相关论文: The one-dimensional equilibrium shape of a crystal

We study the problem of whether the active gravitational mass of an isolated system is equal to the total energy in the tetrad theory of gravitation. The superpotential is derived using the gravitational Lagrangian which is invariant under…

The one dimensional one component plasma has applications to one dimensional particle systems with logarithmic interactions such as charges in a single channel wire or vortex filaments in a fluid convection stream. The exact integral of…

We study the structural properties of a quasi-one-dimensional classical Wigner crystal, confined in the transverse direction by a parabolic potential. With increasing density, the one-dimensional crystal first splits into a zigzag crystal…

The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate…

In this work, we analyze a scalar field model which gives rise to stable bound states in field space characterized by nonzero motion that breaks the underlying time translation symmetry of its Hamiltonian, known as time crystals. We…

The calculation of crystal structure from X-ray diffraction data requires that the phases of the ``structure factors'' (Fourier coefficients) determined by scattering be deduced from the absolute values of those structure factors. Motivated…

Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…

Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is…

For a full shift with Np+1 symbols and for a non-positive potential, locally proportional to the distance to one of N disjoint full shifts with p symbols, we prove that the equilibrium state converges as the temperature goes to 0. The main…

We touch upon a long-standing question of the "true" one-dimensional hydrogen atom solution. From a symmetry point of view, Kepler problem in $d\ge2$ dimension is characterized by geometrical rotational symmetry, $SO(d)$, as well as…

We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has…

Proceeding from the new gravitation equations (Phys.Lett.A,v.156, p.404 (1991)) we argue that the theory in principle allows equilibrium stable configurations of a degenerate electron or neutron gas with very large masses.

In the present article we determine the exact shape of an ideal spring suspended at both ends. Historically, this goes under the name of Elastica problem. The total energy of the suspended spring is a functional depending on two independent…

We analyse the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading ($\ln N/N$) corrections, the remaining free energy is found to depend linearly on 1/N.…

We show that gravitational energy expression simplifies when a new set of coordinates that satisfies a certain asymptotic gauge condition is used. Compared to the ADM formula, positivity of the energy is more transparent in this new…

In the self-sufficient potential formalism, treating all electromagnetic phenomena as natural or forced oscillations of some distributed electromagnetic oscillating system (Minkowski space-time), the electromagnetic potential must be…

The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state…

The evolution of a vacuum component of the Universe is investigated in the quantum as well as the classical regimes. Probably our Universe has arisen as a vacuum fluctuation and very probably that it has had a high symmetry for Planckian…

Coulomb systems in which the particles interact through the $d$-dimensional Coulomb potential but are confined in a flat manifold of dimension $d - 1$ are considered. The Coulomb potential is defined with some boundary condition involving a…

This chapter is a tutorial on techniques and results in free convex algebraic geometry and free real algebraic geometry (RAG). The term free refers to the central role played by algebras of noncommutative polynomials R<x> in free (freely…