arXiv subjects

Michael Ridley

Publications and source records attributed to Michael Ridley.

18 recordsLinked to original sources

arXiv2025

Current cross-correlation spectroscopy of Majorana bound states

The clock speed of topological quantum computers based on Majorana zero mode (MZM)-supporting nanoscale devices is limited by the time taken for electrons to traverse the device. We employ the time-dependent Landauer-B{\"u}ttiker transport theory for current cross-lead correlations in a superconducting nanowire junction hosting MZMs. From the time-dependent quantum noise, we are able to extract traversal times for electrons crossing the system. After demonstrating a linear scaling of traversal times with nanowire length, we present a heuristic formula for the traversal times which accurately captures their behaviour. We then connect our framework to a proposed experimental verification of this discriminant between spurious and genuine MZMs utilizing time-resolved transport measurements.

cond-mat.mes-hall↗

arXiv2025

Many Retrocausal Worlds: A Foundation for Quantum Probability

Recent accounts of probability in the many worlds interpretation of quantum mechanics are vulnerable due to their dependence on probability theory per se. For this reason, the many worlds interpretation continues to suffer from the incoherence and quantitative problems. After discussing various theories of probability, I discuss the incoherence problem and argue that self-locating probabilities centered in time-extended worlds can solve it. I then discuss and refute various solutions to the quantitative problem. I argue that the only tenable way to ground these self-locating probabilities is to identify the mathematical form of the Born rule as a generic pattern in a time-extended wavefunction, and to distribute degrees of belief over the region of wavefunction occupied by this pattern. I then outline a time-symmetric version of quantum mechanics - the Fixed Point Formulation - which, interpreted within a time-symmetric Everettian framework, can provide the foundation for a theory of quantum probability.

quant-ph↗

arXiv2025

Two times or none?

Attempts to treat time on an equivalent footing with space in quantum mechanics have been apparently dominated by `timeless' approaches, such as the one of Page and Wootters, which allow meaningful discussion of a `time operator'. However, there is an alternative, and significantly less studied approach, due to Bauer, which makes use of the `pseudospin' extension of the state space, effectively adding a backwards-time degree of freedom. This two-time approach allows definition of a `time operator' and moreover bears interesting relations with other time-symmetric formulations of quantum mechanics. We review and compare these approaches to quantum time, emphasizing that there is a subtle choice between the timeless framework and the two-time approach. Finally, we sketch a framework in which the timeless philosophy can be combined with two-time quantum mechanics.

quant-ph↗

arXiv2025

Photon-assisted stochastic resonance in nanojunctions

We study stochastic resonance in molecular junctions driven by a periodically-varying external field. This is done using the time-dependent Landauer-B{\"u}ttiker formalism, which follows from exact analytical solutions to the Kadanoff-Baym equations describing the molecular junction subject to an arbitrary time-dependent bias. We focus on a double quantum dot nanojunction and compare the effects of the temperature with the fluctuating bias in the statically-driven case. We then consider the combined effect of AC-driving and white noise fluctuations on the rectified current through the nanojunction, and find a stochastic resonance effect, where at certain driving conditions the bias fluctuations enhance the current signal. The study is then extended to include the color noise in the applied bias, so that the combined effect of the color noise correlation time and driving frequency on stochastic resonance is investigated. We thereby demonstrate that photon-assisted transport can be optimized by a suitably tuned environment.

cond-mat.mes-hall↗

arXiv2023

Quantum probability from temporal structure

The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In $ψ$-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified with fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics with a network of `fixed points' defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre- and post-selection.

quant-ph↗

arXiv2023

Time and event symmetry in quantum mechanics

We investigate two types of temporal symmetry in quantum mechanics. The first type, time symmetry, refers to the inclusion of opposite time orientations on an equivalent physical footing. The second, event symmetry, refers to the inclusion of all time instants in a history sequence on an equivalent physical footing. We find that recent time symmetric interpretations of quantum mechanics fail to respect event symmetry. Building on the recent fixed-point formulation (FPF) of quantum theory, we formulate the notion of an event precisely as a fixed point constraint on the Keldysh time contour. Then, considering a sequence of measurement events in time, we show that both time and event symmetry can be retained in this multiple-time formulation of quantum theory. We then use this model to resolve conceptual paradoxes with time symmetric quantum mechanics within an `all-at-once', atemporal picture.

quant-ph↗

arXiv2022

Can Information Behaviour Inform Machine Learning?

The objective of this paper is to explore the opportunities for human information behaviour research to inform and influence the field of machine learning and the resulting machine information behaviour. Using the development of foundation models in machine learning as an example, the paper illustrates how human information behaviour research can bring to machine learning a more nuanced view of information and informing, a better understanding of information need and how that affects the communication among people and systems, guidance on the nature of context and how to operationalize that in models and systems, and insights into bias, misinformation, and marginalization. Despite their clear differences, the fields of information behaviour and machine learning share many common objectives, paradigms, and key research questions. The example of foundation models illustrates that human information behaviour research has much to offer in addressing some of the challenges emerging in the nascent area of machine information behaviour.

cs.LG↗

arXiv2021

Time-dependent Landauer-Büttiker approach to charge pumping in AC-driven graphene nanoribbons

We apply the recently-developed partition-free time-dependent Landauer-Büttiker (TD-LB) formalism to the study of periodically-driven transport in graphene nanoribbons (GNR). When an AC driving is applied, this formalism can be used to prove generic conditions for the existence of a non-zero DC component of the net current (pump current) through the molecular device. Time-reversal symmetry breaking in the driving field is investigated and found to be insufficient for a non-zero pump current. We then derive explicit formulas for the current response to a particular biharmonic bias. We calculate the pump current through different GNR configurations and find that the sign and existence of a non-zero pump current can be tuned by simple alterations to the static parameters of the TD bias. Further, we investigate transient currents in different GNR configurations. We find a selection rule of even and odd harmonic response signal depending on a broken dynamical inversion symmetry in the bias.

cond-mat.mes-hall↗

arXiv2021

Failed attempt to escape from the quantum pigeon conundrum

A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS 113, 532 (2016)] is refuted. The quantum nature of the violation of the pigeonhole principle with pre- and postselection is clarified.

quant-ph↗

arXiv2021

Quantum interference and the time-dependent radiation of nanojunctions

Using the recently developed time-dependent Landauer-Büttiker formalism and Jefimenko's retarded solutions to the Maxwell equations, we show how to compute the time-dependent electromagnetic field produced by the charge and current densities in nanojunctions out of equilibrium. We then apply this formalism to a benzene ring junction, and show that geometry-dependent quantum interference effects can be used to control the magnetic field in the vicinity of the molecule. Then, treating the molecular junction as a quantum emitter, we demonstrate clear signatures of the local molecular geometry in the non-local radiated power.

cond-mat.mes-hall↗

arXiv2019

Numerically exact counting statistics of energy current in the Kondo regime

We use the inchworm Quantum Monte Carlo method to investigate the full counting statistics of particle and energy currents in a strongly correlated quantum dot. Our method is used to extract the heat fluctuations and entropy production of a quantum thermoelectric device, as well as cumulants of the particle and energy currents. The energy--particle current cross correlations reveal information on the preparation of the system and the interplay of thermal and electric currents. We furthermore demonstrate the signature of a crossover from Coulomb blockade to Kondo physics in the energy current fluctuations, and show how the conventional master equation approach to full counting statistics systematically fails to capture this crossover.

cond-mat.mes-hall↗

arXiv2019

Electron traversal times in disordered graphene nanoribbons

Using the partition-free time-dependent Landauer-B{ü}ttiker formalism for transient current correlations, we study the traversal times taken for electrons to cross graphene nanoribbon (GNR) molecular junctions. We demonstrate electron traversal signatures that vary with disorder and orientation of the GNR. These findings can be related to operational frequencies of GNR-based devices and their consequent rational design.

cond-mat.mes-hall↗

arXiv2019

Lead Geometry and Transport Statistics in Molecular Junctions

We present a numerically exact study of charge transport and its fluctuations through a molecular junction driven out of equilibrium by a bias voltage, using the Inchworm quantum Monte Carlo (iQMC) method. After showing how the technique can be used to address any lead geometry, we concentrate on one dimensional chains as an example. The finite bandwidth of the leads is shown to affect transport properties in ways that cannot be fully captured by quantum master equations: in particular, we reveal an interaction-induced broadening of transport channels that is visible at all voltages, and show how fluctuations of the current are a more sensitive probe of this effect than the mean current.

physics.chem-ph↗

arXiv2018

Numerically exact full counting statistics of the nonequilibrium Anderson impurity model

The time dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron--electron interactions on the time-dependent charge cumulants, first-passage time distributions and $n$-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade- to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single electron transfer events.

cond-mat.mes-hall↗

arXiv2017

Formal equivalence between partitioned and partition-free quenches in quantum transport

In this paper we review the partitioned and partition-free approaches to the calculation of the time-dependent response of a molecular junction to the switch-on of an arbitrary time-dependent bias. Using the non equilibrium Green's function formalism on different time contours, we derive a formal equivalence between these two approaches. This clarifies a recent result of [PRB 95, 104301 (2017)], which is valid for a static bias and single level molecular structure, and extends it to arbitrary time-dependent biases and arbitrarily large molecular structures.

cond-mat.mes-hall↗

arXiv2016

Partition-free theory of time-dependent current correlations in nanojunctions in response to an arbitrary time-dependent bias

Working within the Nonequilibrium Green's Function (NEGF) formalism, a formula for the two-time current correlation function is derived for the case of transport through a nanojunction in response to an arbitrary time-dependent bias. The one-particle Hamiltonian and the Wide Band Limit Approximation (WBLA) are assumed, enabling us to extract all necessary Green's functions and self energies for the system, extending the analytic work presented previously [Ridley et al. Phys. Rev. B (2015)]. We show that our new expression for the two-time correlation function generalises the Büttiker theory of shot and thermal noise on the current through a nanojunction to the time-dependent bias case including the transient regime following the switch-on. Transient terms in the correlation function arise from an initial state that does not assume (as is usually done) that the system is initially uncoupled, i.e. our approach is partition-free. We show that when the bias loses its time-dependence, the long time-limit of the current correlation function depends on the time difference only, as in this case an ideal steady state is reached. This enables derivation of known results for the single frequency power spectrum and for the zero frequency limit of this power spectrum. In addition, we present a technique which for the first time facilitates fast calculations of the transient quantum noise, valid for arbitrary temperature, time and voltage scales. We apply this to the quantum dot and molecular wire systems for both DC and AC biases, and find a novel signature of the traversal time for electrons crossing the wire in the time-dependent cross-lead current correlations.

cond-mat.mes-hall↗

arXiv2015

Calculation of the current response in a nanojunction for an arbitrary time-dependent bias: application to the molecular wire

Recently [Phys. Rev. B 91, 125433 (2015)] we derived a general formula for the time-dependent quantum electron current through a molecular junction subject to an arbitrary time-dependent bias within the Wide Band Limit Approximation (WBLA) and assuming a single particle Hamiltonian. Here we present an efficient numerical scheme for calculating the current and particle number. Using the Padé expansion of the Fermi function, it is shown that all frequency integrals occurring in the general formula for the current can be removed analytically. Furthermore, when the bias in the reservoirs is assumed to be sinusoidal it is possible to manipulate the general formula into a form containing only summations over special functions. To illustrate the method, we consider electron transport through a one-dimensional molecular wire coupled to two leads subject to out-of-phase biases. We also investigate finite size effects in the current response and particle number that results from the switch-on of such a bias.

cond-mat.mes-hall↗

arXiv2014

Current through a multi-lead junction caused by applied bias with arbitrary time-dependence

We apply the Nonequilibrium Green's Function (NEGF) formalism to the problem of a multi-terminal nanojunction subject to an arbitrary time-dependent bias. In particular, we show that taking a generic one-particle system Hamiltonian within the wide band limit approximation (WBLA), it is possible to obtain a closed analytical expression for the current in each lead. Our formula reduces to the well-known result of Jauho et. al. [doi:10.1103/PhysRevB.50.5528] in the limit where the switch-on time is taken to the remote past, and to the result of Tuovinen et. al. [doi:10.1088/1742-6596/427/1/012014] when the bias is maintained at a constant value after the switch-on. As we use a partition-free approach, our formula contains both the long-time current and transient effects due to the sudden switch-on of the bias. Numerical calculations performed for the simple case of a single-level quantum dot coupled to two leads are performed for a sinusoidally-varying bias. At certain frequencies of the driving bias, we observe `ringing' oscillations of the current, whose dependence on the dot level, level width, oscillation amplitude and temperature is also investigated.

cond-mat.mes-hall↗