.1063/1.3670747
extern: 1
intvolume: ' 53'
issue: '1'
month: '01'
publication: Journal of Mathematical Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '4532'
quality_controlled: 0
status: public
title: The gap equation for spin-polarized fermions
type: journal_article
volume: 53
year: '2012'
...
---
_id: '2395'
abstract:
- lang: eng
text: 'We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL)
theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close
to the critical temperature, GL arises as an effective theory on the macroscopic
scale. The relevant scaling limit is semiclassical in nature, and semiclassical
analysis, with minimal regularity assumptions, plays an important part in our
proof. '
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
citation:
ama: Frank R, Hainzl C, Seiringer R, Solovej J. Microscopic derivation of Ginzburg-Landau
theory. Journal of the American Mathematical Society. 2012;25(3):667-713.
doi:10.1090/S0894-0347-2012-00735-8
apa: Frank, R., Hainzl, C., Seiringer, R., & Solovej, J. (2012). Microscopic
derivation of Ginzburg-Landau theory. Journal of the American Mathematical
Society. American Mathematical Society. https://doi.org/10.1090/S0894-0347-2012-00735-8
chicago: Frank, Rupert, Christian Hainzl, Robert Seiringer, and Jan Solovej. “Microscopic
Derivation of Ginzburg-Landau Theory.” Journal of the American Mathematical
Society. American Mathematical Society, 2012. https://doi.org/10.1090/S0894-0347-2012-00735-8.
ieee: R. Frank, C. Hainzl, R. Seiringer, and J. Solovej, “Microscopic derivation
of Ginzburg-Landau theory,” Journal of the American Mathematical Society,
vol. 25, no. 3. American Mathematical Society, pp. 667–713, 2012.
ista: Frank R, Hainzl C, Seiringer R, Solovej J. 2012. Microscopic derivation of
Ginzburg-Landau theory. Journal of the American Mathematical Society. 25(3), 667–713.
mla: Frank, Rupert, et al. “Microscopic Derivation of Ginzburg-Landau Theory.” Journal
of the American Mathematical Society, vol. 25, no. 3, American Mathematical
Society, 2012, pp. 667–713, doi:10.1090/S0894-0347-2012-00735-8.
short: R. Frank, C. Hainzl, R. Seiringer, J. Solovej, Journal of the American Mathematical
Society 25 (2012) 667–713.
date_created: 2018-12-11T11:57:25Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:13Z
day: '01'
doi: 10.1090/S0894-0347-2012-00735-8
extern: 1
intvolume: ' 25'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1102.4001
month: '01'
oa: 1
page: 667 - 713
publication: Journal of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '4531'
quality_controlled: 0
status: public
title: Microscopic derivation of Ginzburg-Landau theory
type: journal_article
volume: 25
year: '2012'
...
---
_id: '2396'
abstract:
- lang: eng
text: A positive temperature analogue of the scattering length of a potential V
can be defined via integrating the difference of the heat kernels of -Δ and, with
Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation
of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi
in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502,
2009), a bound was given in the case of finite range potentials and sufficiently
low temperature. In this paper, we improve the bound and extend it to potentials
of infinite range.
author:
- first_name: Benjamin
full_name: Landon, Benjamin
last_name: Landon
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Landon B, Seiringer R. The scattering length at positive temperature. Letters
in Mathematical Physics. 2012;100(3):237-243. doi:10.1007/s11005-012-0566-5
apa: Landon, B., & Seiringer, R. (2012). The scattering length at positive temperature.
Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-012-0566-5
chicago: Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive
Temperature.” Letters in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s11005-012-0566-5.
ieee: B. Landon and R. Seiringer, “The scattering length at positive temperature,”
Letters in Mathematical Physics, vol. 100, no. 3. Springer, pp. 237–243,
2012.
ista: Landon B, Seiringer R. 2012. The scattering length at positive temperature.
Letters in Mathematical Physics. 100(3), 237–243.
mla: Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive
Temperature.” Letters in Mathematical Physics, vol. 100, no. 3, Springer,
2012, pp. 237–43, doi:10.1007/s11005-012-0566-5.
short: B. Landon, R. Seiringer, Letters in Mathematical Physics 100 (2012) 237–243.
date_created: 2018-12-11T11:57:25Z
date_published: 2012-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:13Z
day: '01'
doi: 10.1007/s11005-012-0566-5
extern: 1
intvolume: ' 100'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1111.1683
month: '06'
oa: 1
page: 237 - 243
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4529'
quality_controlled: 0
status: public
title: The scattering length at positive temperature
type: journal_article
volume: 100
year: '2012'
...
---
_id: '2398'
abstract:
- lang: eng
text: We extend the mathematical theory of quantum hypothesis testing to the general
W*-algebraic setting and explore its relation with recent developments in non-equilibrium
quantum statistical mechanics. In particular, we relate the large deviation principle
for the full counting statistics of entropy flow to quantum hypothesis testing
of the arrow of time.
author:
- first_name: Vojkan
full_name: Jakšić, Vojkan
last_name: Jakšić
- first_name: Yoshiko
full_name: Ogata, Yoshiko
last_name: Ogata
- first_name: Claude
full_name: Pillet, Claude A
last_name: Pillet
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Jakšić V, Ogata Y, Pillet C, Seiringer R. Quantum hypothesis testing and non-equilibrium
statistical mechanics. Reviews in Mathematical Physics. 2012;24(6). doi:10.1142/S0129055X12300026
apa: Jakšić, V., Ogata, Y., Pillet, C., & Seiringer, R. (2012). Quantum hypothesis
testing and non-equilibrium statistical mechanics. Reviews in Mathematical
Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X12300026
chicago: Jakšić, Vojkan, Yoshiko Ogata, Claude Pillet, and Robert Seiringer. “Quantum
Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” Reviews in Mathematical
Physics. World Scientific Publishing, 2012. https://doi.org/10.1142/S0129055X12300026.
ieee: V. Jakšić, Y. Ogata, C. Pillet, and R. Seiringer, “Quantum hypothesis testing
and non-equilibrium statistical mechanics,” Reviews in Mathematical Physics,
vol. 24, no. 6. World Scientific Publishing, 2012.
ista: Jakšić V, Ogata Y, Pillet C, Seiringer R. 2012. Quantum hypothesis testing
and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. 24(6).
mla: Jakšić, Vojkan, et al. “Quantum Hypothesis Testing and Non-Equilibrium Statistical
Mechanics.” Reviews in Mathematical Physics, vol. 24, no. 6, World Scientific
Publishing, 2012, doi:10.1142/S0129055X12300026.
short: V. Jakšić, Y. Ogata, C. Pillet, R. Seiringer, Reviews in Mathematical Physics
24 (2012).
date_created: 2018-12-11T11:57:26Z
date_published: 2012-07-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1142/S0129055X12300026
extern: 1
intvolume: ' 24'
issue: '6'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1109.3804
month: '07'
oa: 1
publication: Reviews in Mathematical Physics
publication_status: published
publisher: World Scientific Publishing
publist_id: '4528'
quality_controlled: 0
status: public
title: Quantum hypothesis testing and non-equilibrium statistical mechanics
type: review
volume: 24
year: '2012'
...
---
_id: '2397'
abstract:
- lang: eng
text: We consider the low-density limit of a Fermi gas in the BCS approximation.
We show that if the interaction potential allows for a two-particle bound state,
the system at zero temperature is well approximated by the Gross-Pitaevskii functional,
describing a Bose-Einstein condensate of fermion pairs.
author:
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Hainzl C, Seiringer R. Low density limit of BCS theory and Bose-Einstein condensation
of Fermion pairs. Letters in Mathematical Physics. 2012;100(2):119-138.
doi:10.1007/s11005-011-0535-4
apa: Hainzl, C., & Seiringer, R. (2012). Low density limit of BCS theory and
Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics.
Springer. https://doi.org/10.1007/s11005-011-0535-4
chicago: Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory
and Bose-Einstein Condensation of Fermion Pairs.” Letters in Mathematical Physics.
Springer, 2012. https://doi.org/10.1007/s11005-011-0535-4.
ieee: C. Hainzl and R. Seiringer, “Low density limit of BCS theory and Bose-Einstein
condensation of Fermion pairs,” Letters in Mathematical Physics, vol. 100,
no. 2. Springer, pp. 119–138, 2012.
ista: Hainzl C, Seiringer R. 2012. Low density limit of BCS theory and Bose-Einstein
condensation of Fermion pairs. Letters in Mathematical Physics. 100(2), 119–138.
mla: Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and
Bose-Einstein Condensation of Fermion Pairs.” Letters in Mathematical Physics,
vol. 100, no. 2, Springer, 2012, pp. 119–38, doi:10.1007/s11005-011-0535-4.
short: C. Hainzl, R. Seiringer, Letters in Mathematical Physics 100 (2012) 119–138.
date_created: 2018-12-11T11:57:25Z
date_published: 2012-05-01T00:00:00Z
date_updated: 2021-01-12T06:57:14Z
day: '01'
doi: 10.1007/s11005-011-0535-4
extern: 1
intvolume: ' 100'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1105.1100
month: '05'
oa: 1
page: 119 - 138
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4530'
quality_controlled: 0
status: public
title: Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs
type: journal_article
volume: 100
year: '2012'
...
---
_id: '240'
abstract:
- lang: eng
text: We investigate the frequency of positive squareful numbers x, y, z≤B for which
x+y=z and present a conjecture concerning its asymptotic behavior.
acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council"
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: K Van
full_name: Valckenborgh, K Van
last_name: Valckenborgh
citation:
ama: Browning TD, Valckenborgh KV. Sums of three squareful numbers. Experimental
Mathematics. 2012;21(2):204-211. doi:10.1080/10586458.2011.605733
apa: Browning, T. D., & Valckenborgh, K. V. (2012). Sums of three squareful
numbers. Experimental Mathematics. Taylor & Francis. https://doi.org/10.1080/10586458.2011.605733
chicago: Browning, Timothy D, and K Van Valckenborgh. “Sums of Three Squareful Numbers.”
Experimental Mathematics. Taylor & Francis, 2012. https://doi.org/10.1080/10586458.2011.605733.
ieee: T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,”
Experimental Mathematics, vol. 21, no. 2. Taylor & Francis, pp. 204–211,
2012.
ista: Browning TD, Valckenborgh KV. 2012. Sums of three squareful numbers. Experimental
Mathematics. 21(2), 204–211.
mla: Browning, Timothy D., and K. Van Valckenborgh. “Sums of Three Squareful Numbers.”
Experimental Mathematics, vol. 21, no. 2, Taylor & Francis, 2012, pp.
204–11, doi:10.1080/10586458.2011.605733.
short: T.D. Browning, K.V. Valckenborgh, Experimental Mathematics 21 (2012) 204–211.
date_created: 2018-12-11T11:45:23Z
date_published: 2012-05-23T00:00:00Z
date_updated: 2021-01-12T06:57:15Z
day: '23'
doi: 10.1080/10586458.2011.605733
extern: 1
intvolume: ' 21'
issue: '2'
month: '05'
page: 204 - 211
publication: Experimental Mathematics
publication_status: published
publisher: Taylor & Francis
publist_id: '7664'
quality_controlled: 0
status: public
title: Sums of three squareful numbers
type: journal_article
volume: 21
year: '2012'
...
---
_id: '2400'
abstract:
- lang: eng
text: If the polaron coupling constant α is large enough, bipolarons or multi-polarons
will form. When passing through the critical α c from above, does the radius of
the system simply get arbitrarily large or does it reach a maximum and then explode?
We prove that it is always the latter. We also prove the analogous statement for
the Pekar-Tomasevich (PT) approximation to the energy, in which case there is
a solution to the PT equation at α c. Similarly, we show that the same phenomenon
occurs for atoms, e. g., helium, at the critical value of the nuclear charge.
Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger
equation, and are very general. They use the fact that the Coulomb repulsion decays
like 1/r, while 'uncertainty principle' localization energies decay more rapidly,
as 1/r 2.
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. Communications
in Mathematical Physics. 2012;313(2):405-424. doi:10.1007/s00220-012-1436-9
apa: Frank, R., Lieb, É., & Seiringer, R. (2012). Binding of polarons and atoms
at threshold. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1436-9
chicago: Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons
and Atoms at Threshold.” Communications in Mathematical Physics. Springer,
2012. https://doi.org/10.1007/s00220-012-1436-9.
ieee: R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,”
Communications in Mathematical Physics, vol. 313, no. 2. Springer, pp.
405–424, 2012.
ista: Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold.
Communications in Mathematical Physics. 313(2), 405–424.
mla: Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” Communications
in Mathematical Physics, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:10.1007/s00220-012-1436-9.
short: R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313
(2012) 405–424.
date_created: 2018-12-11T11:57:27Z
date_published: 2012-07-01T00:00:00Z
date_updated: 2021-01-12T06:57:15Z
day: '01'
doi: 10.1007/s00220-012-1436-9
extern: 1
intvolume: ' 313'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1106.0729
month: '07'
oa: 1
page: 405 - 424
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4527'
quality_controlled: 0
status: public
title: Binding of polarons and atoms at threshold
type: journal_article
volume: 313
year: '2012'
...
---
_id: '2403'
abstract:
- lang: eng
text: We study the effects of random scatterers on the ground state of the one-dimensional
Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii
regime. We prove that Bose-Einstein condensation survives even a strong random
potential with a high density of scatterers. The character of the wavefunction
of the condensate, however, depends in an essential way on the interplay between
randomness and the strength of the two-body interaction. For low density of scatterers
and strong interactions the wavefunction extends over the whole interval. A high
density of scatterers and weak interactions, on the other hand, lead to localization
of the wavefunction in a fragmented subset of the interval.
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
- first_name: Valentin
full_name: Zagrebnov, Valentin A
last_name: Zagrebnov
citation:
ama: Seiringer R, Yngvason J, Zagrebnov V. Disordered Bose-Einstein condensates
with interaction in one dimension. Journal of Statistical Mechanics Theory
and Experiment. 2012;2012(11). doi:10.1088/1742-5468/2012/11/P11007
apa: Seiringer, R., Yngvason, J., & Zagrebnov, V. (2012). Disordered Bose-Einstein
condensates with interaction in one dimension. Journal of Statistical Mechanics
Theory and Experiment. IOP Publishing Ltd. https://doi.org/10.1088/1742-5468/2012/11/P11007
chicago: Seiringer, Robert, Jakob Yngvason, and Valentin Zagrebnov. “Disordered
Bose-Einstein Condensates with Interaction in One Dimension.” Journal of Statistical
Mechanics Theory and Experiment. IOP Publishing Ltd., 2012. https://doi.org/10.1088/1742-5468/2012/11/P11007.
ieee: R. Seiringer, J. Yngvason, and V. Zagrebnov, “Disordered Bose-Einstein condensates
with interaction in one dimension,” Journal of Statistical Mechanics Theory
and Experiment, vol. 2012, no. 11. IOP Publishing Ltd., 2012.
ista: Seiringer R, Yngvason J, Zagrebnov V. 2012. Disordered Bose-Einstein condensates
with interaction in one dimension. Journal of Statistical Mechanics Theory and
Experiment. 2012(11).
mla: Seiringer, Robert, et al. “Disordered Bose-Einstein Condensates with Interaction
in One Dimension.” Journal of Statistical Mechanics Theory and Experiment,
vol. 2012, no. 11, IOP Publishing Ltd., 2012, doi:10.1088/1742-5468/2012/11/P11007.
short: R. Seiringer, J. Yngvason, V. Zagrebnov, Journal of Statistical Mechanics
Theory and Experiment 2012 (2012).
date_created: 2018-12-11T11:57:28Z
date_published: 2012-11-01T00:00:00Z
date_updated: 2021-01-12T06:57:16Z
day: '01'
doi: 10.1088/1742-5468/2012/11/P11007
extern: 1
intvolume: ' 2012'
issue: '11'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1207.7054
month: '11'
oa: 1
publication: Journal of Statistical Mechanics Theory and Experiment
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '4523'
quality_controlled: 0
status: public
title: Disordered Bose-Einstein condensates with interaction in one dimension
type: journal_article
volume: 2012
year: '2012'
...