Author: quantumseminar

Wednesday, March 18, 2026 - 11:30
Aula 305 - Via Golgi 18/20 (Settore didattico)
Università degli Studi di Milano

Zoom link on request (contact Niels Benedikter by email)

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SPEAKER: Lorenzo Pettinari (University of Trento)

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Damping of phonons in Bose gas at low temperature

Condensed Bose gases can be effectively described in terms of quasi-particles, commonly referred to as phonons. Their dynamics are captured by a c-number ondensate Hamiltonian consisting of a quadratic term supplemented by third- and fourth-order perturbative corrections. These additional interaction terms render the phonons unstable, giving rise to two distinct decay processes known as Beliaev and Landau damping. From a mathematical perspective, such decay mechanisms should manifest as a broadening of the Bogoliubov dispersion relation in the thermodynamic limit. To validate this picture, I will present two different approaches to deriving the phonon decay rates. The first is inspired by the W*-algebraic framework of Jaksic-Pillet, employing Standard Representations and perturbative expansions of a suitably chosen vector state. The second method is based on the analysis of two-body correlation functions. Both approaches yield the same imaginary correction to the Bogoliubov dispersion relation, which in turn determines the expected broadening. urthermore, our approaches offer a new perspective on the decay of phonons in terms of the left and right components of these quasi-particles. The talk is based on joint work with Jan Derezi´nski and may be viewed as a modern laboration of the classical contributions of Beliaev, Hohenberg–Martin, and others.

Monday, January 12, 2026 - 14:00
Aula C01 - Via Luigi Mangiagalli, 25
Università degli Studi di Milano

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SPEAKER: Ian Jauslin (Rutgers University)

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A framework to study twisted bilayer graphene in a tight binding model

The study of the electronic properties of twisted bilayer graphene (TBG) has garnered much attention from the condensed matter community recently. TBG is obtained by stacking two graphene monolayers on top of each other, and rotating one of them with respect to the other. Theoretical and experimental analyses have found that the electronic properties of TBG depend very strongly on the angle between the layers. In fact, a handful of “magic” angles have been predicted at which TBG becomes a supercondutor, and this has even been verified experimentally.

The model commonly used to study TBG is an effective one, and was derived by
Bistritzer and MacDonald. In this talk, I will present recent results on developing a framework to study TBG from first principles. To be more exact, we consider a tight-binding model for the electrons, but make no further approximations. Using a renormalization group technique, we construct a perturbative expansion to study TBG that is convergent when the twisting angle satisfies certain diophantine conditions.

This is joint work with V. Mastropietro.

Monday, March 18, 2024 - 11:15
Aula Dottorato (first floor)
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

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SPEAKER: Zhituo Wang (Harbin Institute of Technology)

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Constructive renormalizations of the 2-D Honeycomb-Hubbard model

In this talk I will present some recent progress on the construction of ground state of the 2-dimensional Hubbard model, which is a prototypical model for studying phase transitions in quantum many-body system. Using fermionic cluster expansions and constructive renormalization theory, we proved that the ground state of the 2-d Hubbard model on the honeycomb lattice with triangular Fermi surfaces is not a Fermi liquid in the mathematical precise sense of Salmhofer. I will also discuss the crossover phenomenon in the 2-d square Hubbard model and universalities. This presentation is based on the work arXiv:2108.10852, CMP 401, 2569–2642(2023) and arXiv:2303.13628.

Monday, March 4, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

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SPEAKER: Joachim Kerner (FernUniversität in Hagen)

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On Bose-Einstein Condensation in the Random Kac-Luttinger Model

This talk is concerned with a random many-particle model originally considered by Kac and Luttinger in 1973 in order to study a well-known quantum phase transition known as Bose–Einstein condensation (BEC). Generally speaking, to understand this phase transition in interacting many-particle systems is a current hot topic in mathematical physics. However, due to the complexity of the underlying random one-particle model, the nature of the BEC in the non-interacting Kac-Luttinger model was understood only recently based on results obtained by Alain-Sol Sznitman (ETH). In this talk, our goal will be to understand the impact of repulsive two-particle interactions on this condensate. We will see that, due to the spatial localization of the condensate, strong enough interactions will immediately destroy it. On the other hand, for two-particle interactions of a mean-field type, we prove BEC in the interacting Kac–Luttinger model into a minimizer of a Hartree-type functional. This talk is based on joint work with C. Boccato (Milan), M. Pechmann (Tennessee), and W. Spitzer (Hagen).

The seminar is part of the activities of the project PRIN 2022AKRC5P “Interacting Quantum Systems: Topological Phenomena and Effective Theories” financed by the European Union – Next Generation EU.

Monday, February 26, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

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SPEAKER: Emanuela Giacomelli (LMU München)

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The low density Fermi gas in three dimensions

In recent decades, the study of many-body systems has been an active area of research in both physics and mathematics. In this talk we consider a system of N interacting fermions with spin 1/2 confined in a box in the dilute regime. We are interested in studying the correlation energy, defined as the difference between the energy of the fundamental state and that of the free Fermi gas. We will discuss some recent results on a first-order asymptotic for the correlation energy in the thermodynamic limit, where the number of particles and the size of the box are sent to infinity while keeping the density fixed. In particular, we will present some recent results for the correlation energy that go in the direction of a rigorous proof of the well-known Huang-Yang formula of 1957.

Monday, January 15, 2024 - 11:15
Aula 9
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

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SPEAKER: Clara Torres Latorre (Universitat de Barcelona)

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Regularity theory for elliptic and parabolic PDE

In this talk, we’ll explore how regularity theory is crucial for understanding partial differential equations (PDEs), and how it has consequences in physics and numerical analysis. We’ll first focus on why regularity matters, then take elliptic and parabolic PDEs as examples to talk about classical and recent regularity results. The goal is to give a practical overview, explaining when PDE solutions are smooth or singular.

Thursday, July 13, 2023 - 15:00
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

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SPEAKER: Diwakar Naidu (Universität Tübingen)

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Existence of Bell-type pure jump process for the Klein-Gordon Hamiltonian

In this talk I will present my work on Bell-type jump processes. J.S. Bell in
1984 gave a jump rate formula that predict the probability of configurational
jumps and in turn define a stochastic (Markov) jump process that governs the
evolution of particle configurations. The standard method (by Tumulka et al)
for proving existence of such processes does not work for the Klein-Gordon (KG) Hamiltonian as the jump rates for it are unbounded. We show the existence
of a stationary and independent (Markov) pure jump process (i.e. where the
configurational motion occurs only via jumps) for the particle configuration that
is equivariant, i.e. |Ψ_t|² distributed at every time t, where Ψ evolves with the KG
Hamiltonian, using elements from the theory of Lévy processes. Next, we also
want to extend this obtained process to a broader class of Markov process which also depend on the particle configurations and time using the general theory of Markov processes.

October 9, 2023 - 11:15
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

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SPEAKER: Asbjørn Bækgaard Lauritsen (IST Austria)

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Ground state energy and pressure of a dilute spin-polarized Fermi gas

Recently the study of dilute quantum gases have received much interest, in particular regarding their ground state energies and pressures/free energies at positive temperature. I will present recent work on such problems. Namely that of the ground state energy of a spin-polarized Fermi gas and the extension to the pressure at positive temperature. Compared to the free gas, the energy density/pressure of the interacting gas differs by a term of order a^3 \rho^{8/3} with a the p-wave scattering length of the interaction. One of the main ingredients in the proofs is a rigorous version of a formal cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237-260). I will discuss this expansion and the analysis of its absolute convergence.

Joint work with Robert Seiringer.

June 5, 2023 - 11:15
Aula dottorato, first floor
Università degli Studi di Milano
Via Saldini 50

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SPEAKER: Andreas Deuchert (Universität Zürich)

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Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields

We consider the Bardeen-Cooper-Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg-Landau functional. We also provide an asymptotic formula for the BCS critical temperature as a function of the external fields. This extends our previous results in arXiv:2105.05623 for the constant magnetic field to general magnetic fields with a nonzero magnetic flux through the unit cell. This is joint work with C. Hainzl and M. Maier.