52,013 research outputs found
Canonical Discretization. I. Discrete faces of (an)harmonic oscillator
A certain notion of canonical equivalence in quantum mechanics is proposed.
It is used to relate quantal systems with discrete ones. Discrete systems
canonically equivalent to the celebrated harmonic oscillator as well as the
quartic and the quasi-exactly-solvable anharmonic oscillators are found. They
can be viewed as a translation-covariant discretization of the (an)harmonic
oscillator preserving isospectrality. The notion of the deformation of the
canonical equivalence leading to a dilatation-covariant discretization
preserving polynomiality of eigenfunctions is also presented.Comment: 29 pages, LaTe
Quantum register based on structured diamond waveguide with NV centers
We propose a scheme of quantum information processing with NV-centers
embedded inside diamond nanostructure. Single NV-center placed in the cavity
plays role of an electron spin qubit which evolution is controlled by microwave
pulses. Besides, it couples to the cavity field via optical photon exchange. In
their turn, neighbor cavities are coupled to each other through the photon
hopping to form a bus waveguide mode. This waveguide mode overlaps with all
NV-centers. Entanglement between distant centers is organized by appropriate
tuning of their optical frequency relative to the waveguide frequency via
electrostatic control without lasers. We describe the controlled-Z operation
that is by one order of magnitude faster than in off-resonant laser-assisted
schemes proposed earlier. Spectral characteristics of the one-dimensional chain
of microdisks are calculated by means of numerical modeling, using the approach
analogous to the tight-binding approximation in the solid-state physics. The
data obtained allow to optimize the geometry of the microdisk array for the
effective implementation of quantum operations.Comment: to be published in Proc. of SPI
Distinct dynamical behavior in Erd\H{o}s-R\'enyi networks, regular random networks, ring lattices, and all-to-all neuronal networks
Neuronal network dynamics depends on network structure. In this paper we
study how network topology underpins the emergence of different dynamical
behaviors in neuronal networks. In particular, we consider neuronal network
dynamics on Erd\H{o}s-R\'enyi (ER) networks, regular random (RR) networks, ring
lattices, and all-to-all networks. We solve analytically a neuronal network
model with stochastic binary-state neurons in all the network topologies,
except ring lattices. Given that apart from network structure, all four models
are equivalent, this allows us to understand the role of network structure in
neuronal network dynamics. Whilst ER and RR networks are characterized by
similar phase diagrams, we find strikingly different phase diagrams in the
all-to-all network. Neuronal network dynamics is not only different within
certain parameter ranges, but it also undergoes different bifurcations (with a
richer repertoire of bifurcations in ER and RR compared to all-to-all
networks). This suggests that local heterogeneity in the ratio between
excitation and inhibition plays a crucial role on emergent dynamics.
Furthermore, we also observe one subtle discrepancy between ER and RR networks,
namely ER networks undergo a neuronal activity jump at lower noise levels
compared to RR networks, presumably due to the degree heterogeneity in ER
networks that is absent in RR networks. Finally, a comparison between network
oscillations in RR networks and ring lattices shows the importance of
small-world properties in sustaining stable network oscillations.Comment: 9 pages, 4 figure
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