Zero-Point Energy of an Electron Lattice

The equilibrium properties of the outer crust of cold nonaccreting magnetars (i.e. neutron stars endowed with very strong magnetic fields) are studied using the latest experimental atomic mass data complemented with a microscopic atomic mass model based on the Hartree-Fock-Bogoliubov method. The Landau quantization of electron motion caused by the strong magnetic field is found to have a significant impact on the composition and the equation of state of crustal matter. It is also shown that the outer crust of magnetars could be much more massive than that of ordinary neutron stars.

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“…For point-like ions arranged in a body centered cubic lattice, the lattice energy density is approximately given by [40] …”

Section: Microscopic Model Of Magnetar Crustsmentioning

confidence: 99%

Properties of the outer crust of strongly magnetized neutron stars from Hartree-Fock-Bogoliubov atomic mass models

et al. 2012

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“…When expanding the dynamical matrix in Taylor series about the fluid limit k → 0, it is simple to show that for 1/r interactions this series is in even powers of k, because D(R) is real andD(k) analytic for k → 0 (see [27,38]). It is therefore possible to write the corrections to the eigenvalues of the optical mode as:…”

Section: Corrections To the Fluid Limitmentioning

confidence: 99%

Linear perturbative theory of the discrete cosmologicalN-body problem

Marcos¹,

Baertschiger²,

Joyce

et al. 2006

Phys. Rev. D

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We present a perturbative treatment of the evolution under their mutual self-gravity of particles displaced off an infinite perfect lattice, both for a static space and for a homogeneously expanding space as in cosmological N-body simulations. The treatment, analogous to that of perturbations to a crystal in solid state physics, can be seen as a discrete (i.e. particle) generalization of the perturbative solution in the Lagrangian formalism of a self-gravitating fluid. Working to linear order, we show explicitly that this fluid evolution is recovered in the limit that the initial perturbations are restricted to modes of wavelength much larger than the lattice spacing. The full spectrum of eigenvalues of the simple cubic lattice contains both oscillatory modes and unstable modes which grow slightly faster than in the fluid limit. A detailed comparison of our perturbative treatment, at linear order, with full numerical simulations is presented, for two very different classes of initial perturbation spectra. We find that the range of validity is similar to that of the perturbative fluid approximation (i.e. up to close to "shell-crossing"), but that the accuracy in tracing the evolution is superior. The formalism provides a powerful tool to systematically calculate discreteness effects at early times in cosmological N-body simulations.

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“…17 The elastic constants of a classical Wigner crystal have been calculated by various authors. 18,19 Of particular interest is the case of the hexagonal lattice, which is expected to be the stable crystal structure in two dimensions. 19 The elastic properties of this lattice are formally indistinguishable from those of a homogeneous and isotropic body, i.e., there are only two elastic constants K and , 1 and they are given by 19 Ӎ0.24e 2 n 3/2 and KϭϪ6 .…”

Section: B Low-density Limitmentioning

confidence: 99%

Elasticity of an electron liquid

1999

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The zero-temperature response of an interacting electron liquid to a time-dependent vector potential of wave vector q and frequency , such that qӶq F , qv F Ӷ ӶE F /ប ͑where q F , v F , and E F are the Fermi wave vector, velocity, and energy, respectively͒, is equivalent to that of a continuous elastic medium with nonvanishing shear modulus , bulk modulus K, and viscosity coefficients and . We establish the relationship between the viscoelastic coefficients and the long-wavelength limit of the ''dynamical local-field factors'' G L(T) (q, ), which are widely used to describe exchange-correlation effects in electron liquids. We present several exact results for , including its expression in terms of Landau parameters, and practical approximate formulas for , , and as functions of density. These are used to discuss the possibility of a transverse collective mode in the electron liquid at sufficiently low density. Finally, we consider impurity scattering and/or quasiparticle collisions at nonzero temperature. Treating these effects in the relaxation-time ( ) approximation, explicit expressions are derived for and as functions of frequency. These formulas exhibit a crossover from the collisional regime ( Ӷ1), where ϳ0 and ϳnE F , to the collisionless regime ( ӷ1), where ϳnE F and ϳ0. ͓S0163-1829͑99͒02632-6͔

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Zero-Point Energy of an Electron Lattice

Cited by 284 publications

References 17 publications

Properties of the outer crust of strongly magnetized neutron stars from Hartree-Fock-Bogoliubov atomic mass models

Properties of the outer crust of strongly magnetized neutron stars from Hartree-Fock-Bogoliubov atomic mass models

Linear perturbative theory of the discrete cosmologicalN-body problem

Elasticity of an electron liquid

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