Assessing T cell clonal size distribution: a non-parametric approach

Clonal structure of the human peripheral T-cell repertoire is shaped by a number of homeostatic mechanisms, including antigen presentation, cytokine and cell regulation. Its accurate tuning leads to a remarkable ability to combat pathogens in all their variety, while systemic failures may lead to severe consequences like autoimmune diseases. Here we develop and make use of a non-parametric statistical approach to assess T cell clonal size distributions from recent next generation sequencing data. For 41 healthy individuals and a patient with ankylosing spondylitis, who undergone treatment, we invariably find power law scaling over several decades and for the first time calculate quantitatively meaningful values of decay exponent. It has proved to be much the same among healthy donors, significantly different for an autoimmune patient before the therapy, and converging towards a typical value afterwards. We discuss implications of the findings for theoretical understanding and mathematical modeling of adaptive immunity.Comment: 13 pages, 3 figures, 2 table

Josephson Effect in Pb/I/NbSe2 Scanning Tunneling Microscope Junctions

We have developed a method for the reproducible fabrication of superconducting scanning tunneling microscope (STM) tips. We use these tips to form superconductor/insulator/superconductor tunnel junctions with the STM tip as one of the electrodes. We show that such junctions exhibit fluctuation dominated Josephson effects, and describe how the Josephson product IcRn can be inferred from the junctions' tunneling characteristics in this regime. This is first demonstrated for tunneling into Pb films, and then applied in studies of single crystals of NbSe2. We find that in NbSe2, IcRn is lower than expected, which could be attributed to the interplay between superconductivity and the coexisting charge density wave in this material.Comment: 3 pages, 2 figures. Presented at the New3SC-4 meeting, San Diego, Jan. 16-21 200

Photon waiting time distributions: a keyhole into dissipative quantum chaos

Open quantum systems can exhibit complex states, which classification and quantification is still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intra-cavity photonic mode, is one of the examples. Unraveling the corresponding Markovian master equation into an ensemble of quantum trajectories and employing the recently proposed calculation of quantum Lyapunov exponents [I.I. Yusipov {\it et al.}, Chaos {\bf 29}, 063130 (2019)], we identify `chaotic' and `regular' regimes there. In particular, we show that chaotic regimes manifest an intermediate power-law asymptotics in the distribution of photon waiting times. This distribution can be retrieved by monitoring photon emission with a single-photon detector, so that chaotic and regular states can be discriminated without disturbing the intra-cavity dynamics.Comment: 7 pages, 5 figure

Collective oscillations in spatially modulated exciton-polariton condensate arrays

We study collective dynamics of interacting centers of exciton-polariton condensation in presence of spatial inhomogeneity, as modeled by diatomic active oscillator lattices. The mode formalism is developed and employed to derive existence and stability criteria of plane wave solutions. It is demonstrated that $k_0=0$ wave number mode with the binary elementary cell on a diatomic lattice possesses superior existence and stability properties. Decreasing net on-site losses (balance of dissipation and pumping) or conservative nonlinearity favors multistability of modes, while increasing frequency mismatch between adjacent oscillators detriments it. On the other hand, spatial inhomogeneity may recover stability of modes at high nonlinearities. Entering the region where all single-mode solutions are unstable we discover subsequent transitions between localized quasiperiodic, chaotic and global chaotic dynamics in the mode space, as nonlinearity increases. Importantly, the last transition evokes the loss of synchronization. These effects may determine lasing dynamics of interacting exciton-polariton condensation centers.Comment: 9 pages, 3 figure

Control of a single-particle localization in open quantum systems

We investigate the possibility to control localization properties of the asymptotic state of an open quantum system with a tunable synthetic dissipation. The control mechanism relies on the matching between properties of dissipative operators, acting on neighboring sites and specified by a single control parameter, and the spatial phase structure of eigenstates of the system Hamiltonian. As a result, the latter coincide (or near coincide) with the dark states of the operators. In a disorder-free Hamiltonian with a flat band, one can either obtain a localized asymptotic state or populate whole flat and/or dispersive bands, depending on the value of the control parameter. In a disordered Anderson system, the asymptotic state can be localized anywhere in the spectrum of the Hamiltonian. The dissipative control is robust with respect to an additional local dephasing.Comment: 6 pages, 5 figure

Localization in open quantum systems

In an isolated single-particle quantum system a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that dissipation can drive a disordered system into a steady state with tunable localization properties. This can be achieved with a set of identical dissipative operators, each one acting non-trivially only on a pair of neighboring sites. Operators are parametrized by a uniform phase, which controls selection of Anderson modes contributing to the state. On the microscopic level, quantum trajectories of a system in a localized steady regime exhibit intermittent dynamics consisting of long-time sticking events near selected modes interrupted by jumps between them.Comment: 5 pages, 5 figure

Localization in periodically modulated speckle potentials

Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and drastically alters transport properties of the lattice. In the original Anderson model, the addition of a periodic driving increases, in a certain range of the driving's frequency and amplitude, localization length of the appearing Floquet eigenstates. We go beyond the uncorrelated disorder case and address the experimentally relevant situation when spatial correlations are present in the lattice potential. Their presence induces the creation of an effective mobility edge in the energy spectrum of the system. We find that a slow driving leads to resonant hybridization of the Floquet states, by increasing both the participation numbers and effective widths of the states in the strongly localized band and decreasing values of these characteristics for the states in the quasi-extended band. Strong driving homogenizes the bands, so that the Floquet states loose compactness and tend to be spatially smeared. In the basis of the stationary Hamiltonian, these states retain localization in terms of participation number but become de-localized and spectrum-wide in term of their effective widths. Signatures of thermalization are also observed.Comment: 6 pages, 3 figure