In this talk I will show that the notion of chaos both in quantum and classical Hamiltonian systems can be rigorously formulated through complexity of adiabatic transformations. This complexity is encoded in the fidelity susceptibility or more broadly in the geometric tensor. In classical systems this measure reflects complexity of trajectory-preserving canonical transformations under...
I will present a renormalization group analysis of the problem of the Anderson localization on a Regular Random Graph which is the limit of the RG flow of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs.
I will show how the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables and...
The tension created by the interplay of the contrary forces of chaos and measurements can lead to fascinating emerging phenomena, as exemplified by the recently discovered Measurement-induced Phase Transitions (MiPT) in quantum chaotic many-body systems undergoing continuous or projective measurements.
In this talk, I will demonstrate that this tension still remains when the problem is...
Flocks of animals represent a fascinating archetype of collective behavior in the macroscopic classical world, where the constituents, such as birds, concertedly perform motions and actions as if being one single entity. Here, we address the outstanding question of whether flocks can also form in the microscopic world at the quantum level. For that purpose, we introduce the concept of active...
We consider a time-dependent small quantum system weakly coupled to an environment, whose effective dynamics we address by means of a Lindblad equation. We assume the Hamiltonian part of the Lindbladian is slowly varying in time and the dissipator part has small amplitude. We study the properties of the evolved state of the small system as the adiabatic parameter and coupling constant both go...
In this talk I will review recent theoretical results on the linear, nonlinear and quantum dynamics of the edge modes of a trapped fractional quantum Hall fluid. A generalized nonlinear chiral Luttinger liquid theory will be presented, together with its validation against numerical results obtained with a combination of Monte Carlo and exact diagonalization methods. A first application of this...
This talk is a tale of two halves. In the first part, we will discuss recent progress on the use of variational neural quantum states to describe the non-unitary and/or non-equilibrium dynamics of quantum many-body systems [1,2].
In the second part, we will show how the complex dynamics of quantum systems can be harnessed as a resource for machine learning and neuromorphic devices. In...
Time crystalline structures can be created in periodically driven systems. They are temporal lattices which can reveal different condensed matter behaviours ranging from Anderson localization in time to temporal analogues of many-body localization or topological insulators. However, the potential practical applications of time crystalline structures have not yet been demonstrated.
We pave...
The Yang-Lee edge singularity is a quintessential nonunitary critical phenomenon characterized by anomalous scaling. However, an imaginary magnetic field involved in this phenomenon makes its physical implementation highly nontrivial. We invoke the quantum-classical correspondence and quantum measurement to physically realize the nonunitary quantum criticality in an open quantum system [1]....
Quantum technologies are all about controlling quantum systems. Control is the prerequisite to exploit the two essential elements of quantum physics, non-locality and coherence, for practical applications. This currently faces two major challenges --- to preserve the relevant non-classical features at the level of device operation and to scale the devices up in size.
Control theory...
Two-dimensional time-reversal invariant topological superconductors (TRITOPS) host a Kramers pair of propagating edge states. Their coupling in a Josephson junction can be described by a Dirac Hamiltonian with a mass term that depends on the phase bias of the junction. Notably, this mass term exhibits different characteristics in junctions between TRITOPS compared with those between a TRITOPS...
I will put forth a unifying formalism for the description of the thermodynamics of continuously monitored systems, where measurements are only performed on the environment connected to a system. I will show, in particular, that the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by the...
