Related papers: Exotic Ground States of Directional Pair Potential…
It has been shown numerically that systems of particles interacting with "stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are, counterintuitively, disordered, hyperuniform…
Systems of particles interacting with "stealthy" pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely…
We derive new duality relations that link the energy of configurations associated with a class of soft pair potentials to the corresponding energy of the dual (Fourier-transformed) potential. We apply them by showing how information about…
Bounded interactions are particularly important in soft-matter systems, such as colloids, microemulsions, and polymers. We derive new duality relations for a class of soft potentials, including three-body and higher-order functions, that…
Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space R^d. In the…
We provide numerical constructions of one-dimensional hyperuniform many-particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but…
Density (or state) dependent pair potentials arise naturally from coarse-graining procedures in many areas of condensed matter science. However, correctly using them to calculate physical properties of interest is subtle and cannot be…
Classical ground states (global energy-minimizing configurations) of many-particle systems are typically unique crystalline structures, implying zero enumeration entropy of distinct patterns (aside from trivial symmetry operations). By…
We study the ground-state properties of a two-component fermionic mixture effectively confined in a one-dimensional harmonic trap. We consider scenarios when numbers of particles in components are the same but particles have different…
It has recently been shown that one-dimensional Ising problems can have degenerate, disordered ground states (GSs) over a finite range of coupling onstants, ie, without `fine tuning'. The disorder is however of a special kind, consisting of…
Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state…
Frustrated magnets typically possess a large space of classical ground states. If this degeneracy is not protected by symmetry, thermal fluctuations may `select' certain states via order-by-disorder. In this article, we examine a precursor…
Disordered hyperuniform many-particle systems have attracted considerable recent attention. One important class of such systems is the classical ground states of "stealthy potentials." The degree of order of such ground states depends on a…
If particles interact according to isotropic pair potentials that favor multiple length scales, in principle a large variety of different complex structures can be achieved by self-assembly. We present, motivate, and discuss a conjecture…
We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations…
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large…
We study the ground-state properties of one-dimensional fluids of classical (i.e., non-quantum) particles interacting pairwisely via a potential, at the fixed particle density $\rho$. Restricting ourselves to periodic configurations of…
The nature of extended states in disordered tight binding models with a constant imaginary vector potential is explored. Such models, relevant to vortex physics in superconductors and to population biology, exhibit a delocalization…
We study the existence of one-dimensional localized states supported by linear periodic potentials and a domain-wall-like Kerr nonlinearity. The model gives rise to several new types of asymmetric localized states, including single- and…
We consider ground states of the $N$ coupled fermionic nonlinear Schr\"{o}dinger systems with the Coulomb potential $V(x)$ in the $L^2$-subcritical case. By studying the associated constraint variational problem, we prove the existence of…