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In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…

Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now,…

We consider the two-body problem in a periodic potential, and study the bound-state dispersion of a spin-$\uparrow$ fermion that is interacting with a spin-$\downarrow$ fermion through a short-range attractive interaction. Based on a…

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that…

A brief survey of the author's works on the quantum theory of magnetism. Theoretical foundation and applications of the generalized spin-fermion (sp-d) exchange lattice model to various magnetic systems, e.g., rare-earth metals and…

The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in…

Bound states in the continuum provide a remarkable example of how a simple problem solved about a century ago in quantum mechanics can drive the research on a whole spectrum of resonant phenomena in wave physics. Due to their huge radiative…

A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…

We review the basic concepts of quantum fluids of light and the different techniques that have been developed to exploit driving and dissipation to stabilize and manipulate interesting many-body states. In the weakly interacting regime,…

Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions…

While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…

In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…

Quantum many-body simulation provides a straightforward way to understand fundamental physics and connect with quantum information applications. However, suffering from exponentially growing Hilbert space size, characterization in terms of…

The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics,…

The use of ultra-low temperature cooling and of high hydrostatic pressure techniques has significantly expanded our understanding of the two-dimensional electron gas confined to GaAs/AlGaAs structures. This chapter reviews a selected set of…

Lectures notes for 2004 Les Houches Summer School on "Nanoscopic Quantum Transport". These lectures contain an introduction to Keldysh formalism for interacting bosonic and fermionic systems, presented in the functional integral framework.…

In quantum many-body problems, one of the main difficulties comes from the description of non-negligible interactions which require, at least in principle, an exponential amount of information. Recently, in the context of spin glasses and…

Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an…

Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. The lectures covered quantum mechanics for closed systems like the universe, generalized quantum mechanics, time in…

In this work we investigate the continuous confinement of quantum systems from three to two dimensions. Two different methods will be used and related. In the first one the confinement is achieved by putting the system under the effect of…