Fluctuation relations for a driven Brownian particle

We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski and Gallavotti-Cohen in different special cases

Transport Statistics of Bistable Systems

We consider the transport statistics of classical bistable systems driven by noise. The stochastic path integral formalism is used to investigate the dynamics and distribution of transmitted charge. Switching rates between the two stable states are found from an instanton calculation, leading to an effective two-state system on a long time scale. In the bistable current range, the telegraph noise dominates the distribution, whose logarithm is found to be universally described by a tilted ellipse.Comment: 4 pages, 3 figures, version to appear in Phys. Rev. Let

Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method

We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation is consistent with causality and the sum rule associated with the number conservation in the low momentum limit, in contrast to usual acausal diffusion equations given by using the Fick's law. After employing the Markov approximation, we find that the equation has the similar form to the causal diffusion equation. Our result suggests that current-current correlations are not necessarily adequate as the definition of diffusion constants.Comment: 10 pages, 1 figure, Final version published in Phys. Rev.

On the emergence of very long time fluctuations and 1/f noise in ideal flows

This study shows the connection between three previously observed but seemingly unrelated phenomena in hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulent flows, involving the emergence of fluctuations occurring on very long time scales: the low-frequency 1/f noise in the power frequency spectrum, the delayed ergodicity of complex valued amplitude fluctuations in wavenumber space, and the spontaneous flippings or reversals of large scale fields. Direct numerical simulations of ideal MHD and HD are employed in three space dimensions, at low resolution, for long periods of time, and with high accuracy to study several cases: Different geometries, presence of rotation and/or a uniform magnetic field, and different values of the associated conserved global quantities. It is conjectured that the origin of all these long-time phenomena is rooted in the interaction of the longest wavelength fluctuations available to the system with fluctuations at much smaller scales. The strength of this non-local interaction is controlled either by the existence of conserved global quantities with a back-transfer in Fourier space, or by the presence of a slow manifold in the dynamics.Comment: 17 pages, 21 figures, accepted for publication in Physical Review

One-by-one trap activation in silicon nanowire transistors

Flicker or 1/f noise in metal-oxide-semiconductor field-effect transistors (MOSFETs) has been identified as the main source of noise at low frequency. It often originates from an ensemble of a huge number of charges trapping and detrapping. However, a deviation from the well-known model of 1/f noise is observed for nanoscale MOSFETs and a new model is required. Here, we report the observation of one-by-one trap activation controlled by the gate voltage in a nanowire MOSFET and we propose a new low-frequency-noise theory for nanoscale FETs. We demonstrate that the Coulomb repulsion between electronically charged trap sites avoids the activation of several traps simultaneously. This effect induces a noise reduction by more than one order of magnitude. It decreases when increasing the electron density in the channel due to the electrical screening of traps. These findings are technologically useful for any FETs with a short and narrow channel.Comment: One file with paper and supplementary informatio

Decoherence of a Josephson qubit due to coupling to two level systems

Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two level systems in the oxide barrier produce fluctuations and 1/f noise in the Josephson junction critical current I_o. This in turn leads to fluctuations in the qubit energy splitting that degrades the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.Comment: 23 pages, Latex, 6 encapsulated postscript figure

Linear Stochastic Models of Nonlinear Dynamical Systems

We investigate in this work the validity of linear stochastic models for nonlinear dynamical systems. We exploit as our basic tool a previously proposed Rayleigh-Ritz approximation for the effective action of nonlinear dynamical systems started from random initial conditions. The present paper discusses only the case where the PDF-Ansatz employed in the variational calculation is ``Markovian'', i.e. is determined completely by the present values of the moment-averages. In this case we show that the Rayleigh-Ritz effective action of the complete set of moment-functions that are employed in the closure has a quadratic part which is always formally an Onsager-Machlup action. Thus, subject to satisfaction of the requisite realizability conditions on the noise covariance, a linear Langevin model will exist which reproduces exactly the joint 2-time correlations of the moment-functions. We compare our method with the closely related formalism of principal oscillation patterns (POP), which, in the approach of C. Penland, is a method to derive such a linear Langevin model empirically from time-series data for the moment-functions. The predictive capability of the POP analysis, compared with the Rayleigh-Ritz result, is limited to the regime of small fluctuations around the most probable future pattern. Finally, we shall discuss a thermodynamics of statistical moments which should hold for all dynamical systems with stable invariant probability measures and which follows within the Rayleigh-Ritz formalism.Comment: 36 pages, 5 figures, seceq.sty for sequential numbering of equations by sectio

Academic freedom in Europe: reviewing UNESCO’s recommendation

This paper examines the compliance of universities in the European Union with the UNESCO Recommendation concerning the Status of Higher–Education Teaching Personnel, which deals primarily with protection for academic freedom. The paper briefly surveys the European genesis of the modern research university and academic freedom, before evaluating compliance with the UNESCO recommendation on institutional autonomy, academic freedom, university governance and tenure. Following from this, the paper examines the reasons for the generally low level of compliance with the UNESCO Recommendation within the EU states, and considers how such compliance could be improved

Direct-Current Induced Dynamics in Co90Fe10/Ni80Fe20 Point Contacts

We have directly measured coherent high-frequency magnetization dynamics in ferromagnet films induced by a spin-polarized DC current. The precession frequency can be tuned over a range of several gigahertz, by varying the applied current. The frequencies of excitation also vary with applied field, resulting in a microwave oscillator that can be tuned from below 5 GHz to above 40 GHz. This novel method of inducing high-frequency dynamics yields oscillations having quality factors from 200 to 800. We compare our results with those from single-domain simulations of current-induced dynamics

Conditional statistics of electron transport in interacting nanoscale conductors

Interactions between nanoscale semiconductor structures form the basis for charge detectors in the solid state. Recent experimental advances have demonstrated the on-chip detection of single electron transport through a quantum dot (QD). The discreteness of charge in units of e leads to intrinsic fluctuations in the electrical current, known as shot noise. To measure these single-electron fluctuations a nearby coherent conductor, called a quantum point contact (QPC), interacts with the QD and acts as a detector. An important property of the QPC charge detector is noninvasiveness: the system physically affects the detector, not visa-versa. Here we predict that even for ideal noninvasive detectors such as the QPC, when a particular detector result is observed, the system suffers an informational backaction, radically altering the statistics of transport through the QD as compared to the unconditional shot noise. We develop a theoretical model to make predictions about the joint current probability distributions and conditional transport statistics. The experimental findings reported here demonstrate the reality of informational backaction in nanoscale systems as well as a variety of new effects, such as conditional noise enhancement, which are in essentially perfect agreement with our model calculations. This type of switching telegraph process occurs abundantly in nature, indicating that these results are applicable to a wide variety of systems.Comment: 16 pages, 3 figures, to appear in Nature Physic