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

Faddeev-Jackiw quantisation of nonreciprocal quasi-lumped electrical networks

Following a consistent geometrical description previously introduced in Parra-Rodriguez et al. (2023), we present an exact method for obtaining canonically quantisable Hamiltonian descriptions of nonlinear, nonreciprocal quasi-lumped electrical networks. Utilising the Faddeev-Jackiw method once more, we identify and classify all possible singularities arising in the quest for Hamiltonian descriptions of general quasi-lumped element networks, and we offer systematic solutions to them--a major challenge in the context of canonical circuit quantisation. Accordingly, the solution relies on the correct identification of the reduced classical circuit-state manifold, i.e., a mix of flux and charge fields and functions. Starting from the geometrical description of the transmission line, we provide a complete program including lines coupled to one-port lumped-element networks, as well as multiple lines connected to nonlinear lumped-element networks. On the way, we naturally extend the canonical quantisation of transmission lines coupled through frequency-dependent, nonreciprocal linear systems, such as practical circulators. Additionally, we demonstrate how our method seamlessly facilitates the characterisation of general nonreciprocal, dissipative linear environments. This is achieved by extending the Caldeira-Leggett formalism, utilising continuous limits of series of immittance matrices. We expect this work to become a useful tool in the analysis and design of electrical circuits and of special interest in the context of canonical quantisation of superconducting networks. For instance, this work will provide a solid ground for a precise input-output theory in the presence of nonreciprocal devices, e.g., within waveguide QED platforms.Comment: 27 pages. 11 figures. Comments are welcom