Efficient algorithm for current spectral density calculation in single-electron tunneling and hopping

This write-up describes an efficient numerical method for the Monte Carlo calculation of the spectral density of current in the multi-junction single-electron devices and hopping structures. In future we plan to expand this write-up into a full-size paper.Comment: 4 page

Sub-electron Charge Relaxation via 2D Hopping Conductors

We have extended Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the process of external charge relaxation. In this situation, a conductor of area $L \times W$ shunts an external capacitor $C$ with initial charge $Q_i$. At low temperatures, the charge relaxation process stops at some "residual" charge value corresponding to the effective threshold of the Coulomb blockade of hopping. We have calculated the r.m.s$.$ value $Q_R$ of the residual charge for a statistical ensemble of capacitor-shunting conductors with random distribution of localized sites in space and energy and random $Q_i$, as a function of macroscopic parameters of the system. Rather unexpectedly, $Q_{R}$ has turned out to depend only on some parameter combination: $X_0 \equiv L W \nu_0 e^2/C$ for negligible Coulomb interaction and $X_{\chi} \equiv LW \kappa^2/C^{2}$ for substantial interaction. (Here $\nu_0$ is the seed density of localized states, while $\kappa$ is the dielectric constant.) For sufficiently large conductors, both functions $Q_{R}/e =F(X)$ follow the power law $F(X)=DX^{-\beta}$, but with different exponents: $\beta = 0.41 \pm 0.01$ for negligible and $\beta = 0.28 \pm 0.01$ for significant Coulomb interaction. We have been able to derive this law analytically for the former (most practical) case, and also explain the scaling (but not the exact value of the exponent) for the latter case. In conclusion, we discuss possible applications of the sub-electron charge transfer for "grounding" random background charge in single-electron devices.Comment: 12 pages, 5 figures. In addition to fixing minor typos and updating references, the discussion has been changed and expande

A Numerical Study of Coulomb Interaction Effects on 2D Hopping Transport

We have extended our supercomputer-enabled Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the case of substantial electron-electron Coulomb interaction. Such interaction may not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In particular, the spectral density $S_I (f)$ of current fluctuations exhibits, at sufficiently low frequencies, a $1/f$-like increase which approximately follows the Hooge scaling, even at vanishing temperature. At higher $f$, there is a crossover to a broad range of frequencies in which $S_I (f)$ is nearly constant, hence allowing characterization of the current noise by the effective Fano factor F\equiv S_I(f)/2e \left. For sufficiently large conductor samples and low temperatures, the Fano factor is suppressed below the Schottky value (F=1), scaling with the length $L$ of the conductor as $F = (L_c / L)^{\alpha}$. The exponent $\alpha$ is significantly affected by the Coulomb interaction effects, changing from $\alpha = 0.76 \pm 0.08$ when such effects are negligible to virtually unity when they are substantial. The scaling parameter $L_c$, interpreted as the average percolation cluster length along the electric field direction, scales as $L_c \propto E^{-(0.98 \pm 0.08)}$ when Coulomb interaction effects are negligible and $L_c \propto E^{-(1.26 \pm 0.15)}$ when such effects are substantial, in good agreement with estimates based on the theory of directed percolation.Comment: 19 pages, 7 figures. Fixed minor typos and updated reference

A Numerical Study of Transport and Shot Noise at 2D Hopping

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with the completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field $E$ and temperature $T$, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit $1/f$ noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor $F$. For sufficiently large samples, $F$ scales with conductor length $L$ as $(L_c/L)^{\alpha}$, where $\alpha=0.76\pm 0.08 < 1$, and parameter $L_c$ is interpreted as the average percolation cluster length. At relatively low $E$, the electric field dependence of parameter $L_c$ is compatible with the law $L_c\propto E^{-0.911}$ which follows from directed percolation theory arguments.Comment: 17 pages, 8 figures; Fixed minor typos and updated reference

Efficient algorithm for current spectral density calculation in single-electron tunneling and hopping

This write-up describes an efficient numerical method for the Monte Carlo calculation of the spectral density of current in the multi-junction single-electron devices and hopping structures. In future we plan to expand this write-up into a full-size paper

A numerical study of Coulomb interaction effects on 2D hopping transport

Abstract We have extended our supercomputer-enabled Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the case of substantial electron-electron Coulomb interaction. Such interaction may not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In particular, the spectral density S I ( f ) of current fluctuations exhibits, at sufficiently low frequencies, a 1/ f -like increase which approximately follows the Hooge scaling, even at vanishing temperature. At higher f , there is a crossover to a broad range of frequencies in which S I ( f ) is nearly constant, hence allowing characterization of the current noise by the effective Fano factor F ≡ S I ( f )/2e I . For sufficiently large conductor samples and low temperatures, the Fano factor is suppressed below the Schottky value (F = 1), scaling with the length L of the conductor as F = (L c /L) α . The exponent α is significantly affected by the Coulomb interaction effects, changing from α = 0.76 ± 0.08 when such effects are negligible to virtually unity when they are substantial. The scaling parameter L c , interpreted as the average percolation cluster length along the electric field direction, scales as L c ∝ E −(0.98±0.08) when Coulomb interaction effects are negligible and L c ∝ E −(1.26±0.15) when such effects are substantial, in good agreement with estimates based on the theory of directed percolation

Diagnosis and management of acute variceal bleeding: Asian Pacific Association for Study of the Liver recommendations

Acute variceal bleeding (AVB) is a medical emergency and associated with a mortality of 20% at 6 weeks. Significant advances have occurred in the recent past and hence there is a need to update the existing consensus guidelines. There is also a need to include the literature from the Eastern and Asian countries where majority of patients with portal hypertension (PHT) live. The expert working party, predominantly from the Asia-Pacific region, reviewed the existing literature and deliberated to develop consensus guidelines. The working party adopted the Oxford system for developing an evidence-based approach. Only those statements that were unanimously approved by the experts were accepted. AVB is defined as a bleed in a known or suspected case of PHT, with the presence of hematemesis within 24 h of presentation, and/or ongoing melena, with last melanic stool within last 24 h. The time frame for the AVB episode is 48 h. AVB is further classified as active or inactive at the time of endoscopy. Combination therapy with vasoactive drugs (< 30 min of hospitalization) and endoscopic variceal ligation (door to scope time < 6 h) is accepted as first-line therapy. Rebleeding (48 h of T (0)) is further sub-classified as very early rebleeding (48 to 120 h from T (0)), early rebleeding (6 to 42 days from T (0)) and late rebleeding (after 42 days from T (0)) to maintain uniformity in clinical trials. Emphasis should be to evaluate the role of adjusted blood requirement index (ABRI), assessment of associated comorbid conditions and poor predictors of non-response to combination therapy, and proposed APASL (Asian Pacific Association for Study of the Liver) Severity Score in assessing these patients. Role of hepatic venous pressure gradient in AVB is considered useful. Antibiotic (cephalosporins) prophylaxis is recommended and search for acute ischemic hepatic injury should be done. New guidelines have been developed for management of variceal bleed in patients with non-cirrhotic PHT and variceal bleed in pediatric patients. Management of acute variceal bleeding in Asia-Pacific region needs special attention for uniformity of treatment and future clinical trials