Sensitivity of asymmetric rate-dependent critical systems to initial conditions: insights into cellular decision making

The work reported here aims to address the effects of time-dependent parameters and stochasticity on decision-making in biological systems. We achieve this by extending previous studies that resorted to simple normal forms. Yet, we focus primarily on the issue of the system's sensitivity to initial conditions in the presence of different noise distributions. In addition, we assess the impact of two-way sweeping through the critical region of a canonical Pitchfork bifurcation with a constant external asymmetry. The parallel with decision-making in bio-circuits is performed on this simple system since it is equivalent in its available states and dynamics to more complex genetic circuits. Overall, we verify that rate-dependent effects are specific to particular initial conditions. Information processing for each starting state is affected by the balance between sweeping speed through critical regions, and the type of fluctuations added. For a heavy-tail noise, forward-reverse dynamic bifurcations are more efficient in processing the information contained in external signals, when compared to the system relying on escape dynamics, if it starts at an attractor not favoured by the asymmetry and, in conjunction, if the sweeping amplitude is large

Weak localization, Aharonov-Bohm oscillations and decoherence in arrays of quantum dots

Combining scattering matrix theory with non-linear $\sigma$-model and Keldysh technique we develop a unified theoretical approach enabling one to non-perturbatively study the effect of electron-electron interactions on weak localization and Aharonov-Bohm oscillations in arbitrary arrays of quantum dots. Our model embraces (i) weakly disordered conductors (ii) strongly disordered conductors and (iii) metallic quantum dots. In all these cases at $T \to 0$ the electron decoherence time is found to saturate to a finite value determined by the universal formula which agrees quantitatively with numerous experimental results. Our analysis provides overwhelming evidence in favor of electron-electron interactions as a universal mechanism for zero temperature electron decoherence in disordered conductors.Comment: 19 pages, 13 figures, invited paper, published in a special issue of Fiz. Nizk. Temp. (Kharkov) dedicated to Prof. Igor Kuli

Interaction-Induced Quantum Dephasing in Mesoscopic Rings

Combining nonperturbative techniques with Monte Carlo simulations we demonstrate that quantum coherence effects for a particle on a ring are suppressed beyond a finite length $L_{\phi}$ even at zero temperature if the particle is coupled to a diffusive electron gas by means of long range Coulomb interaction. This length is consistent with $L_{\phi}$ derived from weak-localization-type of analysis.Comment: 4 revtex pages, 2 figure

Superconductor-insulator quantum phase transition in a single Josephson junction

The superconductor-to-insulator quantum phase transition in resistively shunted Josephson junctions is investigated by means of path-integral Monte Carlo simulations. This numerical technique allows us to directly access the (previously unexplored) regime of the Josephson-to-charging energy ratios E_J/E_C of order one. Our results unambiguously support an earlier theoretical conjecture, based on renormalization-group calculations, that at T -> 0 the dissipative phase transition occurs at a universal value of the shunt resistance R_S = h/4e^2 for all values E_J/E_C. On the other hand, finite-temperature effects are shown to turn this phase transition into a crossover, which position depends significantly on E_J/E_C, as well as on the dissipation strength and on temperature. The latter effect needs to be taken into account in order to reconcile earlier theoretical predictions with recent experimental results.Comment: 7 pages, 6 figure

Persistent current noise and electron-electron interactions

We analyze fluctuations of persistent current (PC) produced by a charged quantum particle moving in a ring and interacting with a dissipative environment formed by diffusive electron gas. We demonstrate that in the presence of interactions such PC fluctuations persist down to zero temperature. In the case of weak interactions and/or sufficiently small values of the ring radius $R$ PC noise remains coherent and can be tuned by external magnetic flux $\Phi_x$ piercing the ring. In the opposite limit of strong interactions and/or large values of $R$ fluctuations in the electronic bath strongly suppress quantum coherence of the particle down to $T=0$ and induce incoherent $\Phi_x$-independent current noise in the ring which persists even at $\Phi_x=0$ when the average PC is absent.Comment: 12 pages, 8 figure

Strong Charge Fluctuations in the Single-Electron Box: A Quantum Monte Carlo Analysis

We study strong electron tunneling in the single-electron box, a small metallic island coupled to an electrode by a tunnel junction, by means of quantum Monte Carlo simulations. We obtain results, at arbitrary tunneling strength, for the free energy of this system and the average charge on the island as a function of an external bias voltage. In much of the parameter range an extrapolation to the ground state is possible. Our results for the effective charging energy for strong tunneling are compared to earlier -- in part controversial -- theoretical predictions and Monte Carlo simulations

Doubly stochastic coherence via noise-induced symmetry in bistable neural models

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance

Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibanes et al. [Phys. Rev. Lett. 87, 020601-1 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations

Low-temperature characterization of Nb-Cu-Nb weak links with Ar ion-cleaned interfaces

We characterize niobium-based lateral Superconductor (S) - Normal metal (N) - Superconductor weak links through low-temperature switching current measurements and tunnel spectroscopy. We fabricate the SNS devices in two separate lithography and deposition steps, combined with strong argon ion cleaning before the normal metal deposition in the last step. Our SNS weak link consists of high-quality sputtered Nb electrodes that are contacted with evaporated Cu. The two-step fabrication flow enables great flexibility in the choice of materials and pattern design. A comparison of the temperature-dependent equilibrium critical supercurrent with theoretical predictions indicates that the quality of the Nb-Cu interface is similar to that of evaporated Al-Cu weak links. Aiming at increased sensitivity, range of operation temperatures, and thermal isolation, we investigate how these SNS structures can be combined with shadow-evaporated aluminum tunnel junctions for sensor applications that utilize the superconducting proximity effect. To this end, we demonstrate a hybrid magnetic flux sensor based on a Nb-Cu-Nb SNS junction, where the phase-dependent normal metal density of states is probed with an Al tunnel junction.Comment: 5 pages, 3 figure

Systems Medicine of Cancer: Bringing Together Clinical Data and Nonlinear Dynamics of Genetic Networks.

Editoria