Smooth Potential Research Articles

Perspective on Majorana bound-states in hybrid superconductor-semiconductor nanowires

A personal perspective is given on a decade of research on Majorana bound states (MBS) in hybrid devices of semiconducting nanowires covered with a superconductor. Predicted experimental signatures like zero-bias anomalies turned out to be false positive evidence for topological MBS. Zero-bias conductance peaks have found alternative explanations in terms of material disorder and smooth boundary potentials. A recount is given on various predictions, observations and re-interpretations, as well as the lessons learned in retrospect and an outlook on the future.

A Nekhoroshev-type theorem for the nonlinear Schrödinger equations on the d-dimensional torus

We prove a Nekhoroshev type long time stability result for the following nonlinear Schrödinger (NLS) equations on the d-dimensional torus i u t = − △ u + V ∗ u + ∂ F ( | u | 2 ) ∂ u ¯ ( u , u ¯ ) , x ∈ T d , t ∈ R , where V is a smooth convolution potential, F ( z ) is a real-valued polynomial function in z satisfying F ( 0 ) = F ′ ( 0 ) = 0 . More precisely, it is proved that in modified Sobolev space (see (2)) if the norm of initial datum is smaller than ε ( 0 < ε ≪ 1 ) , then the corresponding solution is bounded by 2 ε over time-intervals of length e e 1 ε . The result generalizes the 1-dimensional case in L. Biasco, J.E. Massetti, M. Procesi. [An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS. Comm Math Phys. 2020;375(3):2089–2153] to d-dimensional NLS equations.

Piecewise linear potentials for false vacuum decay and negative modes

We study bounce solutions and associated negative modes in the class of piecewise linear triangular-shaped potentials that may be viewed as approximations of smooth potentials. In these simple potentials, the bounce solution and action can be obtained analytically for a general spacetime dimension D. The eigenequations for the fluctuations around the bounce are universal and have the form of a Schrödinger-like equation with delta-function potentials. This Schrödinger equation is solved exactly for the negative modes whose number is confirmed to be one. The latter result may justify the usefulness of such piecewise linear potentials in the study of false vacuum decay. Published by the American Physical Society 2024

Noise-induced transport in a periodic square-well potential

We investigate a thermal ratchet based on a Brownian particle in a spatially periodic square-well potential driven by a time-dependent square-wave signal. In this model, we rock the Brownian particle between two square-well potentials tilted in opposite directions to induce a net current. Employing the Stratonovich formula and an independent approach using suitable boundary conditions and a normalization condition, we obtain an exact expression for the current in the adiabatic limit, and we observe that there are optimal values of various parameters at which the current can be maximized. In several parameter regimes, our simple non-linear model displays a behavior distinct from some other models of a rocked ratchet. For example, a reversal in the current direction is observed as the square-wave signal’s amplitude or the thermal bath’s temperature is varied. However, under similar conditions, no such current reversal was seen in the case of a periodically rocked Brownian motor in a sawtooth or a smooth potential. Furthermore, unlike the latter type of rocked Brownian motors, the square-well model yields zero current in the deterministic limit, as thermal energy is indispensable for the functioning of the motor.

Integer quantum Hall transition: An S -matrix approach to random networks

In this paper we propose an S-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work [I. A. Gruzberg, A. Klümper, W. Nuding, and A. Sedrakyan, ]. Random networks are modifications of the Chalker-Coddington (CC) model for the integer quantum Hall transition that more faithfully captures the physics of electrons moving in a strong magnetic field and a smooth disorder potential. This method has considerable advantages compared to the transfer matrix approach and gives the value ν≈2.4 for the critical exponent of the localization length in a random network. This finding confirms our previous result and is surprisingly close to the experimental value νexpt≈2.38 observed at the integer quantum Hall transition but substantially different from the CC value νCC≈2.6. Published by the American Physical Society 2024

Effect of Angular Momentum–Dependent Transparency on the Neutron-Nucleus Cross Section

We study the effect of the angular momentum dependence of the optical potential transparency on the neutron-nucleus cross section. In this work, we derive a functional form of the neutron-nucleus cross section with respect to spherical optical potential using the collision matrix and modify it. We also apply an analytical model (Ramsauer) to the square optical potential and the optical model using the TALYS 1.96 code to get the angular momentum–independent transparency and demonstrate the effect of the angular momentum dependence via comparison of two models. In this work, we calculate the neutron cross sections for 40 ≤ A ≤ 90 nuclei, with energies 100 MeV ≤ En ≤ 200MeV theoretically, the for ℓ ≠ 0 case. We find that the angular momentum dependence of the transparency treats good calculations of the neutron-nucleus cross section; a finite number of angular momentums will contribute appreciably to the nuclear reaction. The present study on smooth optical potential leads to useful insight into the mechanisms of neutron-induced reactions, particularly for medium nuclei at high energies.

Development of a two‐dimensional bipolar electrochemistry technique for high throughput corrosion screening

AbstractBipolar electrochemistry allows testing and analysing the crevice corrosion, pitting corrosion, passivation, general corrosion, and cathodic deposition reactions on one sample after a single experiment. A novel two‐dimensional bipolar electrochemistry setup is designed using two orthogonal feeder electrode arrangements, allowing corrosion screening tests across a far wider potential range with a smooth potential gradient to be assessed. This two‐dimensional bipolar electrochemistry setup was applied here to simultaneously measure for the simultaneous measurement of the nucleation and propagation of pitting and crevice corrosion under a broad range of applied potential on type 420 stainless steel, which has a very short localised corrosion induction time. It reduces the error from corrosion induction to corrosion competition, and all pits and crevice corrosion have no lacy cover. Results show crevice corrosion can gain current density and easier to support its nucleation and propagation at different potential regions more easily than pitting corrosion.

Measuring the substructure mass power spectrum of 23 SLACS strong galaxy–galaxy lenses with convolutional neural networks

ABSTRACT Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy–galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian random field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favouring a high frequency power spectrum across our lens population.

Martingale solutions to stochastic nonlocal Cahn–Hilliard- Navier–Stokes systems with singular potentials driven by multiplicative noise of jump type

Abstract In the diffuse interface theory, the motion of two incompressible viscous fluids and the evolution of their interface are described by the well-known model H. The model consists of the Navier–Stokes equations, nonlinearly coupled with a convective Cahn–Hilliard type equation. Here we consider a stochastic version of the model driven by a noise of Lévy type, and where the standard Cahn–Hilliard equation is replaced by its nonlocal version with a singular (e.g., logarithmic) potential. The case of smooth potentials with arbitrary polynomial growth has been already analyzed in [G. Deugoué, A. Ndongmo Ngana and T. Tachim Medjo, Martingale solutions to stochastic nonlocal Cahn–Hilliard–Navier–Stokes equations with multiplicative noise of jump type, Phys. D 398 2019, 23–68]. Taking advantage of this previous result, we investigate this more challenging and physically relevant case. Global existence of a martingale solution is proved with no-slip and no-flux boundary conditions in both 2D and 3D bounded domains. In the two-dimensional case, we prove the uniqueness of weak solutions when the viscosity is constant.

Orbital evolution of LIGO/Virgo binaries in stellar clusters driven by cluster tides, stellar encounters, and general relativity

ABSTRACT Origin of LIGO/Virgo gravitational wave events may involve production of binaries with relativistic components in dense stellar systems – globular or nuclear star clusters – and their subsequent evolution towards merger. Orbital parameters of these binaries (the inner orbit) and their motion inside the cluster (the outer orbit) evolve due to both external agents – random encounters with cluster stars and cluster tides due to the smooth cluster potential – and the internal ones – various sources of dissipation and precession within the binary. We present a numerical framework – binary evolution in stellar clusters (besc) – that follows the evolution of the binary inner and outer orbits accounting for all these effects simultaneously, enabling efficient Monte Carlo studies. The secular effect of cluster tides is computed in the singly averaged approximation, without averaging over the outer binary orbit. As to stellar encounters, we include the effects of both close and distant flybys on the inner and outer orbits of the binary, respectively. Also, given our focus on the LIGO/Virgo sources, we include the general relativistic precession (which suppresses cluster tides at high eccentricities) and the gravitational wave emission (shrinking the binary orbit). We use besc to illustrate a number of characteristic binary evolutionary outcomes and discuss relative contributions of different physical processes. In particular, we find that stellar encounters often dominate over the cluster tides in the evolution of compact binaries. besc can also be used to study other objects in clusters, e.g. blue stragglers, hot Jupiters, X-ray binaries, etc.

Gravitational waves effects in a Lorentz–violating scenario

This paper focuses on how the production and polarization of gravitational waves are affected by spontaneous Lorentz symmetry breaking, which is driven by a self–interacting vector field. Specifically, we examine the impact of a smooth quadratic potential and a non–minimal coupling, discussing the constraints and causality features of the linearized Einstein equation. To analyze the polarization states of a plane wave, we consider a fixed vacuum expectation value (VEV) of the vector field. Remarkably, we verify that a space–like background vector field modifies the polarization plane and introduces a longitudinal degree of freedom. In order to investigate the Lorentz violation effect on the quadrupole formula, we use the modified Green function. Finally, we show that the space–like component of the background field leads to a third–order time derivative of the quadrupole moment, and the bounds for the Lorentz–breaking coefficients are estimated as well.

Exact prime density reproduced through resonant tunneling across a double barrier system

A solid-state experiment based on quantum tunneling is proposed to reproduce the natural numbers and prime numbers as resonant tunneling energies in a double barrier system (DBS). For getting the prime numbers as eigenvalues the well potential is considered as the superposition of a smooth potential which is estimated using a semi-classical approach and a weak local fluctuating potential. We use the transfer matrix approach and finite element method by taking only the smooth part of the potential to obtain resonant energies which reproduces the local average prime density and the local average prime gap exactly. The methodology when applied to a quadratic potential of the well, produces whole numbers as eigenvalues except for a constant zero-point energy —the energy levels of a simple harmonic oscillator.

Heteroclinic traveling waves of two-dimensional parabolic Allen–Cahn systems

In this paper we show the existence of traveling waves w\colon [0,+\infty) \times \mathbb{R}^{2} \to \mathbb{R}^{k} ( k \geq 2 ) for the parabolic Allen–Cahn system \partial_{t} w - \Delta w = -\nabla_{u} V(w) in [0,+\infty) \times \mathbb{R}^{2} , satisfying some heteroclinic conditions at infinity. The potential V is a nonnegative and smooth multi-well potential, which means that its null set is finite and contains at least two elements. The traveling wave w propagates along the horizontal axis according to a speed c^{\star}&gt;0 and a profile \mathfrak{U} . The profile \mathfrak{U} joins as x_{1} \to \pm \infty (in a suitable sense) two locally minimizing one-dimensional heteroclinics which have different energies, and the speed c^{\star} satisfies certain uniqueness properties. The proof is variational and, in particular, it requires the assumption of an upper bound, depending on V , on the difference between the energies of the one-dimensional heteroclinics.

Universality for free fermions and the local Weyl law for semiclassical Schrödinger operators

We study local asymptotics for the spectral projector associated to a Schrödinger operator -\hbar^{2}\Delta+V on \mathbb{R}^{n} in the semiclassical limit as \hbar\to0 . We prove local uniform convergence of the rescaled integral kernel of this projector towards a universal model, inside the classically allowed region as well as on its boundary. This implies universality of microscopic fluctuations for the corresponding free fermions (determinantal) point processes, both in the bulk and around regular boundary points. Our results apply to a general class of smooth potentials in arbitrary dimension n\ge 1 . These results are complemented by studying both macroscopic and mesoscopic fluctuations of the point process. We obtain tail bounds for macroscopic linear statistics and, provided n\geq 2 , a central limit theorem for both macroscopic and mesoscopic linear statistics in the bulk.

The Enzymatic Function of Kvβ2 Controls Vascular Potassium Channel Activity

Voltage-gated potassium (Kv) channels expressed in vascular smooth muscle control membrane potential and thereby regulate vascular tone and organ perfusion. Native Kv1 channels in the resistance vasculature consist of an alpha pore domain in complex with intracellular beta (Kvβ) proteins, which are active aldo-keto reductases (AKR6A). Recent work suggests that the AKR function of Kvβ2 is required for vascular Kv1 channel NAD(P)(H) redox sensing and O2 sensitivity of resistance arterial tone. Nonetheless, whether acute changes in Kvβ2 AKR function impact vascular Kv1 activity is unknown. We propose that Kv1 gating is sensitive to changes in the levels of endogenous substrates and post-translational modification of Kvβ2. Here, we tested the hypothesis that the availability of the glycolytic byproduct and purported Kvβ substrate, methylglyoxal, and protein kinase C-dependent phosphorylation differentially regulate vascular Kvβ2 function. Using the inside-out configuration of the patch clamp technique, we measured the open probability (nPo) of Kv channels present in patches excised from human coronary smooth muscle cells. Perfusion of methylglyoxal (5 μM) resulted in significantly increased Kv channel nPo (3.3x10−5 ± 9.5x10−6 to 3.2x10−4 ± 2.1x10−4; n=5) and this effect was enhanced (~8-fold) in the presence of 100 μM NADPH, suggesting that Kv sensitivity to methylglyoxal is cofactor-dependent. Based on this, we next tested whether Kvβ phosphorylation regulates AKR catalysis and influences vascular Kv1 redox sensitivity. Using in situ proximity ligation, we found that serine phosphorylation of Kvβ2 in smooth muscle was increased upon treatment with the PKC activator phorbol 12-myristate 13-acetate (PMA; 100 nM), indicating that smooth muscle Kvβ2 is a phosphorylation target under these conditions. In vitro phosphorylation of purified Kvβ2 with PKCα significantly slowed catalysis (11.3 ± 0.3 vs. 6.5 ± 0.2 μmoles/min/mg protein, control and PKCα-treated rat Kvβ2.1, respectively). Pretreatment of cells with 10 nM PMA before excising inside-out membrane patches eliminated the increase in Kv channel nP(o) evoked by methylglyoxal (±NADPH). Moreover, ex vivo treatment of isolated coronary arteries with PMA (10 nM) abolished vasodilation in response to elevated NADH:NAD+ via application of 2–5 mM external L-lactate. Together, these results suggest that vascular smooth muscle Kv1 channels are functionally regulated by endogenous substrates and phosphorylation of intracellular Kvβ proteins. We propose that targeting vascular Kvβ AKR function may represent a novel strategy to modify K+ channel redox sensitivity and thus strengthen the coupling between metabolic demand and organ perfusion. T32-ES011564 and R01HL163818. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Spectral properties of Schrödinger operators with locally $H^{-1}$ potentials

We study half-line Schrödinger operators with locally H^{-1} potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Last–Simon-type description of the absolutely continuous spectrum and sufficient conditions for different spectral types. In the second part, we focus on potentials which are decaying in a local H^{-1} sense; we establish a spectral transition between short-range and long-range potentials and an \ell^{2} spectral transition for sparse singular potentials. The regularization procedure used to handle distributional potentials is also well suited for controlling rapid oscillations in the potential; thus, even within the class of smooth potentials, our results apply in situations which would not classically be considered decaying or even bounded.

Extracellular glucose and dysfunctional insulin receptor signaling independently upregulate arterial smooth muscle TMEM16A expression.

Diabetes alters the function of ion channels responsible for regulating arterial smooth muscle membrane potential, resulting in vasoconstriction. Our prior research demonstrated an elevation of TMEM16A in diabetic arteries. Here, we explored the mechanisms involved in Transmembrane protein 16A (TMEM16A) gene expression. Our data indicate that a Snail-mediated repressor complex regulates arterial TMEM16A gene transcription. Snail expression was reduced in diabetic arteries while TMEM16A expression was upregulated. The TMEM16A promoter contained three canonical E-box sites. Electrophoretic mobility and super shift assays revealed that the -154 nt E-box was the binding site of the Snail repressor complex and binding of the repressor complex decreased in diabetic arteries. High glucose induced a biphasic contractile response in pressurized nondiabetic mouse hindlimb arteries incubated ex vivo. Hindlimb arteries incubated in high glucose also showed decreased phospho-protein kinase D1 and TMEM16A expression. In hindlimb arteries from nondiabetic mice, administration of a bolus dose of glucose activated protein kinase D1 signaling to induce Snail degradation. In both in vivo and ex vivo conditions, Snail expression exhibited an inverse relationship with the expression of protein kinase D1 and TMEM16A. In diabetic mouse arteries, phospho-protein kinase D1 increased while Akt2 and pGSK3β levels declined. These results indicate that in nondiabetic mice, high glucose triggers a transient deactivation of the Snail repressor complex to increase arterial TMEM16A expression independently of insulin signaling. Conversely, insulin resistance activates GSK3β signaling and enhances arterial TMEM16A channel expression. These data have uncovered the Snail-mediated regulation of arterial TMEM16A expression and its dysfunction during diabetes.NEW & NOTEWORTHY The calcium-activated chloride channel, TMEM16A, is upregulated in the diabetic vasculature to cause increased vasoconstriction. In this paper, we have uncovered that the TMEM16A gene expression is controlled by a Snail-mediated repressor complex that uncouples with both insulin-dependent and -independent pathways to allow for upregulated arterial protein expression thereby causing vasoconstriction. The paper highlights the effect of short- and long-term glucose-induced dysfunction of an ion channel expression as a causative factor in diabetic vascular disease.

The high-order estimate of the entire function associated with inverse Sturm–Liouville problems

Abstract The inverse Sturm–Liouville problem with smooth potentials is considered. The high-order estimate of the entire function associated with two Sturm–Liouville problems is established. Applying this estimate expression to inverse Sturm–Liouville problems, we proved that the conclusion in [L. Amour, J. Faupin and T. Raoux, Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials, J. Math. Phys. 50 2009, 3, Article ID 033505] remains true for more general case.

A weakly turbulent solution to the cubic nonlinear harmonic oscillator on ℝ2 perturbed by a real smooth potential decaying to zero at infinity

We build a smooth real potential V(t, x) on ( t 0 , + ∞ ) × R 2 decaying to zero as t → ∞ and a smooth solution to the associated perturbed cubic noninear harmonic oscillator whose Sobolev norms blow up logarithmically as t → ∞ . Adapting the method of Faou and Raphael for the linear case, we modulate the Solitons associated to the nonlinear harmonic oscillator by time-dependent parameters solving a quasi-Hamiltonian dynamical system whose action grows up logarithmically, thus yielding logarithmic growth for the Sobolev norm of the solution.

Smooth hyperelastic potentials for 1D problems of bimodular materials

Smooth hyperelastic potentials for 1D problems of bimodular materials