Related papers: On the three-dimensional shape of a crystal
A method for taking into account the long-range potential of atoms in the framework of the hard-sphere model is proposed. It is shown that thermodynamic quantities can be represented as a sum of three contribution: that of an ideal gas, the…
Minimizing the so-called "Dirichlet energy" with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the…
We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological…
We consider thermodynamics of the excluded volume particles at finite temperature and chemical potential, in the low density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas…
Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical…
We present a sufficient criterion for the emergence of cluster phases in an ensemble of interacting classical particles with repulsive two-body interactions. Through a zero-temperature analysis in the low density region we determine the…
We consider a "symmetric" quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of "rapid" rotation. We examine this problem using a purely numerical approach, as well as a…
Following a strong analogy with two-dimensional physics, the three-body pseudo-potential in one dimension is derived. The Born approximation is then considered in the context of ultracold atoms in a linear harmonic waveguide. In the…
A new kind of the relativistic three-body equations for the three fermion systems are suggested. These equations are derived in the framework of the standard field-theoretical $S$-matrix approach in the time-ordered three dimensional form.…
We demonstrate that unrestricted Hartree-Fock theory applied to electrons in a uniform potential has stable Wigner crystal solutions for $r_s \geq 1.44$ in two dimensions and $r_s \geq 4.5$ in three dimensions. The correlation energies of…
A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the…
The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set $\Omega \subset \mathbb R^3$ with given volume A that minimizes the sum of its surface area…
A microscopic picture of the ``preparation'' of a crystal to the transition to liquid state at the approach to melting temperature is proposed. Basing on simple crystallogeometric considerations and the analysis of the computational results…
We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration…
We revisit the concavity property of the thermodynamic entropy in order to formulate a general proof of the minimum energy principle as well as of other equivalent extremum principles that are valid for thermodynamic potentials and…
For the St$\ddot u$ckelberg-modified massive Abelian 3-form theory in any arbitrary D-dimension of spacetime, we show that its classical gauge symmetry transformations are generated by the first-class constraints. We establish that the…
Consider the energy per particle on the lattice given by $\min_{ \Lambda }\sum_{ \mathbb{P}\in \Lambda} \left|\mathbb{P}\right|^4 e^{-\pi \alpha \left|\mathbb{P}\right|^2 }$, where $\alpha >0$ and $\Lambda$ is a two dimensional lattice. We…
We solve Talagrand's entropy problem: the L_2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley's theorem on classes of {0,1}-valued functions, for which the…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate…