Marius Lemm
@mariuslemm.bsky.social
Professor of #MathematicalPhysics at University of Tübingen
(@unituebingen.bsky.social)
Working on #quantum many-body physics and mathematical analysis
Website: https://www.math.uni-tuebingen.de/de/forschung/maphy/personen/mariuslemm/mariuslemm
(@unituebingen.bsky.social)
Working on #quantum many-body physics and mathematical analysis
Website: https://www.math.uni-tuebingen.de/de/forschung/maphy/personen/mariuslemm/mariuslemm
Reposted by Marius Lemm
A new paper with Bogdan Georgiev, Javier Gomez-Serrano, and Adam Zsolt Wagner: "Mathematical exploration and discovery at scale" arxiv.org/abs/2511.02864. Further discussion is at terrytao.wordpress.com/2025/11/05/m...
Mathematical exploration and discovery at scale
AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines ...
arxiv.org
November 6, 2025 at 3:42 AM
A new paper with Bogdan Georgiev, Javier Gomez-Serrano, and Adam Zsolt Wagner: "Mathematical exploration and discovery at scale" arxiv.org/abs/2511.02864. Further discussion is at terrytao.wordpress.com/2025/11/05/m...
Are the dynamics of disordered quantum many-body systems easier to simulate?
--> Yes, because entanglement spreads slowly for a non-perturbatively long time (a.k.a. "prethermal MBL"). This is true in any dimension.
arxiv.org/pdf/2510.11831
Thanks to my collaborators Ben McDonough and Andy Lucas!
--> Yes, because entanglement spreads slowly for a non-perturbatively long time (a.k.a. "prethermal MBL"). This is true in any dimension.
arxiv.org/pdf/2510.11831
Thanks to my collaborators Ben McDonough and Andy Lucas!
arxiv.org
October 15, 2025 at 7:53 AM
Are the dynamics of disordered quantum many-body systems easier to simulate?
--> Yes, because entanglement spreads slowly for a non-perturbatively long time (a.k.a. "prethermal MBL"). This is true in any dimension.
arxiv.org/pdf/2510.11831
Thanks to my collaborators Ben McDonough and Andy Lucas!
--> Yes, because entanglement spreads slowly for a non-perturbatively long time (a.k.a. "prethermal MBL"). This is true in any dimension.
arxiv.org/pdf/2510.11831
Thanks to my collaborators Ben McDonough and Andy Lucas!
Reposted by Marius Lemm
The future is here: a formalization in Lean of the generalized quantum Stein's lemma!
Amazing that this can be done.
arxiv.org/abs/2510.08672
Amazing that this can be done.
arxiv.org/abs/2510.08672
A Formalization of the Generalized Quantum Stein's Lemma in Lean
The Generalized Quantum Stein's Lemma is a theorem in quantum hypothesis testing that provides an operational meaning to the relative entropy within the context of quantum resource theories. Its origi...
arxiv.org
October 13, 2025 at 5:31 AM
The future is here: a formalization in Lean of the generalized quantum Stein's lemma!
Amazing that this can be done.
arxiv.org/abs/2510.08672
Amazing that this can be done.
arxiv.org/abs/2510.08672
New preprint on Hamiltonian Learning of Coulomb potentials and smooth potentials in continuous space
arxiv.org/abs/2510.08471
Thanks to my collaborators, @hippoquantus.bsky.social , Tim Möbus, and Oliver Siebert!
arxiv.org/abs/2510.08471
Thanks to my collaborators, @hippoquantus.bsky.social , Tim Möbus, and Oliver Siebert!
Learning Coulomb Potentials and Beyond with Fermions in Continuous Space
We present a modular algorithm for learning external potentials in continuous-space free-fermion models including Coulomb potentials in any dimension. Compared to the lattice-based approaches, the con...
arxiv.org
October 10, 2025 at 6:46 AM
New preprint on Hamiltonian Learning of Coulomb potentials and smooth potentials in continuous space
arxiv.org/abs/2510.08471
Thanks to my collaborators, @hippoquantus.bsky.social , Tim Möbus, and Oliver Siebert!
arxiv.org/abs/2510.08471
Thanks to my collaborators, @hippoquantus.bsky.social , Tim Möbus, and Oliver Siebert!
New preprint with @nickrhj.bsky.social
arxiv.org/pdf/2509.22438
Is a typical translation-invariant Hamiltonian gapped or gapless?
---> We prove that for random rank-1 interactions on any bounded-degree graph, the Hamiltonian is *gapped* with high probability as local dimension grows.
arxiv.org/pdf/2509.22438
Is a typical translation-invariant Hamiltonian gapped or gapless?
---> We prove that for random rank-1 interactions on any bounded-degree graph, the Hamiltonian is *gapped* with high probability as local dimension grows.
arxiv.org
October 2, 2025 at 9:34 PM
New preprint with @nickrhj.bsky.social
arxiv.org/pdf/2509.22438
Is a typical translation-invariant Hamiltonian gapped or gapless?
---> We prove that for random rank-1 interactions on any bounded-degree graph, the Hamiltonian is *gapped* with high probability as local dimension grows.
arxiv.org/pdf/2509.22438
Is a typical translation-invariant Hamiltonian gapped or gapless?
---> We prove that for random rank-1 interactions on any bounded-degree graph, the Hamiltonian is *gapped* with high probability as local dimension grows.
Reposted by Marius Lemm
Horng-Tzer Yau has spent decades studying the interplay of randomness and order in matrices. In 2008, Jun Yin, a former physicist, joined Yau’s group. In spring of 2024, the pair made the biggest advance on the problem since the 1980s.
www.quantamagazine.org/new-physics-...
www.quantamagazine.org/new-physics-...
August 22, 2025 at 4:46 AM
Horng-Tzer Yau has spent decades studying the interplay of randomness and order in matrices. In 2008, Jun Yin, a former physicist, joined Yau’s group. In spring of 2024, the pair made the biggest advance on the problem since the 1980s.
www.quantamagazine.org/new-physics-...
www.quantamagazine.org/new-physics-...
Open position in Tübingen!
Assistant Professor of Mathematical Quantum Theory
(non tenure-track, up to 6 years)
Deadline is September 30, 2025.
More info including how to apply: www.mathjobs.org/jobs/list/26...
The last person to hold this position was the formidable @angelacapel.bsky.social
Assistant Professor of Mathematical Quantum Theory
(non tenure-track, up to 6 years)
Deadline is September 30, 2025.
More info including how to apply: www.mathjobs.org/jobs/list/26...
The last person to hold this position was the formidable @angelacapel.bsky.social
MathJobs from the the American Mathematical Society
Mathjobs is an automated job application system sponsored by the AMS.
www.mathjobs.org
August 19, 2025 at 8:35 PM
Open position in Tübingen!
Assistant Professor of Mathematical Quantum Theory
(non tenure-track, up to 6 years)
Deadline is September 30, 2025.
More info including how to apply: www.mathjobs.org/jobs/list/26...
The last person to hold this position was the formidable @angelacapel.bsky.social
Assistant Professor of Mathematical Quantum Theory
(non tenure-track, up to 6 years)
Deadline is September 30, 2025.
More info including how to apply: www.mathjobs.org/jobs/list/26...
The last person to hold this position was the formidable @angelacapel.bsky.social
Reposted by Marius Lemm
After 3 1/2 years of work my course on quantum computing is finally finished — the "Director's Cut" of Understanding Quantum Information and Computation is now available.
arxiv.org/abs/2507.11536
arxiv.org/abs/2507.11536
Understanding Quantum Information and Computation
This is a course on the theory of quantum computing. It consists of 16 lessons, each with a video and written component, covering the basics of quantum information, quantum algorithms (including query...
arxiv.org
July 16, 2025 at 11:06 AM
After 3 1/2 years of work my course on quantum computing is finally finished — the "Director's Cut" of Understanding Quantum Information and Computation is now available.
arxiv.org/abs/2507.11536
arxiv.org/abs/2507.11536
Reposted by Marius Lemm
Colored droplets in corn syrup seemingly blended together can be returned to their original state by reversing the direction of mixing, a form of laminar flow called "Stokes flow".
Credit: UNM Physics & Astronomy
Credit: UNM Physics & Astronomy
July 14, 2025 at 11:54 PM
Colored droplets in corn syrup seemingly blended together can be returned to their original state by reversing the direction of mixing, a form of laminar flow called "Stokes flow".
Credit: UNM Physics & Astronomy
Credit: UNM Physics & Astronomy
Reposted by Marius Lemm
My latest for @nytimes.com -- please repost so your followers can see this for free. www.nytimes.com/interactive/...
How a Puzzle About Fractions Got Brain Scans Rolling (Gift Article)
A story of bowling pins, patterns and medical miracles.
www.nytimes.com
June 30, 2025 at 10:33 AM
My latest for @nytimes.com -- please repost so your followers can see this for free. www.nytimes.com/interactive/...
This year, the fall meeting of the German Physical Society celebrates 100 years of quantum theory
quantum25.dpg-tagungen.de
Göttingen, September 8-12
The deadline for abstract submission is this Saturday, May 31.
quantum25.dpg-tagungen.de
Göttingen, September 8-12
The deadline for abstract submission is this Saturday, May 31.
2. DPG-Herbsttagung: 100 Jahre Quantenmechanik
quantum25.dpg-tagungen.de
May 28, 2025 at 2:10 PM
This year, the fall meeting of the German Physical Society celebrates 100 years of quantum theory
quantum25.dpg-tagungen.de
Göttingen, September 8-12
The deadline for abstract submission is this Saturday, May 31.
quantum25.dpg-tagungen.de
Göttingen, September 8-12
The deadline for abstract submission is this Saturday, May 31.
New preprint with Carla Rubiliani and Jingxuan Zhang
"On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians"
arxiv.org/abs/2505.01786
We prove that the speed of boson propagation is bounded under the optimal long-range condition (for power law exponent \alpha>d+1)
"On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians"
arxiv.org/abs/2505.01786
We prove that the speed of boson propagation is bounded under the optimal long-range condition (for power law exponent \alpha>d+1)
On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians
We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all momen...
arxiv.org
May 8, 2025 at 6:12 PM
New preprint with Carla Rubiliani and Jingxuan Zhang
"On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians"
arxiv.org/abs/2505.01786
We prove that the speed of boson propagation is bounded under the optimal long-range condition (for power law exponent \alpha>d+1)
"On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians"
arxiv.org/abs/2505.01786
We prove that the speed of boson propagation is bounded under the optimal long-range condition (for power law exponent \alpha>d+1)
Reposted by Marius Lemm
Great explanation of the basics of quantum computing and Grover's algorithm by 3Blue1Brown. He also addresses the common misconception of "exponential parallelism".
www.youtube.com/watch?v=RQWp...
www.youtube.com/watch?v=RQWp...
But what is quantum computing? (Grover's Algorithm)
YouTube video by 3Blue1Brown
www.youtube.com
May 3, 2025 at 8:33 PM
Great explanation of the basics of quantum computing and Grover's algorithm by 3Blue1Brown. He also addresses the common misconception of "exponential parallelism".
www.youtube.com/watch?v=RQWp...
www.youtube.com/watch?v=RQWp...
Until recently, we thought that transporting a macroscopic cloud of particles a distance r in time t is suppressed by the usual LR-type light cone
exp(vt-r)
Turns out, the decay rate is proportional to the number of transported particles N
exp(N(vt-r))
arxiv.org/abs/2503.19788
exp(vt-r)
Turns out, the decay rate is proportional to the number of transported particles N
exp(N(vt-r))
arxiv.org/abs/2503.19788
March 26, 2025 at 8:41 AM
Until recently, we thought that transporting a macroscopic cloud of particles a distance r in time t is suppressed by the usual LR-type light cone
exp(vt-r)
Turns out, the decay rate is proportional to the number of transported particles N
exp(N(vt-r))
arxiv.org/abs/2503.19788
exp(vt-r)
Turns out, the decay rate is proportional to the number of transported particles N
exp(N(vt-r))
arxiv.org/abs/2503.19788
If you're an undergraduate student interested in the mathematics of quantum physics and general relativity, consider the
Tübingen International M.Sc. Program in #MathematicalPhysics
www.math.uni-tuebingen.de/en/mmp
Opens for applications today
Tübingen International M.Sc. Program in #MathematicalPhysics
www.math.uni-tuebingen.de/en/mmp
Opens for applications today
Master in Mathematical Physics
www.math.uni-tuebingen.de
March 3, 2025 at 10:17 AM
If you're an undergraduate student interested in the mathematics of quantum physics and general relativity, consider the
Tübingen International M.Sc. Program in #MathematicalPhysics
www.math.uni-tuebingen.de/en/mmp
Opens for applications today
Tübingen International M.Sc. Program in #MathematicalPhysics
www.math.uni-tuebingen.de/en/mmp
Opens for applications today
Reposted by Marius Lemm
I am happy to announce that the Kakeya set conjecture, one of the most sought after open problems in geometric measure theory, has now been proven (in three dimensions) by Hong Wang and Joshua Zahl! arxiv.org/abs/2502.17655 I discuss some ideas of the proof at terrytao.wordpress.com/2025/02/25/t...
Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions
We study sets of $δ$ tubes in $\mathbb{R}^3$, with the property that not too many tubes can be contained inside a common convex set $V$. We show that the union of tubes from such a set must have almos...
arxiv.org
February 26, 2025 at 4:49 AM
I am happy to announce that the Kakeya set conjecture, one of the most sought after open problems in geometric measure theory, has now been proven (in three dimensions) by Hong Wang and Joshua Zahl! arxiv.org/abs/2502.17655 I discuss some ideas of the proof at terrytao.wordpress.com/2025/02/25/t...
Had an amazing week at our Oberwolfach Mini-Workshop
"New Directions in Correlated Quantum Systems"
Huge thanks to our enthusiastic participants from both mathematics & physics!
"New Directions in Correlated Quantum Systems"
Huge thanks to our enthusiastic participants from both mathematics & physics!
February 21, 2025 at 3:26 PM
Had an amazing week at our Oberwolfach Mini-Workshop
"New Directions in Correlated Quantum Systems"
Huge thanks to our enthusiastic participants from both mathematics & physics!
"New Directions in Correlated Quantum Systems"
Huge thanks to our enthusiastic participants from both mathematics & physics!
Reposted by Marius Lemm
ArXiv quant-ph needs to be split up! Paul Ginsparg lists Daniel Gottesman's proposed subcategories at his @aspenphysics.bsky.social talk. He is looking for feedback: please reply, dm, or email.
February 13, 2025 at 11:52 PM
ArXiv quant-ph needs to be split up! Paul Ginsparg lists Daniel Gottesman's proposed subcategories at his @aspenphysics.bsky.social talk. He is looking for feedback: please reply, dm, or email.
My colleague Mitia Duerinckx in Brussels is accepting applications for an open postdoc position in PDE & mathematical physics
It's funded by Mitia's ERC grant "PASTIS: Scaling limits of particle systems and microstructural disorder"
For more info, see mitia.duerinckx.web.ulb.be/postdoc-posi....
It's funded by Mitia's ERC grant "PASTIS: Scaling limits of particle systems and microstructural disorder"
For more info, see mitia.duerinckx.web.ulb.be/postdoc-posi....
Mitia Duerinckx
mitia.duerinckx.web.ulb.be
February 10, 2025 at 9:44 AM
My colleague Mitia Duerinckx in Brussels is accepting applications for an open postdoc position in PDE & mathematical physics
It's funded by Mitia's ERC grant "PASTIS: Scaling limits of particle systems and microstructural disorder"
For more info, see mitia.duerinckx.web.ulb.be/postdoc-posi....
It's funded by Mitia's ERC grant "PASTIS: Scaling limits of particle systems and microstructural disorder"
For more info, see mitia.duerinckx.web.ulb.be/postdoc-posi....
Reposted by Marius Lemm
Uhlmann's theorem states that the fidelity of two (mixed) states can be expressed in terms of their purifications (where the fidelity simplifies). In arxiv.org/abs/2502.01749 we generalize Uhlmann's theorem to Rényi relative entropies.
Uhlmann's theorem for relative entropies
Uhlmann's theorem states that, for any two quantum states $ρ_{AB}$ and $σ_A$, there exists an extension $σ_{AB}$ of $σ_A$ such that the fidelity between $ρ_{AB}$ and $σ_{AB}$ equals the fidelity betwe...
arxiv.org
February 5, 2025 at 6:34 AM
Uhlmann's theorem states that the fidelity of two (mixed) states can be expressed in terms of their purifications (where the fidelity simplifies). In arxiv.org/abs/2502.01749 we generalize Uhlmann's theorem to Rényi relative entropies.
Reposted by Marius Lemm
To reach some consensus about the prospects of near-term (late nisq and early fault tolerant) quantum computing, we had a 3-day discussion event (“Quantum Now”) in Lapland with both optimists and pessimists. This continued at SeeQA 2024 in Oxford. See our conclusions here arxiv.org/abs/2501.05694
Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don't
In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault...
arxiv.org
January 13, 2025 at 4:00 PM
To reach some consensus about the prospects of near-term (late nisq and early fault tolerant) quantum computing, we had a 3-day discussion event (“Quantum Now”) in Lapland with both optimists and pessimists. This continued at SeeQA 2024 in Oxford. See our conclusions here arxiv.org/abs/2501.05694
What is the propagation speed of Bose-Hubbard Hamiltonians when the initial state is a BEC?
We now have an answer in the mean-field regime (with applications to effective dynamics)
arxiv.org/abs/2412.13868
Thanks to my collaborators Simone Rademacher and Jingxuan Zhang!
We now have an answer in the mean-field regime (with applications to effective dynamics)
arxiv.org/abs/2412.13868
Thanks to my collaborators Simone Rademacher and Jingxuan Zhang!
Local enhancement of the mean-field approximation for bosons
We study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive distance...
arxiv.org
December 19, 2024 at 1:28 PM
What is the propagation speed of Bose-Hubbard Hamiltonians when the initial state is a BEC?
We now have an answer in the mean-field regime (with applications to effective dynamics)
arxiv.org/abs/2412.13868
Thanks to my collaborators Simone Rademacher and Jingxuan Zhang!
We now have an answer in the mean-field regime (with applications to effective dynamics)
arxiv.org/abs/2412.13868
Thanks to my collaborators Simone Rademacher and Jingxuan Zhang!
Two open positions in mathematical physics in Tübingen
funded by ERC Starting Grant
"MathQuantProp: The Mathematics of Quantum Propagation"
Ph.D. position
www.mathjobs.org/jobs/list/26...
Postdoc position
www.mathjobs.org/jobs/list/26...
start: mid 2025 (flexible)
deadline: January 15, 2025
funded by ERC Starting Grant
"MathQuantProp: The Mathematics of Quantum Propagation"
Ph.D. position
www.mathjobs.org/jobs/list/26...
Postdoc position
www.mathjobs.org/jobs/list/26...
start: mid 2025 (flexible)
deadline: January 15, 2025
December 4, 2024 at 8:51 PM
Two open positions in mathematical physics in Tübingen
funded by ERC Starting Grant
"MathQuantProp: The Mathematics of Quantum Propagation"
Ph.D. position
www.mathjobs.org/jobs/list/26...
Postdoc position
www.mathjobs.org/jobs/list/26...
start: mid 2025 (flexible)
deadline: January 15, 2025
funded by ERC Starting Grant
"MathQuantProp: The Mathematics of Quantum Propagation"
Ph.D. position
www.mathjobs.org/jobs/list/26...
Postdoc position
www.mathjobs.org/jobs/list/26...
start: mid 2025 (flexible)
deadline: January 15, 2025
New preprint with Tom Wessel:
"Enhanced Lieb-Robinson bounds for commuting long-range interactions"
arxiv.org/abs/2411.19241
We observe that the power-law decay exponent required for a linear light cone improves from 2D+1 to 1 if the interactions are commuting. (Here D=spatial dim.)
"Enhanced Lieb-Robinson bounds for commuting long-range interactions"
arxiv.org/abs/2411.19241
We observe that the power-law decay exponent required for a linear light cone improves from 2D+1 to 1 if the interactions are commuting. (Here D=spatial dim.)
Enhanced Lieb-Robinson bounds for commuting long-range interactions
Recent works have revealed the intricate effect of long-range interactions on information transport in quantum many-body systems: In $D$ spatial dimensions, interactions decaying as a power-law $r^{-α...
arxiv.org
December 2, 2024 at 11:07 AM
New preprint with Tom Wessel:
"Enhanced Lieb-Robinson bounds for commuting long-range interactions"
arxiv.org/abs/2411.19241
We observe that the power-law decay exponent required for a linear light cone improves from 2D+1 to 1 if the interactions are commuting. (Here D=spatial dim.)
"Enhanced Lieb-Robinson bounds for commuting long-range interactions"
arxiv.org/abs/2411.19241
We observe that the power-law decay exponent required for a linear light cone improves from 2D+1 to 1 if the interactions are commuting. (Here D=spatial dim.)
Reposted by Marius Lemm
A few days ago Lawrence Hollom posted a preprint that solves a problem about posets, informally known as the fishbone conjecture, which I am told was extremely central in the area. 🧵
arxiv.org/abs/2411.16844
arxiv.org/abs/2411.16844
A resolution of the Aharoni-Korman conjecture
A poset $P$ is said to satisfy the finite antichain condition, or FAC for short, if it has no infinite antichain. It was conjectured by Aharoni and Korman in 1992 that any FAC poset $P$ possesses a ch...
arxiv.org
November 30, 2024 at 10:51 AM
A few days ago Lawrence Hollom posted a preprint that solves a problem about posets, informally known as the fishbone conjecture, which I am told was extremely central in the area. 🧵
arxiv.org/abs/2411.16844
arxiv.org/abs/2411.16844