103 research outputs found
Asymptotic behaviour of the probability density in one dimension
We demonstrate that the probability density of a quantum state moving freely
in one dimension may decay faster than 1/t. Inverse quadratic and cubic
dependences are illustrated with analytically solvable examples. Decays faster
than 1/t allow the existence of dwell times and delay times.Comment: 5 pages, one eps figure include
Canonical circuit quantization with linear nonreciprocal devices
Nonreciprocal devices effectively mimic the breaking of time-reversal
symmetry for the subspace of dynamical variables that they couple, and can be
used to create chiral information processing networks. We study the systematic
inclusion of ideal gyrators and circulators into Lagrangian and Hamiltonian
descriptions of lumped-element electrical networks. The proposed theory is of
wide applicability in general nonreciprocal networks on the quantum regime. We
apply it to pedagogical and pathological examples of circuits containing
Josephson junctions and ideal nonreciprocal elements described by admittance
matrices, and compare it with the more involved treatment of circuits based on
nonreciprocal devices characterized by impedance or scattering matrices.
Finally, we discuss the dual quantization of circuits containing phase-slip
junctions and nonreciprocal devices.Comment: 12 pages, 4 figures; changes made to match the accepted version in
PR
Quantum Simulator for Transport Phenomena in Fluid Flows
Transport phenomena still stand as one of the most challenging problems in
computational physics. By exploiting the analogies between Dirac and lattice
Boltzmann equations, we develop a quantum simulator based on pseudospin-boson
quantum systems, which is suitable for encoding fluid dynamics transport
phenomena within a lattice kinetic formalism. It is shown that both the
streaming and collision processes of lattice Boltzmann dynamics can be
implemented with controlled quantum operations, using a heralded quantum
protocol to encode non-unitary scattering processes. The proposed simulator is
amenable to realization in controlled quantum platforms, such as ion-trap
quantum computers or circuit quantum electrodynamics processors.Comment: 8 pages, 3 figure
Geometrical description and Faddeev-Jackiw quantization of electrical networks
In lumped-element electrical circuit theory, the problem of solving Maxwell's
equations in the presence of media is reduced to two sets of equations. Those
addressing the local dynamics of a confined energy density, the constitutive
equations, encapsulating local geometry and dynamics, and those that enforce
the conservation of charge and energy in a larger scale that we express
topologically, the Kirchhoff equations. Following a consistent geometrical
description, we develop a new and systematic way to write the dynamics of
general lumped-element electrical circuits as first order differential
equations derivable from a Lagrangian and a Rayleigh dissipation function.
Leveraging the Faddeev-Jackiw method, we identify and classify all
singularities that arise in the search for Hamiltonian descriptions of general
networks. Furthermore we provide systematics to solve those singularities,
which is a key problem in the context of canonical quantization of
superconducting circuits. The core of our solution relies on the correct
identification of the reduced manifold in which the circuit state is
expressible, e.g., a mix of flux and charge degrees of freedom, including the
presence of compact ones. We apply the fully programmable method to obtain
(canonically quantizable) Hamiltonian descriptions of nonlinear and
nonreciprocal circuits which would be cumbersome/singular if pure node-flux or
loop-charge variables are used as a starting configuration space. This work
unifies diverse existent geometrical pictures of electrical network theory, and
will prove useful, for instance, to automatize the computation of exact
Hamiltonian descriptions of superconducting quantum chips.Comment: 19 pages and 10 figures. Comments are welcom
Comment on "Measurement of time of arrival in quantum mechanics"
The analysis of the model quantum clocks proposed by Aharonov et al. [Phys.
Rev. A 57 (1998) 4130 - quant-ph/9709031] requires considering evanescent
components, previously ignored. We also clarify the meaning of the operational
time of arrival distribution which had been investigated.Comment: 3 inlined figures; comment on quant-ph/970903
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