Dynamical screening in bilayer graphene

We calculate 1-loop polarization in bilayer graphene in the 4-band approximation for arbitrary values of frequency, momentum and doping. At low and high energy our result reduces to the polarization functions calculated in the 2-band approximation and in the case of single-layer graphehe, respectively.The special cases of static screening and plasmon modes are analyzed.Comment: 10 pages, 4 figures; references added; typos corrected; high-energy plasmon consideration adde

First Order String Theory and the Kodaira-Spencer Equations. II

The first-order bosonic string theory, perturbed by primary operator, corresponding to the deformation of target-space complex structure is considered. We compute the correlation functions in this theory and study their divergencies. It is found, that consistency of these correlation functions with the world-sheet conformal invariance requires the Kodaira-Spencer equations to be satisfied by target-space Beltrami differentials. This statement is checked explicitly for the three-point and four-point correlators, containing one probe operator. We discuss the origin of these divergences and their relation with beta-functions or effective action and polyvertex structures in BRST approach.Comment: 21 pages, 3 figure

Reply to "Comment on 'Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas'"

In our recent paper [Phys. Rev. E 90, 032132 (2014)] we have studied the dynamics of a mobile impurity particle weakly interacting with the Tonks-Girardeau gas and pulled by a small external force, $F$. Working in the regime when the thermodynamic limit is taken prior to the small force limit, we have found that the Bloch oscillations of the impurity velocity are absent in the case of a light impurity. Further, we have argued that for a light impurity the steady state drift velocity, $V_D$, remains finite in the limit $F\rightarrow 0$. These results are in contradiction with earlier works by Gangardt, Kamenev and Schecter [Phys. Rev. Lett. 102, 070402 (2009), Annals of Physics 327, 639 (2012)]. One of us (OL) has conjectured [Phys. Rev. A 91, 040101 (2015)] that the central assumption of these works - the adiabaticity of the dynamics - can break down in the thermodynamic limit. In the preceding Comment [Phys. Rev. E 92, 016101 (2015)] Schecter, Gangardt and Kamenev have argued against this conjecture and in support of the existence of Bloch oscillations and linearity of $V_D(F)$. They have suggested that the ground state of the impurity-fluid system is a quasi-bound state and that this is sufficient to ensure adiabaticity in the thermodynamic limit. Their analytical argument is based on a certain truncation of the Hilbert space of the system. We argue that extending the results and intuition based on their truncated model on the original many-body problem lacks justification

How instanton combinatorics solves Painlev\'e VI, V and III's

We elaborate on a recently conjectured relation of Painlev\'e transcendents and 2D CFT. General solutions of Painlev\'e VI, V and III are expressed in terms of $c=1$ conformal blocks and their irregular limits, AGT-related to instanton partition functions in $\mathcal{N}=2$ supersymmetric gauge theories with $N_f=0,1,2,3,4$. Resulting combinatorial series representations of Painlev\'e functions provide an efficient tool for their numerical computation at finite values of the argument. The series involve sums over bipartitions which in the simplest cases coincide with Gessel expansions of certain Toeplitz determinants. Considered applications include Fredholm determinants of classical integrable kernels, scaled gap probability in the bulk of the GUE, and all-order conformal perturbation theory expansions of correlation functions in the sine-Gordon field theory at the free-fermion point.Comment: 34 pages, 3 figures; v2: minor improvement

Conformal field theory of Painlev\'e VI

Generic Painlev\'e VI tau function \tau(t) can be interpreted as four-point correlator of primary fields of arbitrary dimensions in 2D CFT with c=1. Using AGT combinatorial representation of conformal blocks and determining the corresponding structure constants, we obtain full and completely explicit expansion of \tau(t) near the singular points. After a check of this expansion, we discuss examples of conformal blocks arising from Riccati, Picard, Chazy and algebraic solutions of Painlev\'e VI.Comment: 24 pages, 1 figure; v3: added refs and minor clarifications, few typos corrected; to appear in JHE

Momentum relaxation of a mobile impurity in a one-dimensional quantum gas

We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks-Girardeau gas. We establish that given an initial momentum $p_0$ the impurity relaxes to a steady state with a non-vanishing momentum $p_\infty.$ The nature of the steady state is found to depend drastically on whether the masses of the impurity and the host are equal or not. This is due to multiple coherent scattering processes leading to a resonant interaction between the impurity and the host in the case of equal masses. The dependence of $p_\infty$ on $p_0$ remains non-trivial even in the limit of vanishing interaction between the impurity and host particles. In this limit $p_\infty(p_0)$ is found explicitly