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 $3.1(137)^{3/2}\approx5000$. For condensed matter manifestations of QED in narrow band-gap semiconductors and Weyl semimetals the optimal number of terms is around $80$ 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 $39^{\circ}$ 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 $F$. 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, $F_{1}$ and $F_{2}>F_{1}$, such as the wake is only present if $F\gtrsim F_{1}$. For $F_{1}\lesssim F \lesssim F_{2}$, the wake consists of the transverse wavefronts confined within a sector of an angle that may be smaller than Kelvin's. An additional $39^{\circ}$ wake made of both the transverse and diverging wavefronts is found for $F\gtrsim F_{2}$. 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