---
_id: '51204'
abstract:
- lang: eng
text: "Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup
$\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup
$\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant
differential operators, and the decay of matrix coefficients. In\r\nparticular,
this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash
G)$ in this general setting."
author:
- first_name: Christopher
full_name: Lutsko, Christopher
last_name: Lutsko
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
orcid: 0000-0001-8893-2045
citation:
ama: Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness
of locally symmetric spaces. Duke Math Journal . 2026;(to appear).
apa: Lutsko, C., Weich, T., & Wolf, L. L. (2026). Polyhedral bounds on the joint
spectrum and temperedness of locally symmetric spaces. Duke Math. Journal
, (to appear).
bibtex: '@article{Lutsko_Weich_Wolf_2026, title={Polyhedral bounds on the joint
spectrum and temperedness of locally symmetric spaces}, volume={(to appear)},
journal={Duke Math. Journal }, author={Lutsko, Christopher and Weich, Tobias and
Wolf, Lasse Lennart}, year={2026} }'
chicago: Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral
Bounds on the Joint Spectrum and Temperedness of Locally Symmetric Spaces.” Duke
Math. Journal (to appear) (2026).
ieee: C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum
and temperedness of locally symmetric spaces,” Duke Math. Journal , vol.
(to appear), 2026.
mla: Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness
of Locally Symmetric Spaces.” Duke Math. Journal , vol. (to appear), 2026.
short: C. Lutsko, T. Weich, L.L. Wolf, Duke Math. Journal (to appear) (2026).
date_created: 2024-02-06T20:35:36Z
date_updated: 2026-02-18T10:37:47Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
arxiv:
- '2402.02530'
language:
- iso: eng
publication: 'Duke Math. Journal '
status: public
title: Polyhedral bounds on the joint spectrum and temperedness of locally symmetric
spaces
type: journal_article
user_id: '49178'
volume: (to appear)
year: '2026'
...
---
_id: '51207'
abstract:
- lang: eng
text: "Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact
type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We
show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic
growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain
that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$."
article_number: '76'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
orcid: 0000-0001-8893-2045
citation:
ama: 'Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case.
Geom Dedicata. 2024;218. doi:https://doi.org/10.1007/s10711-024-00904-4'
apa: 'Weich, T., & Wolf, L. L. (2024). Temperedness of locally symmetric spaces:
The product case. Geom Dedicata, 218, Article 76. https://doi.org/10.1007/s10711-024-00904-4'
bibtex: '@article{Weich_Wolf_2024, title={Temperedness of locally symmetric spaces:
The product case}, volume={218}, DOI={https://doi.org/10.1007/s10711-024-00904-4},
number={76}, journal={Geom Dedicata}, author={Weich, Tobias and Wolf, Lasse Lennart},
year={2024} }'
chicago: 'Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric
Spaces: The Product Case.” Geom Dedicata 218 (2024). https://doi.org/10.1007/s10711-024-00904-4.'
ieee: 'T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product
case,” Geom Dedicata, vol. 218, Art. no. 76, 2024, doi: https://doi.org/10.1007/s10711-024-00904-4.'
mla: 'Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric
Spaces: The Product Case.” Geom Dedicata, vol. 218, 76, 2024, doi:https://doi.org/10.1007/s10711-024-00904-4.'
short: T. Weich, L.L. Wolf, Geom Dedicata 218 (2024).
date_created: 2024-02-06T21:00:55Z
date_updated: 2024-05-07T11:44:34Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: https://doi.org/10.1007/s10711-024-00904-4
external_id:
arxiv:
- '2304.09573'
intvolume: ' 218'
language:
- iso: eng
publication: Geom Dedicata
status: public
title: 'Temperedness of locally symmetric spaces: The product case'
type: journal_article
user_id: '45027'
volume: 218
year: '2024'
...
---
_id: '52876'
article_number: L012043
author:
- first_name: Christian
full_name: Arends, Christian
id: '43994'
last_name: Arends
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
orcid: 0000-0001-8893-2045
- first_name: Jasmin
full_name: Meinecke, Jasmin
last_name: Meinecke
- first_name: Sonja
full_name: Barkhofen, Sonja
id: '48188'
last_name: Barkhofen
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Tim
full_name: Bartley, Tim
id: '49683'
last_name: Bartley
citation:
ama: Arends C, Wolf LL, Meinecke J, Barkhofen S, Weich T, Bartley T. Decomposing
large unitaries into multimode devices of arbitrary size. Physical Review Research.
2024;6(1). doi:10.1103/physrevresearch.6.l012043
apa: Arends, C., Wolf, L. L., Meinecke, J., Barkhofen, S., Weich, T., & Bartley,
T. (2024). Decomposing large unitaries into multimode devices of arbitrary size.
Physical Review Research, 6(1), Article L012043. https://doi.org/10.1103/physrevresearch.6.l012043
bibtex: '@article{Arends_Wolf_Meinecke_Barkhofen_Weich_Bartley_2024, title={Decomposing
large unitaries into multimode devices of arbitrary size}, volume={6}, DOI={10.1103/physrevresearch.6.l012043},
number={1L012043}, journal={Physical Review Research}, publisher={American Physical
Society (APS)}, author={Arends, Christian and Wolf, Lasse Lennart and Meinecke,
Jasmin and Barkhofen, Sonja and Weich, Tobias and Bartley, Tim}, year={2024} }'
chicago: Arends, Christian, Lasse Lennart Wolf, Jasmin Meinecke, Sonja Barkhofen,
Tobias Weich, and Tim Bartley. “Decomposing Large Unitaries into Multimode Devices
of Arbitrary Size.” Physical Review Research 6, no. 1 (2024). https://doi.org/10.1103/physrevresearch.6.l012043.
ieee: 'C. Arends, L. L. Wolf, J. Meinecke, S. Barkhofen, T. Weich, and T. Bartley,
“Decomposing large unitaries into multimode devices of arbitrary size,” Physical
Review Research, vol. 6, no. 1, Art. no. L012043, 2024, doi: 10.1103/physrevresearch.6.l012043.'
mla: Arends, Christian, et al. “Decomposing Large Unitaries into Multimode Devices
of Arbitrary Size.” Physical Review Research, vol. 6, no. 1, L012043, American
Physical Society (APS), 2024, doi:10.1103/physrevresearch.6.l012043.
short: C. Arends, L.L. Wolf, J. Meinecke, S. Barkhofen, T. Weich, T. Bartley, Physical
Review Research 6 (2024).
date_created: 2024-03-26T08:52:05Z
date_updated: 2025-12-04T13:38:49Z
department:
- _id: '623'
- _id: '15'
doi: 10.1103/physrevresearch.6.l012043
intvolume: ' 6'
issue: '1'
keyword:
- General Physics and Astronomy
language:
- iso: eng
publication: Physical Review Research
publication_identifier:
issn:
- 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Decomposing large unitaries into multimode devices of arbitrary size
type: journal_article
user_id: '48188'
volume: 6
year: '2024'
...
---
_id: '31189'
abstract:
- lang: eng
text: "Given a geometrically finite hyperbolic surface of infinite volume it is
a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator
has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization
of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential
operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of
higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe
geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding
principal eigenvalues. A large class of examples fulfilling these\r\nassumptions
are the non-compact quotients by Anosov subgroups."
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
citation:
ama: Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally
symmetric spaces. Communications in Mathematical Physics. 2023;403. doi:https://doi.org/10.1007/s00220-023-04819-1
apa: Weich, T., & Wolf, L. L. (2023). Absence of principal eigenvalues for higher
rank locally symmetric spaces. Communications in Mathematical Physics,
403. https://doi.org/10.1007/s00220-023-04819-1
bibtex: '@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher
rank locally symmetric spaces}, volume={403}, DOI={https://doi.org/10.1007/s00220-023-04819-1},
journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf,
Lasse Lennart}, year={2023} }'
chicago: Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues
for Higher Rank Locally Symmetric Spaces.” Communications in Mathematical
Physics 403 (2023). https://doi.org/10.1007/s00220-023-04819-1.
ieee: 'T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank
locally symmetric spaces,” Communications in Mathematical Physics, vol.
403, 2023, doi: https://doi.org/10.1007/s00220-023-04819-1.'
mla: Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for
Higher Rank Locally Symmetric Spaces.” Communications in Mathematical Physics,
vol. 403, 2023, doi:https://doi.org/10.1007/s00220-023-04819-1.
short: T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).
date_created: 2022-05-11T10:38:11Z
date_updated: 2024-02-06T20:52:40Z
department:
- _id: '10'
- _id: '548'
- _id: '623'
doi: https://doi.org/10.1007/s00220-023-04819-1
external_id:
arxiv:
- '2205.03167'
intvolume: ' 403'
language:
- iso: eng
publication: Communications in Mathematical Physics
publication_identifier:
unknown:
- 1275-1295
status: public
title: Absence of principal eigenvalues for higher rank locally symmetric spaces
type: journal_article
user_id: '49178'
volume: 403
year: '2023'
...
---
_id: '31190'
abstract:
- lang: eng
text: "For a compact Riemannian locally symmetric space $\\Gamma\\backslash G/K$
of\r\narbitrary rank we determine the location of certain Ruelle-Taylor resonances\r\nfor
the Weyl chamber action. We provide a Weyl-lower bound on an appropriate\r\ncounting
function for the Ruelle-Taylor resonances and establish a spectral gap\r\nwhich
is uniform in $\\Gamma$ if $G/K$ is irreducible of higher rank. This is\r\nachieved
by proving a quantum-classical correspondence, i.e. a\r\n1:1-correspondence between
horocyclically invariant Ruelle-Taylor resonant\r\nstates and joint eigenfunctions
of the algebra of invariant differential\r\noperators on $G/K$."
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
orcid: 0000-0001-8893-2045
citation:
ama: Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence.
Analysis & PDE. 2023;16(10):2241–2265. doi:https://doi.org/10.2140/apde.2023.16.2241
apa: Hilgert, J., Weich, T., & Wolf, L. L. (2023). Higher rank quantum-classical
correspondence. Analysis & PDE, 16(10), 2241–2265. https://doi.org/10.2140/apde.2023.16.2241
bibtex: '@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical
correspondence}, volume={16}, DOI={https://doi.org/10.2140/apde.2023.16.2241},
number={10}, journal={Analysis & PDE}, publisher={MSP}, author={Hilgert, Joachim
and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }'
chicago: 'Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical
Correspondence.” Analysis & PDE 16, no. 10 (2023): 2241–2265. https://doi.org/10.2140/apde.2023.16.2241.'
ieee: 'J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,”
Analysis & PDE, vol. 16, no. 10, pp. 2241–2265, 2023, doi: https://doi.org/10.2140/apde.2023.16.2241.'
mla: Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” Analysis
& PDE, vol. 16, no. 10, MSP, 2023, pp. 2241–2265, doi:https://doi.org/10.2140/apde.2023.16.2241.
short: J. Hilgert, T. Weich, L.L. Wolf, Analysis & PDE 16 (2023) 2241–2265.
date_created: 2022-05-11T10:41:35Z
date_updated: 2026-02-18T10:39:36Z
department:
- _id: '10'
- _id: '548'
- _id: '91'
doi: https://doi.org/10.2140/apde.2023.16.2241
external_id:
arxiv:
- '2103.05667'
intvolume: ' 16'
issue: '10'
language:
- iso: eng
page: 2241–2265
publication: Analysis & PDE
publisher: MSP
status: public
title: Higher rank quantum-classical correspondence
type: journal_article
user_id: '49178'
volume: 16
year: '2023'
...
---
_id: '31191'
abstract:
- lang: eng
text: "The kinetic Brownian motion on the sphere bundle of a Riemannian manifold
$M$\r\nis a stochastic process that models a random perturbation of the geodesic
flow.\r\nIf $M$ is a orientable compact constant negatively curved surface, we
show that\r\nin the limit of infinitely large perturbation the $L^2$-spectrum
of the\r\ninfinitesimal generator of a time rescaled version of the process converges
to\r\nthe Laplace spectrum of the base manifold. In addition, we give explicit
error\r\nestimates for the convergence to equilibrium. The proofs are based on\r\nnoncommutative
harmonic analysis of $SL_2(\\mathbb{R})$."
author:
- first_name: Martin
full_name: Kolb, Martin
last_name: Kolb
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
citation:
ama: Kolb M, Weich T, Wolf LL. Spectral Asymptotics for Kinetic Brownian Motion
on Hyperbolic Surfaces. arXiv:190906183. Published online 2019.
apa: Kolb, M., Weich, T., & Wolf, L. L. (2019). Spectral Asymptotics for Kinetic
Brownian Motion on Hyperbolic Surfaces. In arXiv:1909.06183.
bibtex: '@article{Kolb_Weich_Wolf_2019, title={Spectral Asymptotics for Kinetic
Brownian Motion on Hyperbolic Surfaces}, journal={arXiv:1909.06183}, author={Kolb,
Martin and Weich, Tobias and Wolf, Lasse Lennart}, year={2019} }'
chicago: Kolb, Martin, Tobias Weich, and Lasse Lennart Wolf. “Spectral Asymptotics
for Kinetic Brownian Motion on Hyperbolic Surfaces.” ArXiv:1909.06183,
2019.
ieee: M. Kolb, T. Weich, and L. L. Wolf, “Spectral Asymptotics for Kinetic Brownian
Motion on Hyperbolic Surfaces,” arXiv:1909.06183. 2019.
mla: Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic
Surfaces.” ArXiv:1909.06183, 2019.
short: M. Kolb, T. Weich, L.L. Wolf, ArXiv:1909.06183 (2019).
date_created: 2022-05-11T10:42:11Z
date_updated: 2022-05-24T13:06:58Z
department:
- _id: '548'
external_id:
arxiv:
- '1909.06183'
language:
- iso: eng
publication: arXiv:1909.06183
status: public
title: Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces
type: preprint
user_id: '45027'
year: '2019'
...