Month: July 2023

13/07/2023: Diwakar Naidu @ UniMi

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

SPEAKER: Diwakar Naidu (Universität Tübingen)

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. |Ψt|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.

12/07/2023: Giuseppe De Nittis @ PoliMi

Marco FalconiSeminar PoliMi 
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)

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.

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.

12/07/2023: Massimo Moscolari @ PoliMi

Marco FalconiSeminar PoliMi 
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)

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.

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.

9/10/2023: Asbjørn Bækgaard Lauritsen @ UniMi

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

SPEAKER: Asbjørn Bækgaard Lauritsen (IST Austria)

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.

IQMM talk LauritsenDownload