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At 26, during the Reign of Terror in France, Jean-Baptiste Joseph Fourier narrowly avoided the guillotine. A decade later, he made a discovery that changed mathematics forever. @shalmawegs.bsky.social reports:
www.quantamagazine.org/what-is-the-...

What Is the Fourier Transform? | Quanta Magazine

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, de...

www.quantamagazine.org

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Álvaro M. Alhambra @alvalhambra.bsky.social · Aug 23

Trying to fit this in my next grant application

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 23

Completely abhorred by the correct spelling being "simulatability" and not "simulability".

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 11

The most interesting idea I've learnt this week: arxiv.org/abs/2311.10304

In a dissipative setting, if one takes the thermodynamic limit first and then the limit of zero dissipation, you are left with a Liouvillian gap related to the relaxation of the closed system dynamics

Liouvillian-gap analysis of open quantum many-body systems in the weak dissipation limit

Recent experiments have reported that novel physics emerge in open quantum many-body sys- tems due to an interplay of interactions and dissipation, which stimulate theoretical studies of the many-body...

arxiv.org

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 11

One more day, one more chance to pretend that I understand the word "topological"

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Reposted by Álvaro M. Alhambra

Jan Kochanowski @janfkoch.bsky.social · Jul 3

I am very happy to announce that my first published article „Rapid Thermalization of Dissipative Many-Body Dynamics of Commuting Hamiltonians“ is now published in Communications in Mathematical Physics.

rdcu.be/euy1Y

I feel honored and humbled to have been accepted in such a prestigious journal.

Rapid Thermalization of Dissipative Many-Body Dynamics of Commuting Hamiltonians - Communications in Mathematical Physics

Quantum systems typically reach thermal equilibrium rather quickly when coupled to a thermal environment. The usual way of bounding the speed of this process is by estimating the spectral gap of the d...

link.springer.com

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 2

Oh this looks interesting

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 2

If this sounds like I'm a bit annoying as a co-author the answer is yes

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 2

I have many opinions on scientific writing and one of them is that we should typically aim to do better than "closing a gap" in the literature

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 2

Today's addition to the reading list: arxiv.org/abs/2507.00405 - maybe I'll finally understand PSPACE

The Complexity of Thermalization in Finite Quantum Systems

Thermalization is the process through which a physical system evolves toward a state of thermal equilibrium. Determining whether or not a physical system will thermalize from an initial state has been...

arxiv.org

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 2

A bit overwhelmed by how hard it is to keep track of results I want to learn about

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jul 2

Super interesting read!

Álvaro M. Alhambra @alvalhambra.bsky.social · Jun 24

This was, in our mind, one of the most technically interesting open questions in the context of robustness to errors in many body quantum simulation, as put forward in e.g. arxiv.org/abs/2212.04924 - hopefully this further shows how simulating long range models is an interesting avenue to explore!

Quantum advantage and stability to errors in analogue quantum simulators

Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. Howe...

arxiv.org

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Álvaro M. Alhambra @alvalhambra.bsky.social · Jun 24

This shows how equilibrium states are robust to errors under standard conditions, despite the fact that long range interactions can spread information more rapidly!

Álvaro M. Alhambra @alvalhambra.bsky.social · Jun 24

In a new work, we show both numerically and analytically how expectations values of long-range models are robust to imperfections in the underlying Hamiltonian arxiv.org/abs/2506.16451

Stability of thermal equilibrium in long-range quantum systems

Experimental realizations of spin models are irremediably prone to errors, which can propagate through the system corrupting experimental signals. We study how such errors affect the measurement of lo...

arxiv.org