Author: Marco Falconi

July 12, 2023 - 15:00
Aula Seminari III piano, third floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Giuseppe De Nittis (Pontificia Universidad Católica de Chile)

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About the notion of eigenstates in C*-algebras and some application to quantum mechanics

This talk is concerned with the notion of eigenstates of an operator in an abstract C*-algebra. After reviewing some basic and structural results, I will explore the possibility of reinterpreting certain typical concepts of quantum mechanics (dynamical equilibrium states, ground states, gapped states, Fermi surfaces) in terms of (algebraic) eigenstates.

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This is also part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027”. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

July 12, 2023 - 11:00
Aula Seminari III piano, third floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Massimo Moscolari (Politecnico di Milano)

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On the bulk-edge correspondence for (interacting) fermion systems

I will first show that for general 2d random ergodic magnetic Schrödinger operators the bulk magnetization equals the total edge current at any temperature. The equality between the bulk and edge quantum transport indices can be then obtained as a corollary of our purely analytical argument by imposing a gap condition and by taking a “zero temperature” limit. After that, I will briefly show how to extend the equality of bulk magnetization and total edge current to lattice fermion systems with short-range interactions and above a certain critical temperature. The talk is based on joint works with Horia Cornean, Jonas Lampart, Stefan Teufel and Tom Wessel.

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This is also part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027”. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

July 17, 2023 - 16:00
Sala Consiglio, seventh floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Angelo Lucia (Universidad Complutense de Madrid)

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Thermalization of quantum memories

Quantum memories are quantum spins systems designed to protect a quantum state from external noise. Contrary to the classical case, there are reasons to conjecture that there are no two-dimensional quantum memories that survive for long period of times at non-zero temperature.

In this talk, I will discuss a way to rigorously prove this conjecture, by estimating the mixing time of a class of
Quantum Markovian Semigroups. I will then present some recent results, regarding the case of so-called Kitaev’s quantum double models, for which we can perform such estimate and confirm the conjecture.

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This is also part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027”. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

May 25, 2023 - 14h30
Aula Seminario III Piano, Politecnico di Milano
Edificio 14 (Nave), Campus Leonardo

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SPEAKER: Hynek Kovarik (Università degli studi di Brescia)

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Resolvent expansion and time decay of the wave functions of magnetic Hamiltonians in dimension two

I this talk I will present some results on the resolvent expansions of magnetic Hamiltonians at the threshold of the essential spectrum. I will show, in particular, that the nature of the expansion of a two-dimensional magnetic Hamiltonian is completely determined by the flux of the associated magnetic field. Applications to time decay of the wave functions will be discussed as well.