Analytic properties of the Virasoro modular kernel

On the space of generic conformal blocks the modular transformation of the underlying surface is realized as a linear integral transformation. We show that the analytic properties of conformal block implied by Zamolodchikov's formula are shared by the kernel of the modular transformation and illustrate this by explicit computation in the case of the one-point toric conformal block.Comment: 12 pages, v2: minor corrections and additional reference

Fourier expansion in variational quantum algorithms

The Fourier expansion of the loss function in variational quantum algorithms (VQA) contains a wealth of information, yet is generally hard to access. We focus on the class of variational circuits, where constant gates are Clifford gates and parameterized gates are generated by Pauli operators, which covers most practical cases while allowing much control thanks to the properties of stabilizer circuits. We give a classical algorithm that, for an $N$-qubit circuit and a single Pauli observable, computes coefficients of all trigonometric monomials up to a degree $m$ in time bounded by $\mathcal{O}(N2^m)$. Using the general structure and implementation of the algorithm we reveal several novel aspects of Fourier expansions in Clifford+Pauli VQA such as (i) reformulating the problem of computing the Fourier series as an instance of multivariate boolean quadratic system (ii) showing that the approximation given by a truncated Fourier expansion can be quantified by the $L^2$ norm and evaluated dynamically (iii) tendency of Fourier series to be rather sparse and Fourier coefficients to cluster together (iv) possibility to compute the full Fourier series for circuits of non-trivial sizes, featuring tens to hundreds of qubits and parametric gates.Comment: 10+5 pages, code available at https://github.com/idnm/FourierVQA, comments welcom

Conformal symmetry in quasi-free Markovian open quantum systems

Conformal symmetry governs the behavior of closed systems near second-order phase transitions, and is expected to emerge in open systems going through dissipative phase transitions. We propose a framework allowing for a manifest description of conformal symmetry in open Markovian systems. The key difference from the closed case is that both conformal algebra and the algebra of local fields are realized on the space of superoperators. We illustrate the framework by a series of examples featuring systems with quadratic Hamiltonians and linear jump operators, where the Liouvillian dynamics can be efficiently analyzed using the formalism of third quantization. We expect that our framework can be extended to interacting systems using an appropriate generalization of the conformal bootstrap.Comment: 15 pages, supplementary Wolfram Mathematica notebook available at https://github.com/idnm/third_quantization v2: minor revision (references added, typos corrected) v2: Minor revisions done and typos correcte

ZOOMICS: comparative metabolomics of red blood cells from dogs, cows, horses and donkeys during refrigerated storage for up to 42 days

The use of omics technologies in human transfusion medicine has improved our understanding of the red blood cell (RBC) storage lesion(s). Despite significant progress towards understanding the storage lesion(s) of human RBCs, a comparison of basal and post-storage RBC metabolism across multiple species using omics technologies has not yet been reported, and is the focus of this study

Heavy-meson physics and flavour violation with a single generation

We study flavour-violating processes which involve heavy B- and D-mesons and are mediated by Kaluza-Klein modes of gauge bosons in a previously suggested model where three generations of the Standard Model fermions originate from a single generation in six dimensions. We find the bound on the size R of the extra spatial dimensions 1/R>3.3 TeV, which arises from the three-body decay B_s to K mu e. Due to the still too low statistics this bound is much less stringent than the constraint arising from K to mu e, 1/R>64 TeV, which was found in a previous work (Frere et al., JHEP, 2003). Nevertheless, we argue that a clear signature of the model would be an observation of K to mu e and B_s to K mu e decays without observations of other flavour and lepton number changing processes at the same precision level.Comment: 15 page