The temporal evolution of certain aggregates of particles — of neutrons in a multiplying medium, of electron-photon cascades in cosmic rays, say — can be successfully modeled via so-called branching processes. A brief overview of the most popular classes of branching processes is given. In particular the continuous-time Bienaymé-Galton-Watson processes and continuous-state branching processes are described as time-changed Lévy processes that are “skip-free downwards”.
Márton Mestyán: Spin-charge separation effects in the low-temperature transport of one-dimensional Fermi gases
We study the transport properties of the Yang–Gaudin model – a one-dimensional, integrable, spinful Fermi gas – after a junction of two semi-infinite subsystems held at different temperatures. The ensuing dynamics is studied by analyzing the space-time profiles of local observables emerging at large distances x and times t, as a function of ζ=x/t. At equilibrium, the system displays two distinct species of quasiparticles, naturally associated with different physical degrees of freedom. By employing the generalized hydrodynamic approach, we show that when the temperatures are finite no notion of separation can be attributed to the quasiparticles. In this case, the profiles can not be qualitatively distinguished by those associated to quasiparticles of a single species that can form bound states. On the contrary, signatures of separation emerge in the low-temperature regime, where two distinct characteristic velocities appear. In this regime, we analytically show that the profiles display a piecewise constant form and can be understood in terms of two decoupled Luttinger liquids.
* Márton Mestyán, SISSA, Trieste
[1] M. M., B. Bertini, L. Piroli, P. Calabrese, Phys. Rev. B 99, 014305 (2019)
Michele Filippone: Identical Suppression and Universality of the Hall Response in Interacting Quantum Lattices
The Hall effect is known as the voltage drop V perpendicular to the current I and magnetic field B (B⊥ I) measurable in electric conductors. Its importance relies in the fact that, at weak field, the Hall constant R = V/(IB) ≈ -1/(nq) and measures the charge q and density n of charge carriers. Nevertheless, its calculation remains an open problem in strongly correlated systems. We demonstrate the identical suppression of the Hall response in quasi two-dimensional ballistic lattices, which is robust to large variations of magnetic field, Fermi level, temperature, disorder and absence of particle-hole symmetry. This suppression is unexpected and we show its relation to the topological properties of the Fermi surface: namely its central charge. We show that this suppression is commonly achieved in standard (Landauer) quantum transport settings and we rely on DMRG to show that our results equally apply to strongly interacting regimes [1]. Time permitting, I will also discuss how, in some particular cases, interactions do not affect the Hall response at all, universally leading to the non-interacting result R = -1/(nq).
* Michele Filippone, Université de Genève
[1] M. Filippone, C.-E. Bardyn, S. Greschner and T. Giamarchi, To appear soon.
[2] S. Greschner, M. Filippone and T. Giamarchi, arXiv:1809.10927.
Tony Jin: Equilibrium Fluctuations in Maximally Noisy Extended Quantum Systems
I will introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. I focus on periodic boundary conditions and derive the complete stationary distribution of the system. It is proven that the generating function of the latter is provided by the Harish-Chandra-Itzykson-Zuber integral which allows us to access all fluctuations of the system state. The steady state is characterized by non trivial correlations which have a topological nature. In the thermodynamic large system size limit, the system approaches a non random equilibrium state plus occupancy and coherence fluctuations of magnitude scaling proportionally with the inverse of the square root of the volume. The large deviation function for those fluctuations is determined. Although decoherence is effective on the mean steady state, we observe that sub-leading fluctuating coherences are dynamically produced from the inhomogeneities of the initial occupancy profile.
* Tony Jin, LPT ENS Paris
Adrian Ortega: Efficient quantum transport in disordered interacting many-body networks
We give an account of efficient quantum transport over disordered networks in fermionic inter- acting systems. The ingredient necessary to achieve good transport rates is centrosymmetry. We study transport efficiency in the time-dependent [Ann. Phys. 527 (2015)], as well as in the time- independent [Phys. Rev. E 94 (2016)] regimes. Later, we show how robust is the system against several types of perturbations. Finally, we show that in the presence of noise, centrosymmetry sets an upper bound for transport when compared to popular dephasing assisted transport [Phys. Rev. E 98 (2018)].
* Adrian Ortega, Centro Universitario de Ciencias Exactas e Ingeniería, Guadalajara, México
Eric Ragoucy: Integrability in out-of-equilibrium systems
Out-of-equilibrium systems have nowadays an important role in 1d statistical physics. Although an equilibrium state obviously doesn’t exist for such systems, one looks for a steady state (that is stationary in time). It is defined as the zero-eigenvalue eigenstate of the Markov matrix that describe the evolution of the system. Its exact computation is at the core of many researches.
In some cases, the matrix product state ansatz (matrix ansatz for short) allows to compute this steady state. However no general approach for this ansatz is known. On the other hand, many 1d statistical models appear to be integrable, which allows to get eigenstates of the Markov matrix through Bethe ansatz. The goal of this presentation is to show how integrability gives a natural framework to construct the matrix ansatz for 1d systems with boundaries.
It can be done on very general grounds, allowing to construct the matrix ansatz when it is not known, and also to define new models and/or to find boundary conditions ‘adapted’ to the model under consideration. We will illustrate the technique on some examples.
* Eric Ragoucy, Laboratoire d’Annecy-le-Vieux de Physique Théorique, Annecy, France
Mini-workshop on Transport in one-dimension
FMF, University of Ljubljana, 14th to 17th November 2018
Speakers: Fabian Heidrich-Meisner, Herbert Spohn, Peter Prelovšek, Maurizio Fagotti, Joel Moore, Bruno Bertini, Lenart Zadnik, Katja Klobas, Marko Ljubotina and Gyorgy Feher. The schedule can be found here.
The event will take place at the Kuščer Seminar room, 4^{th} floor, Jadranska 19, except for the Wednesday afternoon session, which takes place in the room 3.07, 3^{rd} floor, Jadranska 21.
4th Trieste–Ljubljana meeting
10:00 | coffee and discussions | |
---|---|---|
10:30 | Jacopo De Nardis (ENS Paris): Hydrodynamic diffusion and super-diffusion in integrable models | |
11:30 | Lenart Zadnik (FMF Ljubljana): Spin transport in the Trotterized XXZ model | |
12:05 | Scott Taylor (ICTP): Energy transport and many-body localisation in the disordered XYZ model | |
12:40 | lunch | |
13:30 | discussions | |
15:15 | Katja Klobas (FMF Ljubljana): Time-dependent matrix product ansatz for interacting reversible dynamics | |
15:50 | Tommaso Parolini/Rajat Panda (ICTP): SU(2) symmetry vs many-body localization: a HPC take on the random Heisenberg chain | |
16:25 | Erik Tonni (SISSA): Holographic entanglement entropy in AdS(4)/BCFT(3) | |
17:00 | conclusion |
Vladislav Popkov: Effective evolution of an open quantum system in Zeno regime
We consider a Lindblad time evolution of an open quantum system with dissipation acting on a subset of the degrees of freedom H_{0}, and targeting a unique dark state in H_{0}. It is argued, that in the Zeno limit of strong dissipation, the density matrix of the system traced over the dissipative subspace H_{0}, evolves according to another Lindblad dynamics, with an effective Hamiltonian and weak effective dissipation. This, in turn, allows to calculate the steady state in Zeno limit via a diagonalization of the effective Hamiltonian.
* Vladislav Popkov, Universität Bonn
[1] Link to the preprint.
Lenart Zadnik: Spin transport in the Trotterized XXZ model
I will present work in progress with Marko Ljubotina. We will discuss quasilocal conservation laws in the Trotterized XXZ model and their implications on the spin transport. Interestingly, the model exhibits ballistic transport even for a range of anisotropies which pertain to the gapped regime in the continuous-time limit.
* Lenart Zadnik, Faculty of Mathematics and Physics, University of Ljubljana