628 research outputs found
Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity
A new quasigroup approach to conservation laws in general relativity is
applied to study asymptotically flat at future null infinity spacetime. The
infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to
the Poincar\'e quasigroup and the Noether charge associated with any element of
the Poincar\'e quasialgebra is defined. The integral conserved quantities of
energy-momentum and angular momentum are linear on generators of Poincar\'e
quasigroup, free of the supertranslation ambiguity, posess the flux and
identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page
Smooth Loops and Fiber Bundles: Theory of Principal Q-bundles
A nonassociative generalization of the principal fiber bundles with a smooth
loop mapping on the fiber is presented. Our approach allows us to construct a
new kind of gauge theories that involve higher ''nonassociative'' symmetries.Comment: 20 page
Quantum search using non-Hermitian adiabatic evolution
We propose a non-Hermitian quantum annealing algorithm which can be useful
for solving complex optimization problems. We demonstrate our approach on
Grover's problem of finding a marked item inside of unsorted database. We show
that the energy gap between the ground and excited states depends on the
relaxation parameters, and is not exponentially small. This allows a
significant reduction of the searching time. We discuss the relations between
the probabilities of finding the ground state and the survival of a quantum
computer in a dissipative environment.Comment: 5 pages, 3 figure
Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model
We perform a theoretical study of the dynamics of the electric field
excitations in a microtubule by taking into consideration the realistic
cylindrical geometry, dipole-dipole interactions of the tubulin-based protein
heterodimers, the radial electric field produced by the solvent, and a possible
degeneracy of energy states of individual heterodimers. The consideration is
done in the frames of the classical pseudo-spin model. We derive the system of
nonlinear dynamical ordinary differential equations of motion for interacting
dipoles, and the continuum version of these equations. We obtain the solutions
of these equations in the form of snoidal waves, solitons, kinks, and localized
spikes. Our results will help to a better understanding of the functional
properties of microtubules including the motor protein dynamics and the
information transfer processes. Our considerations are based on classical
dynamics. Some speculations on the role of possible quantum effects are also
made.Comment: 14 pages, 15 figures. The high resolution figure files are available
by reques
Smooth Loops, Generalized Coherent States and Geometric Phases
A description of generalized coherent states and geometric phases in the
light of the general theory of smooth loops is given.Comment: LATeX file, 11 page
Substitutional landscape of a split fluorescent protein fragment using high-density peptide microarrays
Split fluorescent proteins have wide applicability as biosensors for protein-protein interactions, genetically encoded tags for protein detection and localization, as well as fusion partners in super-resolution microscopy. We have here established and validated a novel platform for functional analysis of leave-one-out split fluorescent proteins (LOO-FPs) in high throughput and with rapid turnover. We have screened more than 12,000 variants of the beta-strand split fragment using high-density peptide microarrays for binding and functional complementation in Green Fluorescent Protein. We studied the effect of peptide length and the effect of different linkers to the solid support. We further mapped the effect of all possible amino acid substitutions on each position as well as in the context of some single and double amino acid substitutions. As all peptides were tested in 12 duplicates, the analysis rests on a firm statistical basis allowing for confirmation of the robustness and precision of the method. Based on experiments in solution, we conclude that under the given conditions, the signal intensity on the peptide microarray faithfully reflects the binding affinity between the split fragments. With this, we are able to identify a peptide with 9-fold higher affinity than the starting peptide
Droplet-array (DA) sandwich chip: A versatile platform for High-Throughput Cell Screening based on superhydrophobic-superhydrophilic micropatterning
Complex magnetic monopoles, geometric phases and quantum evolution in vicinity of diabolic and exceptional points
We consider the geometric phase and quantum tunneling in vicinity of diabolic
and exceptional points. We show that the geometric phase associated with the
degeneracy points is defined by the flux of complex magnetic monopole. In
weak-coupling limit the leading contribution to the real part of geometric
phase is given by the flux of the Dirac monopole plus quadrupole term, and the
expansion for its imaginary part starts with the dipolelike field. For a
two-level system governed by the generic non-Hermitian Hamiltonian, we derive a
formula to compute the non-adiabatic complex geometric phase by integral over
the complex Bloch sphere. We apply our results to to study a two-level
dissipative system driven by periodic electromagnetic field and show that in
the vicinity of the exceptional point the complex geometric phase behaves as
step-like function. Studying tunneling process near and at exceptional point,
we find two different regimes: coherent and incoherent. The coherent regime is
characterized by the Rabi oscillations and one-sheeted hyperbolic monopole
emerges in this region of the parameters. In turn with the incoherent regime
the two-sheeted hyperbolic monopole is associated. The exceptional point is the
critical point of the system where the topological transition occurs and both
of the regimes yield the quadratic dependence on time. We show that the
dissipation brings into existence of pulses in the complex geometric phase and
the pulses are disappeared when dissipation dies out. Such a strong coupling
effect of the environment is beyond of the conventional adiabatic treatment of
the Berry phase.Comment: 29 pages, 21 figure
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