Related papers: Isomorphs, hidden scale invariance, and quasiunive…
Scale invariance may be a classical symmetry which is broken radiatively. This provides a simple way to stabilise the scale of electroweak symmetry breaking against radiative corrections. But for such a theory to be fully realistic, it must…
Intermediate energy scale physics plays a very important role in non-equilibrium dynamics of quasi-low dimensional cold atom systems. In this article we obtain the universal scaling relations for the generalized reflection coefficient,…
The Schr\"odinger-Poisson formalism has found a number of applications in cosmology, particularly in describing the growth by gravitational instability of large-scale structure in a universe dominated by ultra-light scalar particles. Here…
We calculate the relative conserved currents, superpotentials and conserved quantities between two homogeneous and isotropic universes. In particular we prove that their relative "energy" (defined as the conserved quantity associated to…
Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are…
Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type…
It is demonstrated by molecular dynamics simulations that liquids interacting via the Buckingham potential are strongly correlating, i.e., have regions of their phase diagram where constant-volume equilibrium fluctuations in the virial and…
In order to provide a formally correct thermodynamical description of inhomogeneous fluids valid on all length scales down to the classical limit we postulate that all extensive quantities have locally extensive analogues. We derive local…
In this paper we consider the one dimensional quantum hydrodynamics (QHD) system, with a genuine hydrodynamic approach. The global existence of weak solutions with large data has been obtained in [2, 3], in several space dimensions, by…
Rapidly rotating, stably stratified three-dimensional inviscid flows conserve both energy and potential enstrophy. We show that in such flows, the forward cascade of potential enstrophy imposes anisotropic constraints on the wavenumber…
We use a one-dimensional (1d) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The core-softened potential mimics the effect of hydrogen bonding. The interest in the 1d system stems…
We consider a special class of quasi-periodic potentials arising in the physics of photonic systems and possessing rotational symmetry of the 8th order. We are interested in the ``scaling'' properties of such potentials, namely, the growth…
In this paper, we propose a general mechanism for the existence of quasicrystals in spatially extended systems (partial differential equations with Euclidean symmetry). We argue that the existence of quasicrystals with higher order…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
An attractive method of obtaining an effective cosmological constant at the present epoch is through the potential energy of a scalar field. Considering models with a perfect fluid and a scalar field, we classify all potentials for which…
We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value on any diffeomorphism supported in a sufficiently small…
Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland…
Zero curvature formulations, pseudo-potentials, modified versions, ``Miura transformations'', and nonlocal symmetries of the Korteweg--de Vries, Camassa-- Holm and Hunter--Saxton equations are investigated from an unified point of view:…
Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…
A liquid is termed strongly correlating if its virial and potential energy thermal equilibrium fluctuations in the NVT ensemble are more than 90% correlated [Phys. Rev. Lett. 100, 015701 (2008)]. The fluctuations of a strongly correlating…