---
_id: '217'
abstract:
- lang: eng
text: We show that the number of nontrivial rational points of height at most B,
which lie on the cubic surface x1 x2 x3 = x4 (x1 + x2 + x3)2, has order of magnitude
B (log B)6. This agrees with Manin's conjecture.
acknowledgement: EPSRC GR/R93155/01
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: Browning TD. The density of rational points on a certain singular cubic surface.
Journal of Number Theory. 2005;119(2):242-283. doi:10.1016/j.jnt.2005.11.007
apa: Browning, T. D. (2005). The density of rational points on a certain singular
cubic surface. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2005.11.007
chicago: Browning, Timothy D. “The Density of Rational Points on a Certain Singular
Cubic Surface.” Journal of Number Theory. Elsevier, 2005. https://doi.org/10.1016/j.jnt.2005.11.007.
ieee: T. D. Browning, “The density of rational points on a certain singular cubic
surface,” Journal of Number Theory, vol. 119, no. 2. Elsevier, pp. 242–283,
2005.
ista: Browning TD. 2005. The density of rational points on a certain singular cubic
surface. Journal of Number Theory. 119(2), 242–283.
mla: Browning, Timothy D. “The Density of Rational Points on a Certain Singular
Cubic Surface.” Journal of Number Theory, vol. 119, no. 2, Elsevier, 2005,
pp. 242–83, doi:10.1016/j.jnt.2005.11.007.
short: T.D. Browning, Journal of Number Theory 119 (2005) 242–283.
date_created: 2018-12-11T11:45:16Z
date_published: 2005-12-27T00:00:00Z
date_updated: 2021-01-12T06:55:45Z
day: '27'
doi: 10.1016/j.jnt.2005.11.007
extern: 1
intvolume: ' 119'
issue: '2'
month: '12'
page: 242 - 283
publication: Journal of Number Theory
publication_status: published
publisher: Elsevier
publist_id: '7695'
quality_controlled: 0
status: public
title: The density of rational points on a certain singular cubic surface
type: journal_article
volume: 119
year: '2005'
...
---
_id: '2307'
abstract:
- lang: eng
text: The human norepinephrine (NE) transporter (hNET) attenuates neuronal signaling
by rapid NE clearance from the synaptic cleft, and NET is a target for cocaine
and amphetamines as well as therapeutics for depression, obsessive-compulsive
disorder, and post-traumatic stress disorder. In spite of its central importance
in the nervous system, little is known about how NET substrates, such as NE, 1-methyl-4-tetrahydropyridinium
(MPP+), or amphetamine, interact with NET at the molecular level. Nor do we understand
the mechanisms behind the transport rate. Previously we introduced a fluorescent
substrate similar to MPP+, which allowed separate and simultaneous binding and
transport measurement (Schwartz, J. W., Blakely, R. D., and DeFelice, L. J. (2003)
J. Biol. Chem. 278, 9768-9777). Here we use this substrate, 4-(4-(dimethylamino)styrl)-N-methyl-pyridinium
(ASP+), in combination with green fluorescent protein-tagged hNETs to measure
substrate-transporter stoichiometry and substrate binding kinetics. Calibrated
confocal microscopy and fluorescence correlation spectroscopy reveal that hNETs,
which are homo-multimers, bind one substrate molecule per transporter subunit.
Substrate residence at the transporter, obtained from rapid on-off kinetics revealed
in fluorescence correlation spectroscopy, is 526 μs. Substrate residence obtained
by infinite dilution is 1000 times slower. This novel examination of substrate-transporter
kinetics indicates that a single ASP + molecule binds and unbinds thousands of
times before being transported or ultimately dissociated from hNET. Calibrated
fluorescent images combined with mass spectroscopy give a transport rate of 0.06
ASP +/hNET-protein/s, thus 36,000 on-off binding events (and 36 actual departures)
occur for one transport event. Therefore binding has a low probability of resulting
in transport. We interpret these data to mean that inefficient binding could contribute
to slow transport rates.
author:
- first_name: Joel
full_name: Schwartz, Joel W
last_name: Schwartz
- first_name: Gaia
full_name: Gaia Novarino
id: 3E57A680-F248-11E8-B48F-1D18A9856A87
last_name: Novarino
orcid: 0000-0002-7673-7178
- first_name: David
full_name: Piston, David W
last_name: Piston
- first_name: Louis
full_name: DeFelice, Louis J
last_name: Defelice
citation:
ama: Schwartz J, Novarino G, Piston D, Defelice L. Substrate binding stoichiometry
and kinetics of the norepinephrine transporter. Journal of Biological Chemistry.
2005;280(19):19177-19184. doi:10.1074/jbc.M412923200
apa: Schwartz, J., Novarino, G., Piston, D., & Defelice, L. (2005). Substrate
binding stoichiometry and kinetics of the norepinephrine transporter. Journal
of Biological Chemistry. American Society for Biochemistry and Molecular Biology.
https://doi.org/10.1074/jbc.M412923200
chicago: Schwartz, Joel, Gaia Novarino, David Piston, and Louis Defelice. “Substrate
Binding Stoichiometry and Kinetics of the Norepinephrine Transporter.” Journal
of Biological Chemistry. American Society for Biochemistry and Molecular Biology,
2005. https://doi.org/10.1074/jbc.M412923200.
ieee: J. Schwartz, G. Novarino, D. Piston, and L. Defelice, “Substrate binding stoichiometry
and kinetics of the norepinephrine transporter,” Journal of Biological Chemistry,
vol. 280, no. 19. American Society for Biochemistry and Molecular Biology, pp.
19177–19184, 2005.
ista: Schwartz J, Novarino G, Piston D, Defelice L. 2005. Substrate binding stoichiometry
and kinetics of the norepinephrine transporter. Journal of Biological Chemistry.
280(19), 19177–19184.
mla: Schwartz, Joel, et al. “Substrate Binding Stoichiometry and Kinetics of the
Norepinephrine Transporter.” Journal of Biological Chemistry, vol. 280,
no. 19, American Society for Biochemistry and Molecular Biology, 2005, pp. 19177–84,
doi:10.1074/jbc.M412923200.
short: J. Schwartz, G. Novarino, D. Piston, L. Defelice, Journal of Biological Chemistry
280 (2005) 19177–19184.
date_created: 2018-12-11T11:56:54Z
date_published: 2005-05-13T00:00:00Z
date_updated: 2021-01-12T06:56:40Z
day: '13'
doi: 10.1074/jbc.M412923200
extern: 1
intvolume: ' 280'
issue: '19'
month: '05'
page: 19177 - 19184
publication: Journal of Biological Chemistry
publication_status: published
publisher: American Society for Biochemistry and Molecular Biology
publist_id: '4619'
quality_controlled: 0
status: public
title: Substrate binding stoichiometry and kinetics of the norepinephrine transporter
type: journal_article
volume: 280
year: '2005'
...
---
_id: '2335'
abstract:
- lang: eng
text: This book contains a unique survey of the mathematically rigorous results
about the quantum-mechanical many-body problem that have been obtained by the
authors in the past seven years. It addresses a topic that is not only rich mathematically,
using a large variety of techniques in mathematical analysis, but is also one
with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein
condensation. The book provides a pedagogical entry into an active area of ongoing
research for both graduate students and researchers. It is an outgrowth of a course
given by the authors for graduate students and post-doctoral researchers at the
Oberwolfach Research Institute in 2004. The book also provides a coherent summary
of the field and a reference for mathematicians and physicists active in research
on quantum mechanics.
alternative_title:
- Oberwolfach Seminars
article_processing_charge: No
author:
- first_name: Élliott
full_name: Lieb, Élliott
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jan
full_name: Solovej, Jan
last_name: Solovej
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: 'Lieb É, Seiringer R, Solovej J, Yngvason J. The Mathematics of the Bose
Gas and Its Condensation. Vol 34. Basel ; Berlin: Birkhäuser Verlag; 2005.
doi:10.1007/b137508'
apa: 'Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2005). The Mathematics
of the Bose gas and its Condensation (Vol. 34). Basel ; Berlin: Birkhäuser
Verlag. https://doi.org/10.1007/b137508'
chicago: 'Lieb, Élliott, Robert Seiringer, Jan Solovej, and Jakob Yngvason. The
Mathematics of the Bose Gas and Its Condensation. Vol. 34. Basel ; Berlin:
Birkhäuser Verlag, 2005. https://doi.org/10.1007/b137508.'
ieee: 'É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, The Mathematics of
the Bose gas and its Condensation, vol. 34. Basel ; Berlin: Birkhäuser Verlag,
2005.'
ista: 'Lieb É, Seiringer R, Solovej J, Yngvason J. 2005. The Mathematics of the
Bose gas and its Condensation, Basel ; Berlin: Birkhäuser Verlag, VIII, 203p.'
mla: Lieb, Élliott, et al. The Mathematics of the Bose Gas and Its Condensation.
Vol. 34, Birkhäuser Verlag, 2005, doi:10.1007/b137508.
short: É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, The Mathematics of the Bose
Gas and Its Condensation, Birkhäuser Verlag, Basel ; Berlin, 2005.
date_created: 2018-12-11T11:57:03Z
date_published: 2005-01-01T00:00:00Z
date_updated: 2021-12-22T08:04:00Z
day: '01'
doi: 10.1007/b137508
extern: '1'
external_id:
arxiv:
- cond-mat/0610117
intvolume: ' 34'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0610117
month: '01'
oa: 1
oa_version: Preprint
page: VIII, 203
place: Basel ; Berlin
publication_identifier:
isbn:
- 978-3-7643-7336-8
publication_status: published
publisher: Birkhäuser Verlag
publist_id: '4591'
quality_controlled: '1'
status: public
title: The Mathematics of the Bose gas and its Condensation
type: book
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 34
year: '2005'
...
---
_id: '2336'
abstract:
- lang: eng
text: |2-
Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, ρ, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4–5 decades ago, and to explore new regimes not treated before. For systems with repulsive (i.e. positive) interaction potentials the experimental low temperature state and the ground state are effectively synonymous — and this fact is used in all modeling. In such cases, the leading term in the energy/particle is 2πħ2 aρ/m where a is the scattering length of the two-body potential. Owing to the delicate and peculiar nature of bosonic correlations (such as the strange N 7/5 law for charged bosons), four decades of research failed to establish this plausible formula rigorously. The only previous lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct asymptotic formula has been obtained by us and this work will be presented. The reason behind the mathematical difficulties will be emphasized. A different formula, postulated as late as 1971 by Schick, holds in two dimensions and this, too, will be shown to be correct. With the aid of the methodology developed to prove the lower bound for the homogeneous gas, several other problems have been successfully addressed. One is the proof by us that the Gross-Pitaevskii equation correctly describes the ground state in the ‘traps’ actually used in the experiments. For this system it is also possible to prove complete Bose condensation and superfluidity as we have shown. On the frontier of experimental developments is the possibility that a dilute gas in an elongated trap will behave like a one-dimensional system; we have proved this mathematically. Another topic is a proof that Foldy’s 1961 theory of a high density Bose gas of charged particles correctly describes its ground state energy; using this we can also prove the N 7/5 formula for the ground state energy of the two-component charged Bose gas proposed by Dyson in 1967. All of this is quite recent work and it is hoped that the mathematical methodology might be useful, ultimately, to solve more complex problems connected with these interesting systems.
alternative_title:
- Mathematical Physics Studies
author:
- 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
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: 'Lieb É, Seiringer R, Solovej J, Yngvason J. The quantum-mechanical many-body
problem: The Bose gas. In: Benedicks M, Jones P, Smirnov S, Winckler B, eds. Perspectives
in Analysis. Vol 27. Springer; 2005:97-183. doi:10.1007/3-540-30434-7_9'
apa: 'Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2005). The quantum-mechanical
many-body problem: The Bose gas. In M. Benedicks, P. Jones, S. Smirnov, &
B. Winckler (Eds.), Perspectives in Analysis (Vol. 27, pp. 97–183). Springer.
https://doi.org/10.1007/3-540-30434-7_9'
chicago: 'Lieb, Élliott, Robert Seiringer, Jan Solovej, and Jakob Yngvason. “The
Quantum-Mechanical Many-Body Problem: The Bose Gas.” In Perspectives in Analysis,
edited by Michael Benedicks, Peter Jones, Stanislav Smirnov, and Björn Winckler,
27:97–183. Springer, 2005. https://doi.org/10.1007/3-540-30434-7_9.'
ieee: 'É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “The quantum-mechanical
many-body problem: The Bose gas,” in Perspectives in Analysis, vol. 27,
M. Benedicks, P. Jones, S. Smirnov, and B. Winckler, Eds. Springer, 2005, pp.
97–183.'
ista: 'Lieb É, Seiringer R, Solovej J, Yngvason J. 2005.The quantum-mechanical many-body
problem: The Bose gas. In: Perspectives in Analysis. Mathematical Physics Studies,
vol. 27, 97–183.'
mla: 'Lieb, Élliott, et al. “The Quantum-Mechanical Many-Body Problem: The Bose
Gas.” Perspectives in Analysis, edited by Michael Benedicks et al., vol.
27, Springer, 2005, pp. 97–183, doi:10.1007/3-540-30434-7_9.'
short: É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, in:, M. Benedicks, P. Jones,
S. Smirnov, B. Winckler (Eds.), Perspectives in Analysis, Springer, 2005, pp.
97–183.
date_created: 2018-12-11T11:57:04Z
date_published: 2005-01-01T00:00:00Z
date_updated: 2021-01-12T06:56:52Z
day: '01'
doi: 10.1007/3-540-30434-7_9
editor:
- first_name: Michael
full_name: Benedicks, Michael
last_name: Benedicks
- first_name: Peter
full_name: Jones, Peter W
last_name: Jones
- first_name: Stanislav
full_name: Smirnov, Stanislav
last_name: Smirnov
- first_name: Björn
full_name: Winckler, Björn
last_name: Winckler
extern: 1
intvolume: ' 27'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0405004
month: '01'
oa: 1
page: 97 - 183
publication: Perspectives in Analysis
publication_status: published
publisher: Springer
publist_id: '4590'
quality_controlled: 0
status: public
title: 'The quantum-mechanical many-body problem: The Bose gas'
type: book_chapter
volume: 27
year: '2005'
...
---
_id: '2359'
abstract:
- lang: eng
text: The validity of substituting a c-number z for the k = 0 mode operator a0 is
established rigorously in full generality, thereby verifying one aspect of Bogoliubov's
1947 theory. This substitution not only yields the correct value of thermodynamic
quantities such as the pressure or ground state energy, but also the value of
|z|2 that maximizes the partition function equals the true amount of condensation
in the presence of a gauge-symmetry-breaking term. This point had previously been
elusive.
author:
- 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
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Lieb É, Seiringer R, Yngvason J. Justification of c-number substitutions in
bosonic hamiltonians. Physical Review Letters. 2005;94(8). doi:10.1103/PhysRevLett.94.080401
apa: Lieb, É., Seiringer, R., & Yngvason, J. (2005). Justification of c-number
substitutions in bosonic hamiltonians. Physical Review Letters. American
Physical Society. https://doi.org/10.1103/PhysRevLett.94.080401
chicago: Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Justification of
C-Number Substitutions in Bosonic Hamiltonians.” Physical Review Letters.
American Physical Society, 2005. https://doi.org/10.1103/PhysRevLett.94.080401.
ieee: É. Lieb, R. Seiringer, and J. Yngvason, “Justification of c-number substitutions
in bosonic hamiltonians,” Physical Review Letters, vol. 94, no. 8. American
Physical Society, 2005.
ista: Lieb É, Seiringer R, Yngvason J. 2005. Justification of c-number substitutions
in bosonic hamiltonians. Physical Review Letters. 94(8).
mla: Lieb, Élliott, et al. “Justification of C-Number Substitutions in Bosonic Hamiltonians.”
Physical Review Letters, vol. 94, no. 8, American Physical Society, 2005,
doi:10.1103/PhysRevLett.94.080401.
short: É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 94 (2005).
date_created: 2018-12-11T11:57:12Z
date_published: 2005-03-04T00:00:00Z
date_updated: 2021-01-12T06:57:00Z
day: '04'
doi: 10.1103/PhysRevLett.94.080401
extern: 1
intvolume: ' 94'
issue: '8'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0412023
month: '03'
oa: 1
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4566'
quality_controlled: 0
status: public
title: Justification of c-number substitutions in bosonic hamiltonians
type: journal_article
volume: 94
year: '2005'
...