Related papers: Progress in the mathematical theory of quantum dis…
We consider quantum trajectories arising from disordered, repeated generalized measurements, which have the structure of Markov chains in random environments (MCRE) with dynamically-defined transition probabilities; we call these disordered…
An exact solution of a Landau model of an order-disorder transition with activated critical dynamics is presented. The model describes a funnel-shaped topography of the order parameter space in which the number of energy lowering…
All-to-all interacting, disordered quantum many-body models have a wide range of applications across disciplines, from spin glasses in condensed-matter physics, over holographic duality in high-energy physics, to annealing algorithms in…
A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204 (2012), arXiv:1206:0783] compares the low-temperature phase of the 3D Edwards-Anderson (EA) model to its mean-field counterpart, the Sherrington-Kirkpatrick (SK) model.…
We present new results reflecting the analogies between the Kob-Andersen model and other glassy systems. Studying the stability of the blocked configurations above and below the transition we also give arguments that supports their…
Understanding how closed quantum systems dynamically approach thermal equilibrium presents a major unresolved problem in statistical physics. Generically, non-integrable quantum systems are expected to thermalize as they comply with the…
We examine the phase diagram of the $p$-interaction spin glass model in a transverse field. We consider a spherical version of the model and compare with results obtained in the Ising case. The analysis of the spherical model, with and…
At low temperature T, a significant difference between the behavior of crystals on the one hand and disordered solids on the other is seen: sufficiently strong disorder can give rise to a transition of the transport properties from…
Motivated by the recent development of quantum technology using quantum annealing technique and the recent works on the static properties of the Sherrington-Kirkpatrick (SK) spin glass model, we study quantum annealing of the spin glass…
Disorder in quantum systems can lead to the disruption of long-range order in the ground state and to the localization of the elementary excitations - famous examples thereof being the Bose glass of interacting bosons in a disordered or…
The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization - delocalization (MBLD) transition when viewed as a closed quantum system.…
In this paper I will review my work on disordered systems -spin glass model with two body and $p>2$ body interactions- with long but finite interaction range $R$. I will describe the relation of these model with Mean Field Theory in the Kac…
We prove the approach to equilibrium of quenched isolated quantum systems for which the change in the Hamiltonian brought about by the quench satisfies a certain closed commutator algebra with all the extensive integrals of motion of the…
We consider nonequilibrium systems such as the Edwards-Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken symmetry pure states. Following a deep quench, we argue that as time goes…
A promising approach to solving hard binary optimisation problems is quantum adiabatic annealing (QA) in a transverse magnetic field. An instantaneous ground state --- initially a symmetric superposition of all possible assignments of $N$…
We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy and crystalline states. The disordered phases…
We investigate the possibility of an Anderson transition below two dimensions in disordered systems of non-interacting electrons with symplectic symmetry. Numerical analysis of energy level statistics and conductance statistics on…
We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken SU(2) spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto the…
Impurities, defects, and other types of imperfections are ubiquitous in realistic quantum many-body systems and essentially unavoidable in solid state materials. Often, such random disorder is viewed purely negatively as it is believed to…
Ising spin glasses in a transverse field exhibit a zero temperature quantum phase transition, which is driven by quantum rather than thermal fluctuations. They constitute a universality class that is significantly different from the…