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

Quantum Many-Body Adiabaticity, Topological Thouless Pump and Driven Impurity in a One-Dimensional Quantum Fluid

When it comes to applying the adiabatic theorem in practice, the key question to be answered is how slow "slowly enough" is. This question can be an intricate one, especially for many-body systems, where the limits of slow driving and large system size may not commute. Recently we have shown how the quantum adiabaticity in many-body systems is related to the generalized orthogonality catastrophe [Phys. Rev. Lett. 119, 200401 (2017)]. We have proven a rigorous inequality relating these two phenomena and applied it to establish conditions for the quantized transport in the topological Thouless pump. In the present contribution we (i) review these developments and (ii) apply the inequality to establish the conditions for adiabaticity in a one-dimensional system consisting of a quantum fluid and an impurity particle pulled through the fluid by an external force. The latter analysis is vital for the correct quantitative description of the phenomenon of quasi Bloch oscillations in a one-dimensional translation invariant impurity-fluid system.Comment: presented at the International Conference on Quantum Technologies, Moscow, July 12 - 16, 201

Time scale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe

The adiabatic theorem is a fundamental result established in the early days of quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational recipes in molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving non-autonomous time evolution in a large Hilbert space. We illustrate our general results by analyzing conditions for the transport quantization in a topological Thouless pump

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