Dynamics of the particle - hole pair creation in graphene

The process of coherent creation of particle - hole excitations by an electric field in graphene is quantitatively described. We calculate the evolution of current density, number of pairs and energy after switching on the electric field. In particular, it leads to a dynamical visualization of the universal finite resistivity without dissipation in pure graphene. We show that the DC conductivity of pure graphene is rather $\frac{\pi e^{2}}{2 h}$ than the often cited value of $\frac{4 e^{2}}{\pi h}$. This value coincides with the AC conductivity calculated and measured recently at optical frequencies. The effect of temperature and random chemical potential (charge puddles) are considered and explain the recent experiment on suspended graphene. A possibility of Bloch oscillations is discussed within the tight binding model.Comment: 4 pages, 2 figure

Ballistic transport, chiral anomaly and emergence of the neutral electron - hole plasma in graphene

The process of coherent creation of particle - hole excitations by an electric field in graphene is quantitatively described using a dynamic "first quantized" approach. We calculate the evolution of current density, number of pairs and energy in ballistic regime using the tight binding model. The series in electric field strength $E$ up to third order in both DC and AC are calculated. We show how the physics far from the two Dirac points enters various physical quantities in linear response and how it is related to the chiral anomaly. The third harmonic generation and the imaginary part of conductivity are obtained. It is shown that at certain time scale $t_{nl}\propto E^{-1/2}$ the physical behaviour dramatically changes and the perturbation theory breaks down. Beyond the linear response physics is explored using an exact solution of the first quantized equations. While for small electric fields the I-V curve is linear characterized by the universal minimal resistivity $\sigma =\pi /2(e^{2}/h)$%, at $t>t_{nl}$ the conductivity grows fast. The copious pair creation (with rate $E^{3/2}$), analogous to Schwinger's electron - positron pair creation from vacuum in QED, leads to creation of the electron - hole plasma at ballistic times of order $t_{nl}$. This process is terminated by a relaxational recombination.Comment: 15 pages, 5 figures

Can Sigma Models Describe Finite Temperature Chiral Transitions?

Large-N expansions and computer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Neveu model is mean field theory. This is a counterexample to the standard 'sigma model' scenario which predicts the 2D Ising model universality class. We trace the breakdown of the standard scenario (dimensional reduction and universality) to the absence of canonical scalar fields in the model. We point out that our results could be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics.Comment: 9 pages, 2 ps figure

θ\theta Effects in Chern-Simons QED2+1{\rm QED}_{2+1} with a Four-Fermi Interaction

We investigate the effects of the Chern-Simons coupling on the high energy behavior in the $(2+1)$-dimensional Chern-Simons QED with a four-Fermi interaction. Using the $1/N$ expansion we discuss the Chern-Simons effects on the critical four-Fermi coupling at $O(1/N)$ and the $\beta$ function around it. High-energy behavior of Green's functions is also discussed. By explicit calculation, we find that the radiative correction to the Chern-Simons coupling vanishes at $O(1/N)$ in the broken phase of the dynamical parity symmetry. We argue that no radiative corrections to the Chern-Simons term arise at higher orders in the $1/N$ expansion.Comment: 13 pages, 6 figures not included, LaTeX, SNUTP 92-9

Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

Dimensional Reduction and Quantum-to-Classical Reduction at High Temperatures

We discuss the relation between dimensional reduction in quantum field theories at finite temperature and a familiar quantum mechanical phenomenon that quantum effects become negligible at high temperatures. Fermi and Bose fields are compared in this respect. We show that decoupling of fermions from the dimensionally reduced theory can be related to the non-existence of classical statistics for a Fermi field.Comment: 11 pages, REVTeX, revised v. to be published in Phys. Rev. D: some points made more explici

The Phase Diagram of Compact QED Coupled to a Four-Fermi Interaction

Compact lattice Quantum Electrodynamics (QED) with four species of fermions is simulated with massless quarks by using the $\chi$QED scheme of adding a four-fermi interaction to the action. Simulations directly in the chiral limit of massless quarks are done with high statistics on $8^4$, and $16^4$ lattices, and the phase diagram, parameterized by the gauge and the four-fermi couplings, is mapped out. The line of monopole condensation transitions is separate from the line of chiral symmetry restoration. The simulation results indicate that the monopole condensation transition is first order while the chiral transition is second order. The challenges in determining the Universality class of the chiral transition are discussed. If the scaling region for the chiral transition is sufficiently wide, the $16^4$ simulations predict critical indices far from mean field values. We discuss a speculative scenario in which anti-screening provided by double-helix strands of monopole and anti-monopole loops are the agent that balances the screening of fermion anti-fermion pairs to produce an ultra-violet fixed point in the electric coupling.Comment: 29 pages, 8 figures and 2 table

On the Triviality of Textbook Quantum Electrodynamics

By adding a small, irrelevant four fermi interaction to the action of lattice Quantum Electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. This allows an ab initio high precision, controlled study of the existence of "textbook" Quantum Electrodynamics with several species of fermions. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivial. The logarithms of triviality, which modify mean field scaling laws, are pinpointed in several observables. The result supports Landau's contention that perturbative QED suffers from complete screening and would have a vanishing fine structure constant in the absence of a cutoff.Comment: reference to Phys. Rev. Lett.80, 4119(1998) adde

Dynamical Symmetry Breaking in Models with the Yukawa Interaction

We discuss models with a massless fermion and a self-interacting massive scalar field with the Yukawa interaction. The chiral condensate and the fermion mass are calculated analytically. It is shown that the models have a phase transition as a function of the squared mass of the scalar field.Comment: 7 pages, no figures, in Eqs. (7) and (11) one coefficient was change

Quantum critical scaling and the Gross-Neveu model in 2+1 dimensions

The quantum critical behavior of the 2+1 dimensional Gross--Neveu model in the vicinity of its zero temperature critical point is considered. The model is known to be renormalisable in the large $N$ limit, which offers the possibility to obtain expressions for various thermodynamic functions in closed form. We have used the concept of finite--size scaling to extract information about the leading temperature behavior of the free energy and the mass term, defined by the fermionic condensate and determined the crossover lines in the coupling (\g) -- temperature ($T$) plane. These are given by T\sim|\g-\g_c|, where \g_c denotes the critical coupling at zero temperature. According to our analysis no spontaneous symmetry breaking survives at finite temperature. We have found that the leading temperature behavior of the fermionic condensate is proportional to the temperature with the critical amplitude $\frac{\sqrt{5}}3\pi$. The scaling function of the singular part of the free energy is found to exhibit a maximum at $\frac{\ln2}{2\pi}$ corresponding to one of the crossover lines. The critical amplitude of the singular part of the free energy is given by the universal number $\frac13[\frac1{2\pi}\zeta(3)-\mathrm{Cl}_2(\frac{\pi}3)]=-0.274543...$, where $\zeta(z)$ and $\mathrm{Cl}_2(z)$ are the Riemann zeta and Clausen's functions, respectively. Interpreted in terms the thermodynamic Casimir effect, this result implies an attractive Casimir "force". This study is expected to be useful in shedding light on a broader class of four fermionic models.Comment: 6 pages, 3 figure