---
_id: '9001'
abstract:
- lang: eng
text: Quantum illumination is a sensing technique that employs entangled signal-idler
beams to improve the detection efficiency of low-reflectivity objects in environments
with large thermal noise. The advantage over classical strategies is evident at
low signal brightness, a feature which could make the protocol an ideal prototype
for non-invasive scanning or low-power short-range radar. Here we experimentally
investigate the concept of quantum illumination at microwave frequencies, by generating
entangled fields using a Josephson parametric converter which are then amplified
to illuminate a room-temperature object at a distance of 1 meter. Starting from
experimental data, we simulate the case of perfect idler photon number detection,
which results in a quantum advantage compared to the relative classical benchmark.
Our results highlight the opportunities and challenges on the way towards a first
room-temperature application of microwave quantum circuits.
acknowledgement: "This work was supported by the Institute of Science and Technology
Austria (IST Austria), the European Research Council under grant agreement number
758053 (ERC StG QUNNECT) and the EU’s Horizon 2020 research and innovation programme
under grant agreement number 862644 (FET Open QUARTET). S.B. acknowledges support
from the Marie Skłodowska Curie\r\nfellowship number 707438 (MSC-IF SUPEREOM), DV
acknowledge support from EU’s Horizon 2020 research and innovation programme under
grant agreement number 732894 (FET Proactive HOT) and the Project QuaSeRT funded
by the QuantERA ERANET Cofund in Quantum Technologies, and J.M.F from the Austrian
Science Fund (FWF) through BeyondC (F71), a NOMIS foundation research grant, and
the EU’s Horizon 2020 research and\r\ninnovation programme under grant agreement
number 732894 (FET Proactive\r\nHOT)."
article_number: '9266397'
article_processing_charge: No
author:
- first_name: Shabir
full_name: Barzanjeh, Shabir
id: 2D25E1F6-F248-11E8-B48F-1D18A9856A87
last_name: Barzanjeh
orcid: 0000-0003-0415-1423
- first_name: Stefano
full_name: Pirandola, Stefano
last_name: Pirandola
- first_name: David
full_name: Vitali, David
last_name: Vitali
- first_name: Johannes M
full_name: Fink, Johannes M
id: 4B591CBA-F248-11E8-B48F-1D18A9856A87
last_name: Fink
orcid: 0000-0001-8112-028X
citation:
ama: 'Barzanjeh S, Pirandola S, Vitali D, Fink JM. Microwave quantum illumination
with a digital phase-conjugated receiver. In: IEEE National Radar Conference
- Proceedings. Vol 2020. IEEE; 2020. doi:10.1109/RadarConf2043947.2020.9266397'
apa: 'Barzanjeh, S., Pirandola, S., Vitali, D., & Fink, J. M. (2020). Microwave
quantum illumination with a digital phase-conjugated receiver. In IEEE National
Radar Conference - Proceedings (Vol. 2020). Florence, Italy: IEEE. https://doi.org/10.1109/RadarConf2043947.2020.9266397'
chicago: Barzanjeh, Shabir, Stefano Pirandola, David Vitali, and Johannes M Fink.
“Microwave Quantum Illumination with a Digital Phase-Conjugated Receiver.” In
IEEE National Radar Conference - Proceedings, Vol. 2020. IEEE, 2020. https://doi.org/10.1109/RadarConf2043947.2020.9266397.
ieee: S. Barzanjeh, S. Pirandola, D. Vitali, and J. M. Fink, “Microwave quantum
illumination with a digital phase-conjugated receiver,” in IEEE National Radar
Conference - Proceedings, Florence, Italy, 2020, vol. 2020, no. 9.
ista: 'Barzanjeh S, Pirandola S, Vitali D, Fink JM. 2020. Microwave quantum illumination
with a digital phase-conjugated receiver. IEEE National Radar Conference - Proceedings.
RadarConf: National Conference on Radar vol. 2020, 9266397.'
mla: Barzanjeh, Shabir, et al. “Microwave Quantum Illumination with a Digital Phase-Conjugated
Receiver.” IEEE National Radar Conference - Proceedings, vol. 2020, no.
9, 9266397, IEEE, 2020, doi:10.1109/RadarConf2043947.2020.9266397.
short: S. Barzanjeh, S. Pirandola, D. Vitali, J.M. Fink, in:, IEEE National Radar
Conference - Proceedings, IEEE, 2020.
conference:
end_date: 2020-09-25
location: Florence, Italy
name: 'RadarConf: National Conference on Radar'
start_date: 2020-09-21
date_created: 2021-01-10T23:01:17Z
date_published: 2020-09-21T00:00:00Z
date_updated: 2023-08-24T11:10:49Z
day: '21'
department:
- _id: JoFi
doi: 10.1109/RadarConf2043947.2020.9266397
ec_funded: 1
external_id:
arxiv:
- '1908.03058'
isi:
- '000612224900089'
intvolume: ' 2020'
isi: 1
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1908.03058
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 26336814-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '758053'
name: A Fiber Optic Transceiver for Superconducting Qubits
- _id: 237CBA6C-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '862644'
name: Quantum readout techniques and technologies
- _id: 258047B6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '707438'
name: 'Microwave-to-Optical Quantum Link: Quantum Teleportation and Quantum Illumination
with cavity Optomechanics SUPEREOM'
- _id: 257EB838-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '732894'
name: Hybrid Optomechanical Technologies
publication: IEEE National Radar Conference - Proceedings
publication_identifier:
isbn:
- '9781728189420'
issn:
- 1097-5659
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
record:
- id: '7910'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Microwave quantum illumination with a digital phase-conjugated receiver
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2020
year: '2020'
...
---
_id: '9007'
abstract:
- lang: eng
text: Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle
method to count “sufficiently free” rational points of bounded height on arbitrary
smooth projective hypersurfaces of low degree that are defined over the rationals.
article_processing_charge: No
article_type: original
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Sawin W. Free rational points on smooth hypersurfaces. Commentarii
Mathematici Helvetici. 2020;95(4):635-659. doi:10.4171/CMH/499
apa: Browning, T. D., & Sawin, W. (2020). Free rational points on smooth hypersurfaces.
Commentarii Mathematici Helvetici. European Mathematical Society. https://doi.org/10.4171/CMH/499
chicago: Browning, Timothy D, and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.”
Commentarii Mathematici Helvetici. European Mathematical Society, 2020.
https://doi.org/10.4171/CMH/499.
ieee: T. D. Browning and W. Sawin, “Free rational points on smooth hypersurfaces,”
Commentarii Mathematici Helvetici, vol. 95, no. 4. European Mathematical
Society, pp. 635–659, 2020.
ista: Browning TD, Sawin W. 2020. Free rational points on smooth hypersurfaces.
Commentarii Mathematici Helvetici. 95(4), 635–659.
mla: Browning, Timothy D., and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.”
Commentarii Mathematici Helvetici, vol. 95, no. 4, European Mathematical
Society, 2020, pp. 635–59, doi:10.4171/CMH/499.
short: T.D. Browning, W. Sawin, Commentarii Mathematici Helvetici 95 (2020) 635–659.
date_created: 2021-01-17T23:01:11Z
date_published: 2020-12-07T00:00:00Z
date_updated: 2023-08-24T11:11:36Z
day: '07'
department:
- _id: TiBr
doi: 10.4171/CMH/499
external_id:
arxiv:
- '1906.08463'
isi:
- '000596833300001'
intvolume: ' 95'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1906.08463
month: '12'
oa: 1
oa_version: Preprint
page: 635-659
publication: Commentarii Mathematici Helvetici
publication_identifier:
eissn:
- '14208946'
issn:
- '00102571'
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Free rational points on smooth hypersurfaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 95
year: '2020'
...
---
_id: '9114'
abstract:
- lang: eng
text: "Microwave photonics lends the advantages of fiber optics to electronic sensing
and communication systems. In contrast to nonlinear optics, electro-optic devices
so far require classical modulation fields whose variance is dominated by electronic
or thermal noise rather than quantum fluctuations. Here we demonstrate bidirectional
single-sideband conversion of X band microwave to C band telecom light with a
microwave mode occupancy as low as 0.025 ± 0.005 and an added output noise of
less than or equal to 0.074 photons. This is facilitated by radiative cooling
and a triply resonant ultra-low-loss transducer operating at millikelvin temperatures.
The high bandwidth of 10.7 MHz and total (internal) photon conversion\r\nefficiency
of 0.03% (0.67%) combined with the extremely slow heating rate of 1.1 added output
noise photons per second for the highest available pump power of 1.48 mW puts
near-unity efficiency pulsed quantum transduction within reach. Together with
the non-Gaussian resources of superconducting qubits this might provide the practical
foundation to extend the range and scope of current quantum networks in analogy
to electrical repeaters in classical fiber optic communication."
acknowledged_ssus:
- _id: M-Shop
acknowledgement: "The authors acknowledge the support of T. Menner, A. Arslani, and
T. Asenov from the Miba machine shop for machining the microwave cavity, and thank
S. Barzanjeh, F. Sedlmeir, and C. Marquardt for fruitful discussions. This work
is supported by IST Austria and the European Research Council under Grant No. 758053
(ERC StG QUNNECT). W.H. is the recipient of an ISTplus postdoctoral fellowship with
funding from the European Union’s Horizon 2020 research and innovation program under
the Marie Skłodowska-Curie Grant No. 754411.\r\nG.A. is the recipient of a DOC fellowship
of the Austrian Academy of Sciences at IST Austria. J.M.F. acknowledges support
from the Austrian Science Fund (FWF) through BeyondC (F71) and the European Union’s
Horizon 2020 research and innovation program under Grant No. 899354 (FET Open SuperQuLAN).
H.G.L.S. acknowledges support from the Aotearoa/New Zealand’s MBIE Endeavour Smart
Ideas Grant No UOOX1805."
article_number: '020315'
article_processing_charge: No
article_type: original
author:
- first_name: William J
full_name: Hease, William J
id: 29705398-F248-11E8-B48F-1D18A9856A87
last_name: Hease
orcid: 0000-0001-9868-2166
- first_name: Alfredo R
full_name: Rueda Sanchez, Alfredo R
id: 3B82B0F8-F248-11E8-B48F-1D18A9856A87
last_name: Rueda Sanchez
orcid: 0000-0001-6249-5860
- first_name: Rishabh
full_name: Sahu, Rishabh
id: 47D26E34-F248-11E8-B48F-1D18A9856A87
last_name: Sahu
orcid: 0000-0001-6264-2162
- first_name: Matthias
full_name: Wulf, Matthias
id: 45598606-F248-11E8-B48F-1D18A9856A87
last_name: Wulf
orcid: 0000-0001-6613-1378
- first_name: Georg M
full_name: Arnold, Georg M
id: 3770C838-F248-11E8-B48F-1D18A9856A87
last_name: Arnold
orcid: 0000-0003-1397-7876
- first_name: Harald G.L.
full_name: Schwefel, Harald G.L.
last_name: Schwefel
- first_name: Johannes M
full_name: Fink, Johannes M
id: 4B591CBA-F248-11E8-B48F-1D18A9856A87
last_name: Fink
orcid: 0000-0001-8112-028X
citation:
ama: Hease WJ, Rueda Sanchez AR, Sahu R, et al. Bidirectional electro-optic wavelength
conversion in the quantum ground state. PRX Quantum. 2020;1(2). doi:10.1103/prxquantum.1.020315
apa: Hease, W. J., Rueda Sanchez, A. R., Sahu, R., Wulf, M., Arnold, G. M., Schwefel,
H. G. L., & Fink, J. M. (2020). Bidirectional electro-optic wavelength conversion
in the quantum ground state. PRX Quantum. American Physical Society. https://doi.org/10.1103/prxquantum.1.020315
chicago: Hease, William J, Alfredo R Rueda Sanchez, Rishabh Sahu, Matthias Wulf,
Georg M Arnold, Harald G.L. Schwefel, and Johannes M Fink. “Bidirectional Electro-Optic
Wavelength Conversion in the Quantum Ground State.” PRX Quantum. American
Physical Society, 2020. https://doi.org/10.1103/prxquantum.1.020315.
ieee: W. J. Hease et al., “Bidirectional electro-optic wavelength conversion
in the quantum ground state,” PRX Quantum, vol. 1, no. 2. American Physical
Society, 2020.
ista: Hease WJ, Rueda Sanchez AR, Sahu R, Wulf M, Arnold GM, Schwefel HGL, Fink
JM. 2020. Bidirectional electro-optic wavelength conversion in the quantum ground
state. PRX Quantum. 1(2), 020315.
mla: Hease, William J., et al. “Bidirectional Electro-Optic Wavelength Conversion
in the Quantum Ground State.” PRX Quantum, vol. 1, no. 2, 020315, American
Physical Society, 2020, doi:10.1103/prxquantum.1.020315.
short: W.J. Hease, A.R. Rueda Sanchez, R. Sahu, M. Wulf, G.M. Arnold, H.G.L. Schwefel,
J.M. Fink, PRX Quantum 1 (2020).
date_created: 2021-02-12T10:41:28Z
date_published: 2020-11-23T00:00:00Z
date_updated: 2023-08-24T11:16:36Z
day: '23'
ddc:
- '530'
department:
- _id: JoFi
doi: 10.1103/prxquantum.1.020315
ec_funded: 1
external_id:
isi:
- '000674680100001'
file:
- access_level: open_access
checksum: b70b12ded6d7660d4c9037eb09bfed0c
content_type: application/pdf
creator: dernst
date_created: 2021-02-12T11:16:16Z
date_updated: 2021-02-12T11:16:16Z
file_id: '9115'
file_name: 2020_PRXQuantum_Hease.pdf
file_size: 2146924
relation: main_file
success: 1
file_date_updated: 2021-02-12T11:16:16Z
has_accepted_license: '1'
intvolume: ' 1'
isi: 1
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 26336814-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '758053'
name: A Fiber Optic Transceiver for Superconducting Qubits
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 9B868D20-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '899354'
name: Quantum Local Area Networks with Superconducting Qubits
- _id: 26927A52-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F07105
name: Integrating superconducting quantum circuits
- _id: 2671EB66-B435-11E9-9278-68D0E5697425
name: Coherent on-chip conversion of superconducting qubit signals from microwaves
to optical frequencies
publication: PRX Quantum
publication_identifier:
issn:
- 2691-3399
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/how-to-transport-microwave-quantum-information-via-optical-fiber/
record:
- id: '13071'
relation: research_data
status: public
- id: '12900'
relation: dissertation_contains
status: public
- id: '13175'
relation: dissertation_contains
status: public
status: public
title: Bidirectional electro-optic wavelength conversion in the quantum ground state
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 1
year: '2020'
...
---
_id: '9194'
abstract:
- lang: eng
text: Quantum transduction, the process of converting quantum signals from one form
of energy to another, is an important area of quantum science and technology.
The present perspective article reviews quantum transduction between microwave
and optical photons, an area that has recently seen a lot of activity and progress
because of its relevance for connecting superconducting quantum processors over
long distances, among other applications. Our review covers the leading approaches
to achieving such transduction, with an emphasis on those based on atomic ensembles,
opto-electro-mechanics, and electro-optics. We briefly discuss relevant metrics
from the point of view of different applications, as well as challenges for the
future.
acknowledgement: "During the writing of this article we became aware of another review
of quantum transduction with somewhat different emphasis [99].\r\nWe would like
to thank the participants of the transduction workshop at Caltech in September 2018
for helpful and stimulating discussions. We particularly thank John Bartholomew,
Andrei Faraon, Johannes Fink, Jeff Holzgrafe, Linbo Shao, Marko Lončar, Daniel Oblak,
and Oskar Painter.\r\nN L and N S acknowledge support from the Alliance for Quantum
Technologies' (AQT) Intelligent Quantum Networks and Technologies (INQNET) research
program and by DOE/HEP QuantISED program grant, QCCFP (Quantum Communication Channels
for Fundamental Physics), award number DE-SC0019219. NS further acknowledges support
by the Natural Sciences and Engineering Research Council of Canada (NSERC). SB acknowledges
support from the Marie Skłodowska Curie fellowship number 707 438 (MSC-IF SUPEREOM).
JPC acknowledges support from the Caltech PMA prize postdoctoral fellowship. MS
acknowledges support from the ARL-CDQI and the National Science Foundation. CS acknowledges
NSERC, Quantum Alberta, and the Alberta Major Innovation Fund."
article_number: '020501'
article_processing_charge: No
article_type: review
author:
- first_name: Nikolai
full_name: Lauk, Nikolai
last_name: Lauk
- first_name: Neil
full_name: Sinclair, Neil
last_name: Sinclair
- first_name: Shabir
full_name: Barzanjeh, Shabir
id: 2D25E1F6-F248-11E8-B48F-1D18A9856A87
last_name: Barzanjeh
orcid: 0000-0003-0415-1423
- first_name: Jacob P
full_name: Covey, Jacob P
last_name: Covey
- first_name: Mark
full_name: Saffman, Mark
last_name: Saffman
- first_name: Maria
full_name: Spiropulu, Maria
last_name: Spiropulu
- first_name: Christoph
full_name: Simon, Christoph
last_name: Simon
citation:
ama: Lauk N, Sinclair N, Barzanjeh S, et al. Perspectives on quantum transduction.
Quantum Science and Technology. 2020;5(2). doi:10.1088/2058-9565/ab788a
apa: Lauk, N., Sinclair, N., Barzanjeh, S., Covey, J. P., Saffman, M., Spiropulu,
M., & Simon, C. (2020). Perspectives on quantum transduction. Quantum Science
and Technology. IOP Publishing. https://doi.org/10.1088/2058-9565/ab788a
chicago: Lauk, Nikolai, Neil Sinclair, Shabir Barzanjeh, Jacob P Covey, Mark Saffman,
Maria Spiropulu, and Christoph Simon. “Perspectives on Quantum Transduction.”
Quantum Science and Technology. IOP Publishing, 2020. https://doi.org/10.1088/2058-9565/ab788a.
ieee: N. Lauk et al., “Perspectives on quantum transduction,” Quantum
Science and Technology, vol. 5, no. 2. IOP Publishing, 2020.
ista: Lauk N, Sinclair N, Barzanjeh S, Covey JP, Saffman M, Spiropulu M, Simon C.
2020. Perspectives on quantum transduction. Quantum Science and Technology. 5(2),
020501.
mla: Lauk, Nikolai, et al. “Perspectives on Quantum Transduction.” Quantum Science
and Technology, vol. 5, no. 2, 020501, IOP Publishing, 2020, doi:10.1088/2058-9565/ab788a.
short: N. Lauk, N. Sinclair, S. Barzanjeh, J.P. Covey, M. Saffman, M. Spiropulu,
C. Simon, Quantum Science and Technology 5 (2020).
date_created: 2021-02-25T08:32:29Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2023-08-24T11:17:48Z
day: '01'
ddc:
- '530'
department:
- _id: JoFi
doi: 10.1088/2058-9565/ab788a
ec_funded: 1
external_id:
isi:
- '000521449500001'
file:
- access_level: open_access
checksum: a8562c42124a66b86836fe2489eb5f4f
content_type: application/pdf
creator: dernst
date_created: 2021-03-02T09:47:13Z
date_updated: 2021-03-02T09:47:13Z
file_id: '9215'
file_name: 2020_QuantumScience_Lauk.pdf
file_size: 974399
relation: main_file
success: 1
file_date_updated: 2021-03-02T09:47:13Z
has_accepted_license: '1'
intvolume: ' 5'
isi: 1
issue: '2'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 258047B6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '707438'
name: 'Microwave-to-Optical Quantum Link: Quantum Teleportation and Quantum Illumination
with cavity Optomechanics SUPEREOM'
publication: Quantum Science and Technology
publication_identifier:
issn:
- 2058-9565
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Perspectives on quantum transduction
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 5
year: '2020'
...
---
_id: '9039'
abstract:
- lang: eng
text: We give a short and self-contained proof for rates of convergence of the Allen--Cahn
equation towards mean curvature flow, assuming that a classical (smooth) solution
to the latter exists and starting from well-prepared initial data. Our approach
is based on a relative entropy technique. In particular, it does not require a
stability analysis for the linearized Allen--Cahn operator. As our analysis also
does not rely on the comparison principle, we expect it to be applicable to more
complex equations and systems.
acknowledgement: "This work was supported by the European Union's Horizon 2020 Research
and Innovation\r\nProgramme under Marie Sklodowska-Curie grant agreement 665385
and by the Deutsche\r\nForschungsgemeinschaft (DFG, German Research Foundation)
under Germany's Excellence Strategy, EXC-2047/1--390685813."
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
- first_name: Theresa M.
full_name: Simon, Theresa M.
last_name: Simon
citation:
ama: 'Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 2020;52(6):6222-6233. doi:10.1137/20M1322182'
apa: 'Fischer, J. L., Laux, T., & Simon, T. M. (2020). Convergence rates of
the Allen-Cahn equation to mean curvature flow: A short proof based on relative
entropies. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/20M1322182'
chicago: 'Fischer, Julian L, Tim Laux, and Theresa M. Simon. “Convergence Rates
of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative
Entropies.” SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics, 2020. https://doi.org/10.1137/20M1322182.'
ieee: 'J. L. Fischer, T. Laux, and T. M. Simon, “Convergence rates of the Allen-Cahn
equation to mean curvature flow: A short proof based on relative entropies,” SIAM
Journal on Mathematical Analysis, vol. 52, no. 6. Society for Industrial and
Applied Mathematics, pp. 6222–6233, 2020.'
ista: 'Fischer JL, Laux T, Simon TM. 2020. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 52(6), 6222–6233.'
mla: 'Fischer, Julian L., et al. “Convergence Rates of the Allen-Cahn Equation to
Mean Curvature Flow: A Short Proof Based on Relative Entropies.” SIAM Journal
on Mathematical Analysis, vol. 52, no. 6, Society for Industrial and Applied
Mathematics, 2020, pp. 6222–33, doi:10.1137/20M1322182.'
short: J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis
52 (2020) 6222–6233.
date_created: 2021-01-24T23:01:09Z
date_published: 2020-12-15T00:00:00Z
date_updated: 2023-08-24T11:15:16Z
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doi: 10.1137/20M1322182
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publication: SIAM Journal on Mathematical Analysis
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title: 'Convergence rates of the Allen-Cahn equation to mean curvature flow: A short
proof based on relative entropies'
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