arXiv subjects

F. Marsiglio

Publications and source records attributed to F. Marsiglio.

At least 19 recordsLinked to original sources

arXiv2025

The Modified Airy Function Approximation Applied to the Double-Well Potential

The single harmonic oscillator and double-well potentials are important systems in quantum mechanics. The single harmonic oscillator is {\it the} paradigm in physics, and is taught in nearly all beginner undergraduate classes, while the double-well potential illustrates the two important principles of quantum tunnelling and linear superposition. While exact analytical solutions of the Schrodinger equation exist for both of these potentials, they are also employed to benchmark the use of approximate techniques which may be the only recourse for more complicated potentials. In this paper, we review the Wentzel-Kramers-Brillouin (WKB) approximation for both these potentials. While this approximation is known for its accurate energies, we will instead emphasize how poor the WKB wave functions are. The inaccuracy of the WKB wave functions will then motivate us to adopt the lesser-known Modified Airy Function (MAF) approximation, which alleviates the deficiencies of the WKB wave functions. We will review the MAF solution to the simple harmonic oscillator potential, and then apply the MAF to the double-well potential. We find accurate eigenvalues and, more importantly, very accurate wave functions. We conclude with the suggestion that an introduction to the MAF should be included in undergraduate courses to complement the WKB.

quant-ph↗

arXiv2024

Reply to "Is $MgB_2$ a superconductor? Comment on "Evidence Against Superconductivity in Flux Trapping Experiments on Hydrides Under High Pressure" "

The preceding Comment [1], previously posted as arXiv:2312.04495 [2], on our paper J. Supercond. Nov. Mag. 35, 3141 (2022) [3] provides a welcome opportunity to clarify what we understand to be pervading misconceptions by Eremets, Minkov and coauthors in regard to our analysis [3] of their trapped flux experiments in hydrides under pressure [4]. We hope that this Reply [5] will help readers interested in hydride superconductivity sort out between different claims and counterclaims in the literature and inform their views based on verifiable facts.

cond-mat.supr-con↗

arXiv2024

Comment on "Trapped flux in a small crystal of CaKFe$_4$As$_4$ at ambient pressure and in a diamond anvil pressure cell" by S. L. Bud'ko et al

In their paper arXiv:2405.08189, Supercond. Sci. Technol. 37 (2024) 065010 [1], Bud'ko et al. present experimental results for trapped magnetic flux for a tiny sample of a type II superconductor. The paper aims to provide evidence in support of the interpretation that similar measurements performed in samples of hydrogen-rich materials under high pressure by Minkov, Bud'ko and coauthors [2] are conclusive evidence [3] for superconductivity in hydrides under pressure. Here we point out that the new evidence presented by Bud'ko et al. [1] further supports our interpretation [4],[5] that the reported measurements of trapped flux on hydrides under pressure [2] are evidence that the samples are $not$ superconducting.

cond-mat.supr-con↗

arXiv2024

Reply to "Comment on `Nonstandard superconductivity or no superconductivity in hydrides under high pressure' "

In Ref. [1] we surveyed the known hydride superconductors, and compared their resistive behavior to that of typical known superconductors, including conventional (e.g. NbN and MgB$_2$) and unconventional (e.g. YBCO) superconductors, and concluded that the behavior of the hydrides was indicative of nonstandard or no superconductivity. In the preceding comment, Talantsev, Minkov, Balakirev and Eremets [2] (arXiv:2311.07865) claim that we presented a "flawed analysis and a selective and inaccurate report of published data." Here we show that this claim is wrong.

cond-mat.supr-con↗

arXiv2023

On the interpretation of flux trapping experiments in hydrides

In Ref. [1], Minkov et al. reported measurements of the magnetic moment that remains after a magnetic field is turned on and then turned off for hydride materials under high pressure in a diamond anvil cell. In Refs. [2,3], Minkov et al. reported magnetization measurements on the same samples as a function of applied magnetic field. Here we argue that the latter indicate that the signal measured in the former does not provide evidence for superconductivity in these samples. Instead, the measured signal likely originates in ferromagnetism of either the sample or the background.

cond-mat.supr-con↗

arXiv2023

On magnetic field screening and trapping in hydrogen-rich high-temperature superconductors: unpulling the wool over readers' eyes

In Nat Commun 13, 3194 (2022) [1], Minkov et al. reported magnetization measurements on hydrides under pressure that claimed to find a diamagnetic signal below a critical temperature demonstrating the existence of superconductivity. Here we present an analysis of raw data recently released [2] by the authors of [1] that shows that the measured data do not support their claim that the samples exhibit a diamagnetic response indicative of superconductivity. We also point out that Ref. [1] in its original form omitted essential information that resulted in presentation of a distorted picture of reality, and that important information on transformations performed on measured data remains undisclosed. Our analysis also calls into question the conclusions of Minkov et al's trapped flux experiments reported in Nat. Phys. (2023) [3] as supporting superconductivity in these materials. This work together with earlier work implies that there is no magnetic evidence for the existence of high-temperature superconductivity in hydrides under pressure.

cond-mat.supr-con↗

arXiv2022

A Wave Packet Approach to Resonant Scattering

Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with finite width to illustrate the deterioration of resonance with decreasing wave packet width, and suggest an approximate wave function for the transmitted and reflected components, derived from aspects of both the wave packet and plane wave approaches. A comparison with exact numerical calculations shows excellent agreement, and provides insight into the scattering process.

quant-ph↗

arXiv2022

Electrical conductivity and nuclear magnetic resonance relaxation rate of Eliashberg superconductors in the weak-coupling limit

Electrical conductivity is an important transport response in superconductors, enabling clear signatures of dynamical interactions to be observed. Of primary interest in this paper is to study characteristics of the electron-phonon interaction in weak-coupling Eliashberg theory (Eth), and to note the distinctions with Bardeen-Cooper-Schrieffer (BCS) theory. Recent analysis of weak-coupling Eth has shown that while there are modifications from the BCS results, certain dimensionless ratios are in agreement. Here we show that the conductivities in BCS theory and Eth fundamentally differ, with the latter having an imaginary gap component that damps a divergence. We focus on the dirty limit, and for both BCS theory and Eth we derive expressions for the low-frequency limit of the real conductivity. For Eth specifically, there are two limits to consider, depending on the relative size of the frequency and the imaginary part of the gap. In the case of identically zero frequency, we derive an analytical expression for the nuclear magnetic resonance relaxation rate. Our analysis of the conductivity complements the previous study of the Meissner response and provides a thorough understanding of weak-coupling Eth.

cond-mat.supr-con↗

arXiv2022

Evidence against superconductivity in flux trapping experiments on hydrides under high pressure & On magnetic field screening and expulsion in hydride superconductors

It has recently been reported that hydrogen-rich materials under high pressure trap magnetic flux, a tell-tale signature of superconductivity [arXiv:2206.14108v1]. Here we point out that under the protocol used in these experiments the measured results indicate that the materials don't trap magnetic flux. Instead, the measured results are either experimental artifacts or originate in magnetic properties of the sample or its environment unrelated to superconductivity, Together with other experimental evidence analyzed earlier, this clearly indicates that these materials are not superconductors. {\bf In a second part, we discuss magnetic field screening and expulsion.}

cond-mat.supr-con↗

arXiv2022

Impact of Retardation in the Holstein-Hubbard Model: a two-site Calculation

Eliashberg theory provides a theoretical framework for understanding the phenomenon of superconductivity when pairing between two electrons is mediated by phonons, and retardation effects are fully accounted for. However, when a direct Coulomb interaction between two electrons is also present, this interaction is only partially accounted for. In this work we use a well-defined Hamiltonian, the Hubbard-Holstein model, to examine this competition more rigorously, using exact diagonalization on a two-site system. We find that the direct electron-electron repulsion between two electrons has a significantly more harmful effect on pairing than suggested through the standard treatment of this interaction.

cond-mat.supr-con↗

arXiv2021

Clear evidence against superconductivity in hydrides under high pressure

The Meissner effect, magnetic field expulsion, is a hallmark of superconductivity. Associated with it, superconductors exclude applied magnetic fields. Recently Minkov et al. presented experimental results reportedly showing "definitive evidence of the Meissner effect" in sulfur hydride and lanthanum hydride under high pressure [1], and more recently Eremets et al. argued that "the arguments against superconductivity (in hydrides) can be either refuted or explained" [2]. Instead, we show here that the evidence presented in those papers does not support the case for superconductivity in these materials. Together with experimental evidence discussed in earlier papers, we argue that this strongly suggests that hydrides under pressure are not high-temperature superconductors.

cond-mat.supr-con↗

arXiv2021

Absence of evidence of superconductivity in sulfur hydride in optical reflectance experiments

Capitani and coworkers [1] reported that infrared optical reflectance measurements provided evidence for a superconducting transition in sulfur hydride [2] under 150 GPa pressure, and that the transition is driven by the electron-phonon interaction. Here we argue that the measured data did not provide evidence that the system undergoes a transition to a superconducting state, nor do the data support any role of phonons in driving a transition. Rather, the data are consistent with the system remaining in the normal state down to temperature 50K, the lowest temperature measured in the experiment. This calls into further question [3,4] the generally accepted view [5] that sulfur hydride under pressure is a high temperature superconductor.

cond-mat.supr-con↗

arXiv2021

Flux trapping in superconducting hydrides under high pressure

High-temperature conventional superconductivity in hydrogen-rich materials under high pressure has been reportedly found in twelve different compounds in recent years. However, the experimental evidence on which these claims are based has recently been called into question. Here we discuss the measurement of trapped magnetic flux, that should establish definitively that these materials are indeed high-temperature superconductors. Its absence should confirm claims to the contrary.

cond-mat.supr-con↗

arXiv2021

Meissner effect in nonstandard superconductors

It was recently pointed out that so-called "superhydrides", hydrogen-rich materials that appear to become superconducting at high temperatures and pressures, exhibit physical properties that are different from both conventional and unconventional standard type I and type II superconductors [1,2]. Here we consider magnetic field expulsion in the first material in this class discovered in 2015, sulfur hydride [3]. A nuclear resonant scattering experiment has been interpreted as demonstration that the Meissner effect takes place in this material [4,5]. Here we point out that the observed effect, under the assumption that the system is in thermodynamic equilibrium, implies a Meissner pressure [6] in this material that is {\it much larger} than that of standard superconductors. This suggests that hydride superconductors are qualitatively different from the known standard superconductors {\it if} they are superconductors.

cond-mat.supr-con↗

arXiv2021

Nonstandard superconductivity or no superconductivity in hydrides under high pressure

Over the past six years, superconductivity at high temperatures has been reported in a variety of hydrogen-rich compounds under high pressure. That high-temperature superconductivity should exist in these materials is expected according to the conventional theory of superconductivity, as shown by detailed calculations. However here we argue that experimental observations rule out conventional superconductivity in these materials. Our results indicate that either these materials are unconventional superconductors of a novel kind, which we term `nonstandard superconductors', or alternatively that they are not superconductors. If the former, we point out that the critical current in these materials should be five orders of magnitude larger than in standard superconductors, potentially opening up the way to important technological applications. If the latter, which we believe is more likely, we suggest that the signals interpreted as superconductivity are either experimental artifacts or they signal other interesting physics but not superconductivity.

cond-mat.supr-con↗

arXiv2021

Absence of magnetic evidence for superconductivity in hydrides under high pressure

It is generally believed that magnetization measurements on sulfur hydride under high pressure performed in 2015 [1] provided "final convincing evidence of superconductivity" [2] in that material, in agreement with theoretical predictions [3,4]. Supported by this precedent, drops in resistance that were later observed in several other hydrides under high pressure [2,5] have been generally accepted as evidence of superconductivity without corroborating evidence from magnetic measurements. In this paper we challenge the original interpretation that the magnetic measurements on sulfur hydride performed in 2015 were evidence of superconductivity. We point out that a large paramagnetic contribution to the magnetic susceptibility was detected below Tc and argue that its temperature dependence rules out the possibility that it would be a background signal; instead the temperature dependence indicates that the paramagnetic behavior originated in the sample. We discuss possible explanations for this remarkable behavior and conclude that standard superconductors would not show such behavior. We also survey all the other published data from magnetic measurements on this class of materials and conclude that they do not provide strong evidence for superconductivity. Consequently, we call into question the generally accepted view that conventional superconductivity in hydrogen-rich materials at high temperature and pressure is a reality, and discuss the implications if it is not.

cond-mat.supr-con↗

arXiv2021

Scattering Problems via Real-time Wave Packet Scattering

In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more intuitive physical picture than the traditional plane wave approach. Moreover, a general matrix diagonalization method that is easily accessible to undergraduate students taking a first course in quantum mechanics is used. Beginning with a brief review of wave packet transport in the continuum limit, comparisons are made with its counterpart in a lattice. The numerical results obtained through the diagonalization method are then benchmarked against analytic results. The case of a resonant dimer is investigated in the lattice, and several resonant values of the mean wave packet momentum are identified. The transmission coefficients obtained for a plane wave incident on a step potential and rectangular barrier are compared by investigating an equivalent scenario in a lattice. Lastly, we present several short simulations of the scattering process which emphasize how a simple methodology can be used to visualize some remarkable phenomena.

physics.ed-ph↗

arXiv2021

Phonon Self-Energy Effects in Migdal-Eliashberg Theory

Recent work on an electron-phonon model in two-dimensions is reviewed and some new results are presented. We utilize both Quantum Monte Carlo simulations and Migdal-Eliashberg theory. The type of electron-ion coupling considered is on-site. Competing instabilities are charge density wave (CDW) and singlet superconductivity. When the electron band is half-filled, the charge density wave dominates. Away from half-filling CDW correlations actually suppress superconductivity.

cond-mat.supr-con↗