ERC FUNDED PROJECTS

This proposal puts forth a novel strategy to tackle large quantum systems. A variety of highly sophisticated methods such as quantum Monte Carlo, configuration interaction, coupled cluster, tensor networks, Feynman diagrams, dynamical mean-field theory, density functional theory, and semi-classical techniques have been developed to deal with the enormous complexity of the many-particle Schrödinger equation. The goal of our proposal is not to add another method to these standard techniques but, instead, we develop a systematic way of combining them. The essential ingredient is a novel way of decomposing the wave function without approximation into factors that describe subsystems of the full quantum system. This so-called exact factorization is asymmetric. In the case of two subsystems, one factor is a wave function satisfying a regular Schrödinger equation, while the other factor is a conditional probability amplitude satisfying a more complicated Schrödinger-like equation with a non-local, non-linear and non-Hermitian “Hamiltonian”. Since each subsystem is necessarily smaller than the full system, the above standard techniques can be applied more efficiently and, most importantly, different standard techniques can be applied to different subsystems. The power of the exact factorization lies in its versatility. Here we apply the technique to five different scenarios: The first two deal with non-adiabatic effects in (i) molecules and (ii) solids. Here the natural subsystems are electrons and nuclei. The third scenario deals with nuclear motion in (iii) molecules attached to semi-infinite metallic leads, requiring three subsystems: the electrons, the nuclei in the leads which ultimately reduce to a phonon bath, and the molecular nuclei which may perform large-amplitude movements, such as current-induced isomerization, (iv) purely electronic correlations, and (v) the interaction of matter with the quantized electromagnetic field, i.e., electrons, nuclei and photons.

2 443 932 €

Start date: 2019-09-01, End date: 2024-08-31

FractFrict is a comprehensive study of the space-time dynamics that lead to the failure of both bulk materials and frictionally bound interfaces. In these systems, failure is precipitated by rapidly moving singular fields at the tips of propagating cracks or crack-like fronts that cause material damage at microscopic scales. These generate damage that is macroscopically reflected as characteristic large-scale, modes of material failure. Thus, the structure of the fields that microscopically drive failure is critically important for an overall understanding of how macroscopic failure occurs. The innovative real-time measurements proposed here will provide fundamental understanding of the form of the singular fields, their modes of regularization and their relation to the resultant macroscopic modes of failure. Encompassing different classes of bulk materials and material interfaces. We aim to: [1] To establish a fundamental understanding of the dynamics of the near-tip singular fields, their regularization modes and how they couple to the macroscopic dynamics in both frictional motion and fracture. [2] To determine the types of singular failure processes in different classes of materials and interfaces (e.g. the brittle to ductile transition in amorphous materials, the role of fast fracture processes in frictional motion). [3] To establish local (microscopic) laws of friction/failure and how they evolve into their macroscopic counterparts [4]. To identify the existence and origins of crack instabilities in bulk and interface failure The insights obtained in this research will enable us to manipulate and/or predict material failure modes. The results of this study will shed considerable new light on fundamental open questions in fields as diverse as material design, tribology and geophysics.

2 265 399 €

Start date: 2010-12-01, End date: 2016-11-30

We present a novel constructive approach for realizations of topological states of matter. Our approach starts with well-understood building blocks, and proceeds towards coupling them to create the desired states. This approach promises both a guide for a tunable experimental realization of states which have not been observed so far, and a theoretical tool for deeper understanding of different topological states, their dualities and inter-relations. We will apply the constructive approach in two different directions. In the first direction our goal will be the construction of topological superconductors. Our tool will be Josephson junctions in which superconductors are coupled by two- and three-dimensional electronic non-superconducting systems. Two dimensional examples include transition metal dichalcogenides, Quantum Hall states, Quantum Anomalous Hall states, and the (111) bi-layer state, which may be viewed as a fractionalized electron-hole condensate. Three dimensional examples include Weyl semi-metals and weak topological insulators. In the second direction our goal is the construction of fractionalized spin liquid states. Our building block will be a Majorana-Cooper box, which is a superconducting quantum dot coupled to semi-conducting wires that host Majorana zero modes. We will consider arrays of such boxes. The ratio of the box's charging energy to inter-box tunnel-coupling determines whether the array is superconducting or insulating. We will aim to use insulating arrays for realizing fractionalized and non-abelian spin liquids, study the transition to the superconducting state, and search for possible relations between the topological properties on both sides of the transition. A deeper comprehension and a feasible path for realization of these states would have a profound effect on the field of topological matter and will open novel avenues for universal topological quantum computers.

1 532 163 €

Start date: 2018-10-01, End date: 2023-09-30

At the boundaries of physics research it is constantly necessary to introduce new tools and methods to expand the horizons and address fundamental issues. In this proposal, we will develop and then apply radically new tools that will enable groundbreaking progress in the field of vortex matter in superconductors and will be of great importance to condensed matter physics and nanoscience. We propose a new scanning magnetic imaging method based on self-aligned fabrication of Josephson junctions with characteristic sizes of 10 nm and superconducting quantum interference devices (SQUID) with typical diameter of 100 nm on the end of a pulled quartz tip. Such nano-SQUID on a tip will provide high-sensitivity high-bandwidth mapping of static and dynamic magnetic fields on nanometer scale that is significantly beyond the state of the art. We will develop a new washboard frequency dynamic microscopy for imaging of site-dependent vortex velocities over a remarkable range of over six orders of magnitude in velocity that is expected to reveal the most interesting dynamic phenomena in vortex mater that could not be investigated so far. Our study will provide a novel bottom-up comprehension of microscopic vortex dynamics from single vortex up to numerous predicted dynamic phase transitions, including disorder-dependent depinning processes, plastic deformations, channel flow, metastabilities and memory effects, moving smectic, moving Bragg glass, and dynamic melting. We will also develop a hybrid technology that combines a single electron transistor with nano-SQUID which will provide an unprecedented simultaneous nanoscale imaging of magnetic and electric fields. Using these tools we will carry out innovative studies of additional nano-systems and exciting quantum phenomena, including quantum tunneling in molecular magnets, spin injection and magnetic domain wall dynamics, vortex charge, unconventional superconductivity, and coexistence of superconductivity and ferromagnetism.

2 000 000 €

Start date: 2008-12-01, End date: 2013-11-30