Related papers: Properties of Quantum Graphity at Low Temperature
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…
We consider sampling in the so-called low-temperature regime, which is typically characterised by non-local behaviour and strong global correlations. Canonical examples include sampling independent sets on bipartite graphs and sampling from…
Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable…
This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions interactions arise naturally in several…
Using the theory of diffusion in graphs, we propose a model to study mesoscopic transport through a diffusive quantum dot. The graph consists of three quasi-1D regions: a central region describing the dot, and two identical left- and right-…
Ohm's law describes the proportionality of current density and electric field. In solid-state conductors, Ohm's law emerges due to electron scattering processes that relax the electrical current. Here, we use nitrogen-vacancy center…
Owing to its peculiar energy dispersion, the quantum capacitance property of graphene can be exploited in a two-dimensional layered capacitor configuration. Using graphene and boron nitride respectively as the electrodes and the insulating…
We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical…
We present a quantum statistical analysis of a microscopic mean-field model of structural glasses at low temperatures. The model can be thought of as arising from a random Born von Karman expansion of the full interaction potential. The…
A graph homomorphism from the rooted $d$-branching tree $\phi: T^d \to H$ is said to be cold if the values of $\phi$ for vertices arbitrarily far away from the root can restrict the value of $\phi$ at the root. Warmth is a graph parameter…
We introduce a new graph parameter called the cooling number, inspired by the spread of influence in networks and its predecessor, the burning number. The cooling number measures the speed of a slow-moving contagion in a graph; the lower…
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…
Thermal operations are an operational model of non-equilibrium quantum thermodynamics. In the absence of coherence between energy levels, exact state transition conditions under thermal operations are known in terms of a mathematical…
We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…
The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models…
Quantum oscillations of metallic systems at low temperatures is one of the key rules to experimentally access their electronic properties, such as energy spectrum, scattering mechanisms, geometry of Fermi surface and many other features.…
This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the…