60 research outputs found
Optimal number of terms in QED series
In 1952 Dyson put forward a simple and powerful argument indicating that the
perturbative expansions of QED are asymptotic. His argument can be related to
Chandrasekhar's limit on the mass of a star for stability against gravitational
collapse. Combining these two arguments we estimate the optimal number of terms
of the QED series to be 3.1(137)^{3/2}=5000
Optimal number of terms in QED series and its consequence in condensed matter implementations of QED
In 1952 Dyson put forward a simple and powerful argument indicating that the
perturbative expansions of QED are asymptotic. His argument can be related to
Chandrasekhar's limit on the mass of a star for stability against gravitational
collapse. Combining these two arguments we estimate the optimal number of terms
of the QED series to be . For condensed matter
manifestations of QED in narrow band-gap semiconductors and Weyl semimetals the
optimal number of terms is around while in graphene the utility of the
perturbation theory is severely limited.Comment: 10 pages, minor changes, version to be published in PRA. arXiv admin
note: substantial text overlap with arXiv:1309.689
Superfluid Hydrodynamics of an Electron Gas in a Superstrong Magnetic Field
We derive the equations of hydrodynamics of a fully polarized electron gas
placed in a strong magnetic field. These equations reveal the existence of
solitons - immobile or propagating domain wall-like defects whose plane is
perpendicular to the field direction. The solitons are used to construct weakly
excited states, and novel nonuniform persistent current states of the system.Comment: 4 paqes, 3 figure
Brownian motion of the electron and the Lamb shift at finite temperature
By enhancing electron position fluctuations, equilibrium electromagnetic
radiation modifies the potential for an electron in a Hydrogen atom. This can
have significant effects for weakly bound states and especially at finite
temperature. This implies a 2% correction to Bethe's value for 2S-2P Lamb shift
for weak fluctuations, but the effect is an order of magnitude larger for
strong fluctuations where it provides direct measure of the proton diameter.Comment: 4 page
Nonlinear plasma waves in an electron gas
The nature of traveling wave solutions to equations of hydrodynamics of a
generic three-dimensional electron gas with parabolic dispersion law depends on
whether the motion is subsonic or supersonic. Solitons representing localized
depressions of the electrostatic potential and electron density are predicted
to exist in the subsonic regime: at rest the solitons are dark while in motion
they are grey. Two types of periodic waves are found in the supersonic regime:
(i) smooth waves whose small amplitude limit is described by harmonic theory,
and (ii) waves with sharp troughs and smooth crests of the potential with the
electrons accumulating in the troughs.Comment: 4+ pages, 3 Figures, to be published as a Letter in J. Phys.
Steady flows, nonlinear gravitostatic waves and Zeldovich pancakes in a Newtonian gas
We show that equations of Newtonian hydrodynamics and gravity describing
one-dimensional steady gas flow possess nonlinear periodic solutions. In the
case of a zero-pressure gas the solution exhibits hydrodynamic similarity and
is universal: it is a lattice of integrable density singularities coinciding
with maxima of the gravitational potential. With finite pressure effects
included, there exists critical matter density that separates two regimes of
behavior. If the average density is below the critical, the solution is a
density wave which is in phase with the wave of the gravitational potential. If
the average density is above the critical, the waves of the density and
potential are out of phase. Traveling plane gravitostatic waves are also
predicted and their properties elucidated. Specifically, subsonic wave is made
out of two out of phase oscillations of matter density and gravitational
potential. If the wave is supersonic, the density-potential oscillations are in
phase.Comment: 5 pages, 3 figures, version to be published as a Rapid Communication
in Phys. Rev.
Quantum dissociation of an edge of a Luttinger liquid
In a Luttinger liquid phase of one-dimensional molecular matter the strength
of zero-point motion can be characterized by dimensionless De Boer's number
quantifying the interplay of quantum fluctuations and two-body interactions.
Selecting the latter in the Morse form we show that dissociation of the
Luttinger liquid is a process initiated at the system edge. The latter becomes
unstable against quantum fluctuations at a value of De Boer's number which is
smaller than that of the bulk instability which parallels the classical
phenomenon of surface melting.Comment: 4 pages, 3 figure
Kelvin-Froude wake patterns of a traveling pressure disturbance
According to Kelvin, a point pressure source uniformly traveling over the
surface of deep calm water leaves behind universal wake pattern confined within
sector and consisting of the so-called transverse and diverging
wavefronts. Actual ship wakes differ in their appearance from both each other
and Kelvin's prediction. The difference can be attributed to a deviation from
the point source limit and for given shape of the disturbance quantified by the
Froude number . We show that within linear theory effect of arbitrary
disturbance on the wake pattern can be mimicked by an effective pressure
distribution. Further, resulting wake patterns are qualitatively different
depending on whether water-piercing is present or not ("sharp" vs "smooth"
disturbances). For smooth pressure sources, we generalize Kelvin's stationary
phase argument to encompass finite size effects and classify resulting wake
patterns. Specifically, we show that there exist two characteristic Froude
numbers, and , such as the wake is only present if
. For , the wake consists of
the transverse wavefronts confined within a sector of an angle that may be
smaller than Kelvin's. An additional wake made of both the
transverse and diverging wavefronts is found for . If the
pressure source has sharp boundary, the wake is always present and features
additional interference effects. Specifically, for a constant pressure line
segment source mimicking slender ship the wake pattern can be understood as due
to two opposing effect wakes resembling (but not identical to) Kelvin's and
originating at segment's ends.Comment: 17 pages, 8 Figures. Generality of results is illustrated via
connections to linear response theory and Fourier-Kochin representation of
the wake. Extra Figure and references added. Results are unchanged. Version
accepted for publication in European Journal of Mechanics/B Fluid
Anomalous screening in two-dimensional materials with an extremum ring in the dispersion law
A variety of two-dimensional materials possess a band structure with an
energy extremal ridge along a ring in momentum space. Examples are biased
bilayer graphene, and surfaces and interfaces with a Rashba spin-orbit
interaction where at low doping the carriers fill an annulus. This topological
feature causes an anomalous screening behavior, which we study using the
Thomas-Fermi theory. Specifically, reducing the doping is predicted to enhance
the linear screening response, while at zero doping the size of the screening
cloud surrounding a Coulomb impurity is found to increase as the cube root of
the impurity charge.Comment: 4+ pages, 1 figure, minor changes, version to be published in Phys.
Rev.
The Bose molecule in one dimension
We give the Green function, momentum distribution, two-particle correlation
function, and structure factor for the bound state of N indistinguishable
bosons with an attractive delta-function interaction in one dimension, and an
argument showing that this boson "molecule" has no excited states other than
dissociation into separated pieces.Comment: 10 pages, 3 figure
- β¦