Published July 2009 | Version v1
Journal article Metadata-only

Mathematical issues in the modelling of supersolids

Creators

  • 1. CMAP, UMR 7641, Ecole Polytechnique, 91128, Palaiseau Cedex (France)
  • 2. UPMC University Paris 06, UMR 7598, Laboratoire J.-L. Lions, F-75005, Paris (France)
  • 3. Department of Mathematics, University of Toronto, Toronto, M5S 2E4 Canada (Canada)

Description

We study a model of supersolids or quantum crystals introduced in (Josserand et al 2007 Phys. Rev. Lett. 98 195301, Josserand et al 2007 Eur. Phys. J. S. T. 146 47–61), following recent experiments in helium 4. This model is based on a Gross–Pitaevskii energy with a nonlocal interaction term. We give a description of the ground state in the limit of strong interaction, and relate it to a sphere packing problem. We also study the effect of rotation. In dimension one, we prove that the ground state has a periodic structure

Availability note (English)

Available from http://dx.doi.org/10.1088/0951-7715/22/7/006

Additional details

Identifiers

DOI
10.1088/0951-7715/22/7/006;
PII
S0951-7715(09)87325-8;

Publishing Information

Journal Title
Nonlinearity (Print)
Journal Volume
22
Journal Issue
7
Journal Page Range
p. 1589-1614
ISSN
0951-7715

INIS

Country of Publication
United Kingdom
Country of Input or Organization
International Atomic Energy Agency (IAEA)
INIS RN
45035000
Subject category
S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
Descriptors DEI
CRYSTALS; GROUND STATES; HELIUM 4; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; PERIODICITY; QUANTUM MECHANICS; ROTATION; SOLIDS; WAVE EQUATIONS
Descriptors DEC
DIFFERENTIAL EQUATIONS; ENERGY LEVELS; EQUATIONS; EVEN-EVEN NUCLEI; HELIUM ISOTOPES; ISOTOPES; LIGHT NUCLEI; MECHANICS; MOTION; NUCLEI; PARTIAL DIFFERENTIAL EQUATIONS; STABLE ISOTOPES; VARIATIONS