Related papers: Properties of Quantum Graphity at Low Temperature
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
The quantum circuit model is the default for encoding an algorithm intended for a NISQ computer or a quantum computing simulator. A simple graph and through it, a graph state - quantum state physically manifesting an abstract graph…
In this work we present (and encourage the use of) the Williamson theorem and its consequences in several contexts in physics. We demonstrate this theorem using only basic concepts of linear algebra and symplectic matrices. As an immediate…
Proceeding from the model of a two-dimensional elastic continuum, we describe the characteristic features of thermal expansion of graphene using an approach that goes beyond the quasi-harmonic approximation. The negative value of the…
In this paper we study spectral properties of adjacency and Laplace operators on percolation subgraphs of Cayley graphs of amenable, finitely generated groups. In particular we describe the asymptotic behaviour of the integrated density of…
Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath.…
Electrons in quantum matter behave like a fluid when the quantum-mechanical carrier-carrier scattering dominates over other relaxation mechanisms. By combining a microscopic treatment of electron-electron interactions within the random…
We present a sufficient condition for the presence of spontaneous magnetization for the Ising model on a general graph, related to its long-range topology. Applying this condition we are able to prove the existence of a phase transition at…
We show that energy dissipation in slowly-driven, Markovian quantum systems at low temperature is linked to the geometry of the driving protocol through the quantum (or Fubini-Study) metric. Utilizing these findings, we establish lower…
Quantum lattice systems are rigorously studied at low temperatures. When the Hamiltonian of the system consists of a potential (diagonal) term and a - small - off-diagonal matrix containing typically quantum effects, such as a hopping…
Variational geometries describing corrugated graphene sheets are proposed. The isothermal thermomechanical properties of these sheets are described by a 2-dimensional Weyl space. The equation that couples the Weyl geometry with isothermal…
The formation of metallic nanofilaments bridging two electrodes across an insulator is a mechanism for resistive switching. Examples of such phenomena include atomic synapses, which constitute a distinct class of memristive devices whose…
Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting…
The instability of a Fermi surface against Ising nematic order destroys the quasiparticle character of the low-energy degrees of freedom. Therefore, observables exhibit deviations from Fermi liquid behavior which gives rise to the term…
We examine transmission through a quantum graph vertex to which auxiliary edges with constant potentials are attached. We find a characterization of vertex couplings for which the transmission probability from a given "input" line to a…
The Feynman-Vernon path integral formalism is used to derive the density matrix of a quantum oscillator that is linearly coupled to an environmental reservoir. Although low-temperature reservoirs thermalize the oscillator to the usual…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
Molecular dynamics simulations are a central computational methodology in materials design for relating atomic composition to mechanical properties. However, simulating materials with atomic-level resolution on a macroscopic scale is…
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order…
We show that after a quantum quench of the parameter controlling the number of particles in a Fermi-Hubbard model on scale free graphs, the distribution of energy modes follows a power law dependent on the quenched parameter and the…