arXiv subjects

Ph. Jacquod

Publications and source records attributed to Ph. Jacquod.

At least 19 recordsLinked to original sources

arXiv2021

Matrix Perturbation Theory of Inter-Area Oscillations

Interconnecting power systems has a number of advantages such as better electric power quality, increased reliability of power supply, economies of scales through production and reserve pooling and so forth. Simultaneously, it may jeopardize the overall system stability with the emergence of so-called inter-area oscillations, which are coherent oscillations involving groups of rotating machines separated by large distances up to thousands of kilometers. These often weakly damped modes may have harmful consequences for grid operation, yet despite decades of investigations, the mechanisms that generate them are still poorly understood, and the existing theories are based on assumptions that are not satisfied in real power grids where such modes are observed. Here we construct a matrix perturbation theory of large interconnected power systems that clarifies the origin and the conditions for the emergence of inter-area oscillations. We show that coherent inter-area oscillations emerge from the zero-modes of a multi-area network Laplacian matrix, which hybridize only weakly with other modes, even under significant capacity of the inter-area tie-lines, i.e. even when the standard assumption of area partitioning is not satisfied. The general theory is illustrated on a two-area system, and numerically applied to the well-connected PanTaGruEl model of the synchronous grid of continental Europe.

nlin.AO↗

arXiv2019

Transient Performance of Electric Power Networks under Colored Noise

New classes of performance measures have been recently introduced to quantify the transient response to external disturbances of coupled dynamical systems on complex networks. These performance measures are time-integrated quadratic forms in the system's coordinates or their time derivative. So far, investigations of these performance measures have been restricted to Dirac-$δ$ impulse disturbances, in which case they can be alternatively interpreted as giving the long time output variances for stochastic white noise power demand/generation fluctuations. Strictly speaking, the approach is therefore restricted to power fluctuating on time scales shorter than the shortest time scales in the swing equations. To account for power productions from new renewable energy sources, we extend these earlier works to the relevant case of colored noise power fluctuations, with a finite correlation time $τ> 0$. We calculate a closed-form expression for generic quadratic performance measures. Applied to specific cases, this leads to a spectral representation of performance measures as a sum over the non-zero modes of the network Laplacian. Our results emphasize the competition between inertia, damping and the Laplacian modes, whose balance is determined to a large extent by the noise correlation time scale $τ$.

math.OC↗

arXiv2016

Topologically Protected Loop Flows in High Voltage AC Power Grids

Geographical features such as mountain ranges or big lakes and inland seas often result in large closed loops in high voltage AC power grids. Sizable circulating power flows have been recorded around such loops, which take up transmission line capacity and dissipate but do not deliver electric power. Power flows in high voltage AC transmission grids are dominantly governed by voltage angle differences between connected buses, much in the same way as Josephson currents depend on phase differences between tunnel-coupled superconductors. From this previously overlooked similarity we argue here that circulating power flows in AC power grids are analogous to supercurrents flowing in superconducting rings and in rings of Josephson junctions. We investigate how circulating power flows can be created and how they behave in the presence of ohmic dissipation. We show how changing operating conditions may generate them, how significantly more power is ohmically dissipated in their presence and how they are topologically protected, even in the presence of dissipation, so that they persist when operating conditions are returned to their original values. We identify three mechanisms for creating circulating power flows, (i) by loss of stability of the equilibrium state carrying no circulating loop flow, (ii) by tripping of a line traversing a large loop in the network and (iii) by reclosing a loop that tripped or was open earlier. Because voltage angles are uniquely defined, circulating power flows can take on only discrete values, much in the same way as circulation around vortices is quantized in superfluids.

nlin.AO↗

arXiv2013

Universal Features of Spin Transport and Breaking of Unitary Symmetries

When time-reversal symmetry is broken, quantum coherent systems with and without spin rotational symmetry exhibit the same universal behavior in their electric transport properties. We show that spin transport discriminates between these two cases. In systems with large charge conductance, spin transport is essentially insensitive to the breaking of time-reversal symmetry. However, in the opposite limit of a single exit channel, spin currents vanish identically in the presence of time-reversal symmetry, but are turned on by breaking it with an orbital magnetic field.

cond-mat.mes-hall↗

arXiv2013

Local Temperature of Out-of-Equilibrium Quantum Electron Systems

We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature measured by the probe (i) is independent of details of the system-probe coupling, (ii) is equal to the temperature obtained from an independent current-noise measurement, (iii) satisfies the transitivity condition expressed by the zeroth law of thermodynamics, and (iv) is consistent with Carnot's theorem. This local temperature therefore characterizes the system in the common sense of equilibrium thermodynamics, but remains well defined even in out-of-equilibrium situations with no local equilibrium.

cond-mat.stat-mech↗

arXiv2012

Spin transistor action from Onsager reciprocity and SU(2) gauge theory

We construct a local gauge transformation to show how, in confined systems, a generic, weak nonhomogeneous SU(2) spin-orbit Hamiltonian reduces to two U(1) Hamiltonians for spinless fermions at opposite magnetic fields, to leading order in the spin-orbit strength. Using an Onsager relation, we further show how the resulting spin conductance vanishes in a two-terminal setup, and how it is turned on by either weakly breaking time-reversal symmetry or opening additional transport terminals. We numerically check our theory for mesoscopic cavities as well as Aharonov-Bohm rings.

cond-mat.mes-hall↗

arXiv2010

Coherent Destruction of Coulomb Blockade Peaks in Molecular Junctions

Coherent electronic transport in single-molecule junctions is investigated in the Coulomb blockade regime. Both the transmission phase and probability are calculated for junctions with various contact symmetries. A dramatic suppression of the Coulomb blockade peaks is predicted for junctions where multiple atomic orbitals of the molecule couple to a single electrode although the charging steps are unaffected.

cond-mat.mes-hall↗

arXiv2010

Electrical probing of the spin conductance of mesoscopic cavities

We investigate spin-dependent transport in three--terminal mesoscopic cavities with spin--orbit coupling. Focusing on the inverse spin Hall effect, we show how injecting a pure spin current or a polarized current from one terminal generates additional charge current and/or voltage across the two output terminals. This allows to extract the spin conductance of the cavity from two purely electrical measurements on the output. We use random matrix theory to show that the spin conductance of chaotic ballistic cavities fluctuates universally about zero mesoscopic average and describe experimental implementations of mesoscopic spin to charge current converters.

cond-mat.mes-hall↗

arXiv2010

Geometric Correlations and Breakdown of Mesoscopic Universality in Spin Transport

We construct a unified semiclassical theory of charge and spin transport in chaotic ballistic and disordered diffusive mesoscopic systems with spin-orbit interaction. Neglecting dynamic effects of spin-orbit interaction, we reproduce the random matrix theory results that the spin conductance fluctuates universally around zero average. Incorporating these effects in the theory, we show that geometric correlations generate finite average spin conductances, but that they do not affect the charge conductance to leading order. The theory, which is confirmed by numerical transport calculations, allows us to investigate the entire range from the weak to the previously unexplored strong spin-orbit regime, where the spin rotation time is shorter than the momentum relaxation time.

cond-mat.mes-hall↗

arXiv2010

Scattering Theory of Current-Induced Spin Polarization

We construct a novel scattering theory to investigate magnetoelectrically induced spin polarizations. Local spin polarizations generated by electric currents passing through a spin-orbit coupled mesoscopic system are measured by an external probe. The electrochemical and spin-dependent chemical potentials on the probe are controllable and tuned to values ensuring that neither charge nor spin current flow between the system and the probe, on time-average. For the relevant case of a single-channel probe, we find that the resulting potentials are exactly independent of the transparency of the contact between the probe and the system. Assuming that spin relaxation processes are absent in the probe, we therefore identify the local spin-dependent potentials in the sample at the probe position, and hence the local current-induced spin polarization, with the spin-dependent potentials in the probe itself. The statistics of these local chemical potentials is calculated within random matrix theory. While they vanish on spatial and mesoscopic average, they exhibit large fluctuations, and we show that single systems typically have spin polarizations exceeding all known current-induced spin polarizations by a parametrically large factor. Our theory allows to calculate quantum correlations between spin polarizations inside the sample and spin currents flowing out of it. We show that these large polarizations correlate only weakly with spin currents in external leads, and that only a fraction of them can be converted into a spin current in the linear regime of transport, which is consistent with the mesoscopic universality of spin conductance fluctuations. We numerically confirm the theory.

cond-mat.mes-hall↗

arXiv2009

Controlling the Sign of Magnetoconductance in Andreev Quantum Dots

We construct a theory of coherent transport through a ballistic quantum dot coupled to a superconductor. We show that the leading-order quantum correction to the two-terminal conductance of these Andreev quantum dots may change sign depending on (i) the number of channels carried by the normal leads or (ii) the magnetic flux threading the dot. In contrast, spin-orbit interaction may affect the magnitude of the correction, but not always its sign. Experimental signatures of the effect include a non-monotonic magnetoconductance curve and a transition from an insulator-like to a metal-like temperature dependence of the conductance. Our results are applicable to ballistic or disordered dots.

cond-mat.mes-hall↗

arXiv2009

Coherent Thermoelectric Effects in Mesoscopic Andreev Interferometers

We investigate thermoelectric transport through Andreev interferometers. We show that the ratio of the thermal and the charge conductance exhibits large oscillations with the phase difference $ϕ$ between the two superconducting contacts, and that the Wiedemann-Franz law holds only when $ϕ=π$. A large average thermopower furthermore emerges whenever there is an asymmetry in the dwell times to reach the superconducting contacts. When this is the case, the thermopower is odd in $ϕ$. In contrast, when the average times to reach either superconducting contact are the same, the average thermopower is zero, however mesoscopic effects (analogous to universal conductance fluctuations) lead to a sample-dependent thermopower which is systematically even in $ϕ$.

cond-mat.supr-con↗

arXiv2009

Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom

This review summarizes and amplifies on recent investigations of coupled quantum dynamical systems in the short wavelength limit. We formulate and attempt to answer three fundamental questions: (i) What drives a dynamical quantum system to behave classically ? (ii) What determines the rate at which two coupled quantum--mechanical systems become entangled ? (iii) How does irreversibility occur in quantum systems with few degrees of freedom ? We embed these three questions in the broader context of the quantum--classical correspondence, which motivates the use of short--wavelength approximations to quantum mechanics such as the trajectory-based semiclassical methods and random matrix theory. Doing so, we propose a novel investigative procedure towards decoherence and the emergence of classicality out of quantumness in dynamical systems coupled to external degrees of freedom. We reproduce known results derived using master equation or Lindblad approaches but also generate novel ones. In particular we show how local exponential instability also affects the temporal evolution of quantum chaotic dynamical systems. We extensively rely on numerical experiments to illustrate our findings and briefly comment on possible extensions to more complex problems involving environments with $n \gg 1$ interacting dynamical systems, going beyond the uncoupled harmonic oscillator model of Caldeira and Leggett.

quant-ph↗

arXiv2007

Macroscopic Resonant Tunneling through Andreev Interferometers

We investigate the conductance through and the spectrum of ballistic chaotic quantum dots attached to two s-wave superconductors, as a function of the phase difference $ϕ$ between the two order parameters. A combination of analytical techniques -- random matrix theory, Nazarov's circuit theory and the trajectory-based semiclassical theory -- allows us to explore the quantum-to-classical crossover in detail. When the superconductors are not phase-biased, $ϕ=0$, we recover known results that the spectrum of the quantum dot exhibits an excitation gap, while the conductance across two normal leads carrying $N_{\rm N}$ channels and connected to the dot via tunnel contacts of transparency $Γ_{\rm N}$ is $\propto Γ_{\rm N}^2 N_{\rm N}$. In contrast, when $ϕ=π$, the excitation gap closes and the conductance becomes $G \propto Γ_{\rm N} N_{\rm N}$ in the universal regime. For $Γ_{\rm N} \ll 1$, we observe an order-of-magnitude enhancement of the conductance towards $G \propto N_{\rm N}$ in the short-wavelength limit. We relate this enhancement to resonant tunneling through a macroscopic number of levels close to the Fermi energy. Our predictions are corroborated by numerical simulations.

cond-mat.mes-hall↗

arXiv2007

Superconductivity-induced macroscopic resonant tunneling

We show analytically and by numerical simulations that the conductance through $π$-biased chaotic Josephson junctions is enhanced by several orders of magnitude in the short-wavelength regime. We identify the mechanism behind this effect as {\it macroscopic resonant tunneling} through a macroscopic number of low-energy quasi-degenerate Andreev levels.

cond-mat.mes-hall↗

arXiv2006

Mesoscopic Spin Hall Effect

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is large compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average. For a fixed sample configuration, the transverse spin current has a finite typical value ~e^2 V/h, proportional to the longitudinal bias V on the sample, and corresponding to about one excess open channel for one of the two spin species. Our analytical results are in agreement with numerical results in a diffusive system [W. Ren et al., Phys. Rev. Lett. 97, 066603 (2006)] and are further confirmed by numerical simulation in a chaotic cavity.

cond-mat.mes-hall↗

arXiv2006

Semiclassical Theory of Quantum Chaotic Transport: Phase-Space Splitting, Coherent Backscattering and Weak Localization

We investigate transport properties of quantized chaotic systems in the short wavelength limit. We focus on non-coherent quantities such as the Drude conductance, its sample-to-sample fluctuations, shot-noise and the transmission spectrum, as well as coherent effects such as weak localization. We show how these properties are influenced by the emergence of the Ehrenfest time scale $\tE$. Expressed in an optimal phase-space basis, the scattering matrix acquires a block-diagonal form as $\tE$ increases, reflecting the splitting of the system into two cavities in parallel, a classical deterministic cavity (with all transmission eigenvalues either 0 or 1) and a quantum mechanical stochastic cavity. This results in the suppression of the Fano factor for shot-noise and the deviation of sample-to-sample conductance fluctuations from their universal value. We further present a semiclassical theory for weak localization which captures non-ergodic phase-space structures and preserves the unitarity of the theory. Contrarily to our previous claim [Phys. Rev. Lett. 94, 116801 (2005)], we find that the leading off-diagonal contribution to the conductance leads to the exponential suppression of the coherent backscattering peak and of weak localization at finite $\tE$. This latter finding is substantiated by numerical magnetoconductance calculations.

cond-mat.mes-hall↗

arXiv2005

Semiclassical Theory of Quantum Chaotic Transport: Phase-Space Splitting

This paper is withdrawn. While almost all findings reported here remain valid, some of our comments on the fate of weak localization corrections to the conductance in the deep semiclassical limit are now obsolete. Contrarily to what was suggested here, we find an exponential suppression of weak localization at finite Ehrenfest time. For more details, see cond-mat/0512662 .

cond-mat.mes-hall↗