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Both ``phason'' elastic constants have been measured from Monte Carlo simulations of a random-tiling icosahedral quasicrystal model with a Hamiltonian. The low-temperature limit approximates the ``canonical-cell'' tiling used to describe…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
Almost all observed square-triangle quasicrystals in soft-matter systems contain a large number of point-like defects, yet the role these defects play in stabilizing the quasicrystal phase remains poorly understood. In this work, we…
We present in this work a generalization of the solution of Gorenstein and Yang to the inconsistency problem of thermodynamics for systems of quasi-particles whose masses depend on both the temperature and the chemical potential. We work…
Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of structural periodicity challenge methods of experimental structure determination. Here we employ quantum-based total-energy calculations to predict the structure…
Despite an artificial intelligence-assisted modeling of disordered crystals is a widely used and well-tried method of new materials design, the issues of its robustness, reliability, and stability are still not resolved and even not…
Attempts to understand zero temperature phase transitions have forced physicists to consider a regime where the standard paradigms of condensed matter physics break down [1-4]. These quantum critical systems lack a simple description in…
We develop a finite-temperature perturbation theory for quasi-one-dimensional quantum spin systems, in the manner suggested by H.J. Schulz (1996) and use this formalism to study their dynamical response. The corrections to the random-phase…
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The…
Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schr\"odinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra…
The dynamics of quasicrystals is more complicated than the dynamics of periodic solids and difficult to study in experiments. Here, we investigate a decagonal and a dodecagonal quasicrystal using molecular dynamics simulations of the…
Recent discovery of the superconducting ground state in Quasicrystals (QCs) has opened up an exciting new avenue for superconductivity based on QCs. However, theoretical studies to date have largely focused on a limited subset of…
Quantum thermodynamics with open systems is often based on the quantum optical weak-coupling master equation or on operational repeated interaction models, whereas early works on thermalisation and on decoherence theory were mostly…
We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants. These approximant structures imply a deterministic decoration of tiles by atoms that can be extended quasiperiodically. Experimentally observed structural…
Droplets of a pure fluid, such as water, in an open container surrounded by gas, are thermodynamically unstable and evaporate quickly. In a recent paper [Archer et al. J. Chem. Phys. {\bf 159}, 194403 (2023)] we employed lattice density…
Based on density functional theory the noncentrosymmetric superconductor Mo_3Al_2C in its well established {\beta}-Mn type ($P4_{1}32$) crystal structure is investigated. In particular, its thermodynamical and dynamical stabilities are…
To study temperature dependent elastic constants, a new computational method is proposed by combining continuum elasticity theory and first principles calculations. A Gibbs free energy function with one variable with respect to strain at…
This paper summarises a two-hour discussion at the Ninth International Conference on Quasicrystals, including nearly 20 written comments sent afterwards, concerning (i) the meaning [if any] of clusters in quasicrystals; (ii) phason…
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a…