2,760 research outputs found
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
Quantum jumps on Anderson attractors
In a closed single-particle quantum system, spatial disorder induces Anderson
localization of eigenstates and halts wave propagation. The phenomenon is
vulnerable to interaction with environment and decoherence, that is believed to
restore normal diffusion. We demonstrate that for a class of experimentally
feasible non-Hermitian dissipators, which admit signatures of localization in
asymptotic states, quantum particle opts between diffusive and ballistic
regimes, depending on the phase parameter of dissipators, with sticking about
localization centers. In diffusive regime, statistics of quantum jumps is
non-Poissonian and has a power-law interval, a footprint of intermittent
locking in Anderson modes. Ballistic propagation reflects dispersion of an
ordered lattice and introduces a new timescale for jumps with non-monotonous
probability distribution. Hermitian dephasing dissipation makes localization
features vanish, and Poissonian jump statistics along with normal diffusion are
recovered.Comment: 6 pages, 5 figure
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
Anderson localization or nonlinear waves? A matter of probability
In linear disordered systems Anderson localization makes any wave packet stay
localized for all times. Its fate in nonlinear disordered systems is under
intense theoretical debate and experimental study. We resolve this dispute
showing that at any small but finite nonlinearity (energy) value there is a
finite probability for Anderson localization to break up and propagating
nonlinear waves to take over. It increases with nonlinearity (energy) and
reaches unity at a certain threshold, determined by the initial wave packet
size. Moreover, the spreading probability stays finite also in the limit of
infinite packet size at fixed total energy. These results are generalized to
higher dimensions as well.Comment: 4 pages, 3 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
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
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