arXiv subjects

Dragos-Victor Anghel

Publications and source records attributed to Dragos-Victor Anghel.

At least 19 recordsLinked to original sources

arXiv2024

Unveiling the Quantum Toroidal Dipole

The electromagnetic response of matter is governed by three fundamental multipole families: electric, magnetic, and toroidal. While the electric and magnetic are cornerstones of physics, the toroidal dipole (TD) has eluded direct, quantitative measurement for over 60 years. Its far-field signature is masked by the electric dipole, and its behavior in the quantum regime remains largely unexplored. We address this long-standing problem by presenting a complete quantum-mechanical formalism for the TD in a nanostructure and proposing the first spectroscopic method for its direct measurement. We analyze a particle confined to a toroidal manifold subjected to an external current. We demonstrate that the resulting Aharonov-Bohm-like energy shifts in the system's spectrum are directly proportional to the expectation value of the TD operator. The transition energies exhibit a linear dependence on this current, with a quantized slope that directly reveals the change in the TD quantum number between eigenstates. This provides a clear experimental blueprint to unveil, measure, and characterize this elusive third multipole moment and its quantum nature, opening new avenues in quantum metamaterials, nanoscience, and the study of fundamental symmetries.

quant-ph↗

arXiv2022

The eigenvalues and eigenfunctions of the toroidal dipole operator in a mesoscopic system

We give analytical expressions for the eigenvalues and generalized eigenfunctions of $\hat{T}_3$, the $z$-axis projection of the toroidal dipole operator, in a system consisting of a particle confined in a thin film bent into a torus shape. We find the quantization rules for the eigenvalues, which are essential for describing measurements of $\hat{T}_3$. The eigenfunctions are not square-integrable, so they do not belong to the Hilbert space of wave functions, but they can be interpreted in the formalism of rigged Hilbert spaces as kernels of distributions. While these kernels appear to be problematic at first glance due to singularities, they can actually be used in practical computations. In order to illustrate this, we prescribe their action explicitly and we also provide a normalization procedure.

quant-ph↗

arXiv2022

The self-adjoint toroidal dipole operator in nanostructures

The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole ${\bf T}$ (the lowest order multipole) is the most common. In quantum systems, this corresponds to the toroidal dipole operator $\hat{\bf T}$, with the projections $\hat{T}_i$ ($i=1,2,3$) on the coordinate axes. Here we analyze a quantum particle in a system with cylindrical symmetry, which is a typical system in which toroidal moments appear. We find the expressions for the Hamiltonian, momenta, and toroidal dipole operators in adequate curvilinear coordinates, which allow us to find analytical expressions for the eigenfunctions of the momentum operators. While the toroidal dipole is hermitian, it is not self-adjoint, but in the new set of coordinates the operator $\hat{T}_3$ splits into two components, one of which is (only) hermitian, whereas the other one is self-adjoint. The self-adjoint component is the one that is physically significant and represents an observable. Furthermore, we numerically diagonalize the Hamiltonian and the toroidal dipole operator and find their eigenfunctions and eigenvalues. We write the partition function and calculate the thermodynamic quantities for a system of ideal particles on a torus. Besides proving that the toroidal dipole is self-adjoint and therefore an observable (a finding of fundamental relevance) such systems open up the possibility of making metamaterials that exploit the quantization and the quantum properties of the toroidal dipoles.

quant-ph↗

arXiv2021

Observables compatible to the toroidal moment operator

The quantum operator $\hat{T}_3$, corresponding to the projection of the toroidal moment on the $z$ axis, admits several self-adjoint extensions, when defined on the whole $\mathbb{R}^3$ space. $\hat{T}_3$ commutes with $\hat{L}_3$ (the projection of the angular momentum operator on the $z$ axis) and they have a \textit{natural set of coordinates} $(k,u,ϕ)$ where $ϕ$ is the azimuthal angle. The second set of \textit{natural coordinates} is $(k_1,k_2,u)$, where $k_1 = k\cosϕ$, $k_2 = k\sinϕ$. In both sets, $\hat{T}_3 = -i\hbar\partial/\partial u$, so any operator that is a function of $k$ and the partial derivatives with respect to the \textit{natural variables} $(k, u, ϕ)$ commute with $\hat{T}_3$ and $\hat{L}_3$. Similarly, operators that are functions of $k_1$, $k_2$, and the partial derivatives with respect to $k_1$, $k_2$, and $u$ commute with $\hat{T}_3$. Therefore, we introduce here the operators $\hat{p}_{k} \equiv -i \hbar \partial/\partial k$, $\hat{p}^{(k1)} \equiv -i \hbar \partial/\partial k_1$, and $\hat{p}^{(k2)} \equiv -i \hbar \partial/\partial k_2$ and express them in the $(x,y,z)$ coordinates. One may also invert the relations and write the typical operators, like the momentum $\hat{\bf p} \equiv -i\hbar {\bf \nabla}$ or the kinetic energy $\hat{H}_0 \equiv -\hbar^2Δ/(2m)$ in terms of the "toroidal" operators $\hat{T}_3$, $\hat{p}^{(k)}$, $\hat{p}^{(k1)}$, $\hat{p}^{(k2)}$, and, eventually, $\hat{L}_3$. The formalism may be applied to specific physical systems, like nuclei, condensed matter systems, or metamaterials. We exemplify it by calculating the momentum operator and the free particle Hamiltonian in terms of \textit{natural coordinates} in a thin torus, where the general relations get considerably simplified.

quant-ph↗

arXiv2020

The theory of the chain fountain revisited

We analyze the chain fountain effect--the chain siphoning when falling from a container onto the floor. We argue that the main reason for this effect is the inertia of the chain, whereas the momentum received by the beads of the chain from the bottom of the container (typically called ``kicks'') plays no significant role. The inertia of the chain leads to an effect similar to pulling the chain over a pulley placed up in the air, above the container. In the model used before by the majority of researchers (the so-called ``scientific consensus''), it was assumed that up to half of the mechanical work done by the tension in the chain may be wasted when transformed into kinetic energy during the pickup process. This prevented the chain to rise unless the energy transfer in the pickup process is improved by ``kicks'' from the bottom of the container. Here we show that the ``kicks'' are unnecessary and both, energy and momentum are conserved--as they should be, in the absence of dissipation--if one properly considers the tension and the movement of the chain. By doing so, we conclude that the velocity acquired by the chain is high enough to produce the fountain effect. Simple experiments validate our model and certain configurations produce the highest chain fountain, although ``kicks'' are impossible.

physics.class-ph↗

arXiv2019

Multiple solutions for the equilibrium populations in BCS superconductors

It was recently shown that the BCS formalism leads to several solutions for the energy gap and the equilibrium quasiparticle distribution, with a phase transition temperature which depends on the position of the chemical potential within the attraction band (the attraction band AB is defined as the single-particle energy interval in which the pairing interaction is manifested). Moreover, in some cases, the phase transition may be of the first, not of the second order. Here I will find two sets of solutions for any temperature below the phase transition temperature. I will also show that, when the AB is symmetric with respect to the chemical potential (the textbook BCS problem) there are still two solutions, with different energy gaps: one solution is the typical (textbook) BCS solution, whereas the other one has a smaller energy gap and non-zero quasiparticle populations down to zero temperature. At zero temperature, the energy gap corresponding to the second solution is one third of the typical BCS solution.

cond-mat.supr-con↗

arXiv2018

Crossover in the electron-phonon heat exchange in layered nanostructures

We study theoretically the effect of the effective dimensionality of the phonon gas distribution on the heat exchange between electrons and phonons in layered nanostructures. If we denote the electrons temperature by $T_e$ and the phonons temperature by $T_{ph}$, then the total heat power $P$ is proportional--in general--to $T_e^x - T_{ph}^x$, the exponent $x$ being dependent on the effective dimensionality of the phonon gas distribution. If we vary the temperature in a wide enough range, the effective dimensionality of the phonon gas distribution changes going through a crossover around some temperature, $T_C$. These changes are reflected by a change in $x$. On one hand, in a temperature range well below a crossover temperature $T_C$ only the lowest branches of the phonon modes are excited. They form a (quasi) two-dimensional gas, with $x=3.5$. On the other hand, well above $T_C$, the phonon gas distribution is quasi three-dimensional and one would expect to recover the three dimensional results, with $x = 5$. But this is not the case in our layered structure. The exponent $x$ has a complicated, non-monotonous dependence on temperature forming a "plateau region" just after the crossover temperature range, with $x$ between 4.5 and 5. After the plateau region, $x$ decreases, reaching values between 3.5 and 4 at the highest temperature used in our numerical calculations, which is more than 40 times higher than $T_C$.

cond-mat.mes-hall↗

arXiv2018

The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies

The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is maximized at equilibrium. We say that the macroscopic systems are extensive and so it is also the entropy. For a mesoscopic system, by definition, the size and the contacts with other systems influence its thermodynamic properties and therefore, if we define an entropy, this cannot be a homogeneous of order one function in the extensive variables. So, mesoscopic systems and their entropies are non-extensive. While for macroscopic systems and homogeneous entropies the equilibrium conditions are clearly defined, it is not so clear how the non-extensive entropies should be applied for the calculation of equilibrium properties of mesoscopic systems--for example it is not clear what is the role played by the boundaries and the contacts between the subsystems. We propose here a general definition of the entropy in the equilibrium state, which is applicable to both, macroscopic and mesoscopic systems. This definition still leaves an apparent ambiguity in the definition of the entropy of a mesoscopic system, but this we recognize as the signature of the anthropomorphic character of the entropy (see Jaynes, Am. J. Phys. 33, 391, 1965). To exemplify our approach, we analyze four formulas for the entropy (two for extensive and two for non-extensive entropies) and calculate the equilibrium (canonical) distribution of probabilities by two methods for each. We show that these methods, although widely used, are not equivalent and one of them is a consequence of our definition of the entropy of a compound system.

cond-mat.stat-mech↗

arXiv2017

New phenomenology from an old theory--new equilibrium states in the BCS model

I analyze the low temperature limit of the BCS theory of s-wave single-band superconductors, when the attraction band may be asymmetric with respect to the chemical potential. I discuss equilibrium systems, taking consistently into account the variation of the energy and of the total number of particles with the populations of the quasiparticle energy levels. I show that the equation for the energy gap has two solutions, one of which is stable and the other one is metastable. When the chemical potential is the center of the attraction band (the standard BCS assumption), the energy gap in the stable solution is $Δ_0$, whereas in the metastable one is $Δ_0/3$. If the chemical potential is not in the center of the attraction band, then a quasiparticle imbalance appears. If the absolute value of the difference between the chemical potential and center of the attraction band is bigger than $2Δ_0$, then the superconducting energy gap cannot be formed. If the number of particles is conserved and the attraction band is asymmetric, then the stable solution is unphysical and only metastable solutions are realized.

cond-mat.supr-con↗

arXiv2016

An amendment of the BCS theory of superconductivity

Although the BCS theory of superconductivity is a well established theory, we have shown that the phenomenology predicted by this model is much richer than previously believed. By releasing the constraint that the attraction band is symmetric with respect to the chemical potential of the system, we observed that the energy gap may have more than one solution, the quasiparticle imbalance may appear in equilibrium, and the transition between the superconducting and the normal metal phases may be of the first order. The temperature of the superconductor-normal metal phase transition changes with the asymmetry of the attraction band and if we plot the phase transition temperature vs the chemical potential, we obtain a bell shaped curve, similarly to the superconducting dome, generally formed in high-Tc superconductors, but also in superconductors with narrow conduction bands. While the pairing interaction is a microscopic characteristic of the system, determined by the effective interactions between constituent quasiparticles, the chemical potential is a macroscopic quantity, which can be changed by external conditions, like doping and pressure. Furthermore, if the conduction band of the system is narrow, then the attraction band is constrained to the conduction band and the chemical potential is not necessary in the center, as it happens in some of the bands in In-doped Pb$_z$Sn$_{1-z}$ and in MgB$_{2}$. For these reasons, the constraint that the attraction band is symmetric with respect to the chemical potential may be released.

cond-mat.supr-con↗

arXiv2016

The role of the chemical potential in the BCS theory

We study the effect of the chemical potential on the results of the BCS theory of superconductivity. We assume that the pairing interaction is manifested between electrons of single-particle energies in an interval $[μ- \hbarω_c, μ+ \hbarω_c]$, where $μ$ and $ω_c$ are parameters of the model--$μ$ needs not be equal to the chemical potential of the system, denoted here by $μ_R$. The BCS results are recovered if $μ= μ_R$. If $μ\ne μ_R$ the physical properties change significantly: the energy gap $Δ$ is smaller than the BCS gap, a population imbalance appears, and the superconductor-normal metal phase transition is of the first order. The quasiparticle imbalance is an equilibrium property that appears due to the asymmetry with respect to $μ_R$ of the single-particle energy interval in which the pairing potential is manifested. For $μ_R - μ$ taking values in some ranges, the equation for $Δ$ may have more than one solution at the same temperature, forming branches of solutions when $Δ$ is plotted vs $μ_R-μ$ at fixed $T$. The solution with the highest energy gap, which corresponds to the BCS solution when $μ= μ_R$, cease to exist if $|μ-μ_R| \ge 2Δ_0$ ($Δ_0$ is the BCS gap at zero temperature). Therefore the superconductivity is conditioned by the existence of the pairing interaction and also by the value of $μ_R - μ$.

cond-mat.supr-con↗

arXiv2015

The application of the fractional exclusion statistics to the BCS theory--a redefinition of the quasiparticle energies

The effective energy of a superconductor $E_{eff}(T)$ at temperature $T$ is defined as the difference between the total energy at temperature $T$ and the total energy at 0~K. We call the energy of the condensate, ${\mathcal E}_c$, the difference between $E_{eff}$ and the sum of the quasiparticle energies $E_{qp}$. ${\mathcal E}_c$, $E_{qp}$, as well as the BCS quasiparticle energy $ε$ are positive and depend on the gap energy $Δ$, which, in turn, depends on the populations of the quasiparticle states (equivalently, they depend on $T$). So from the energy point of view the superconductor is a Fermi liquid of non-ideal quasiparticles. We show that the choice of quasiparticles is not unique, but there is an infinite range of possibilities. Some of these possibilities have been explored in the context of the fractional exclusion statistics (FES), which is a general method of describing interacting particle systems as ideal gases. We apply FES here and transform the Fermi liquid of BCS excitations into an ideal gas by redefining the quasiparticle energies. The new FES quasiparticles exhibit the same energy gap as the BCS quasiparticles, but a different DOS, which is finite at any quasiparticle energy. We also discuss the effect of the remnant electron-electron interaction (electron-electron interaction beyond the BCS pairing model) and show that this can stabilize the BCS condensate, increasing the critical temperature.

cond-mat.supr-con↗

arXiv2015

The stumbling block of the Gibbs entropy: the reality of the negative absolute temperatures

The second Tisza-Callen postulate of equilibrium thermodynamics states that for any system exists a function of the system's extensive parameters, called entropy, defined for all equilibrium states and having the property that the values assumed by the extensive parameters in the absence of a constraint are those that maximize the entropy over the manifold of constrained equilibrium states. By analyzing the evolution of systems of positive and negative absolute temperatures, we show that this postulate is satisfied by the Boltzmann formula for the entropy and is violated by the Gibbs formula. Therefore the Gibbs formula is not a generally valid expression for the entropy. Viceversa, if we assume, by reductio ad absurdum, that for some thermodynamic systems the equilibrium state is determined by the Gibbs' prescription and not by Boltzmann's, this implies that such systems have macroscopic fluctuations and therefore do not reach thermodynamic equilibrium.

cond-mat.stat-mech↗

arXiv2015

Electron-phonon heat exchange in layered nano-systems

We analyze the heat power $P$ between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes in a temperature range in which the phonon gas has a quasi two-dimensional distribution. The quantization of the electrons wavenumbers in the direction perpendicular to the film surfaces lead to the formation of quasi two-dimensional electronic sub-bands. The electron-phonon coupling is treated in the deformation potential model and, if we denote by $T_e$ the electrons temperature and by $T_{ph}$ the phonons temperature, we find that $P\equiv P^{(0)}(T_{e})-P^{(1)}(T_{e},T_{ph})$; $P^{(0)}$ is the power "emitted" by the electron system to the phonons and $P^{(1)}$ is the power "absorbed" by the electrons from the phonons. Due to the quantization of the electronic states, $P$ vs $(d,T_e)$ and $P$ vs $(d,T_{ph})$ show very strong oscillations with $d$, forming sharp crests almost parallel to the temperature axes. In the valleys between the crests, $P \propto T_e^{3.5} - T_{ph}^{3.5}$. From valley to crest, $P$ increases by more than one order of magnitude and on the crests $P$ does not have a simple power law dependence on temperature. The strong modulation of $P$ with the thickness of the film may provide a way to control the electron-phonon heat power and the power dissipation in thin metallic films. Eventually the same mechanism may be used to detect small variations of $d$ or surface contamination. On the other hand, the surface imperfections of the metallic films may make it difficult to observe the oscillations of $P$ with $d$ and eventually due to averaging the effects the heat flow would have a more smooth dependence on the thickness in real experiments.

cond-mat.mes-hall↗

arXiv2014

The BCS theory amended

In the standard theory of superconductivity a quasiparticle excitation changes the energy of the system by the quasiparticle energy. But the number of excitations determine also the gap energy which further determines the energy of the condensate and the energy spectrum of quasiparticles. Such extra contributions to the total energy of the system--which are not taken into account in the standard formalism--led us to a redefinition of the quasiparticle energies and of the quasiparticle populations by the usual method of the maximization of the superconductor partition function. The result of this correction is a critical temperature which is lower than the BCS critical temperature and a finite jump of the energy gap at the phase transition. The discontinuity of the energy gap at the critical temperature marks a first order phase transition which is also in disagreement with the standard BCS interpretation. The fact that the standard BCS formalism is theoretically inconsistent is revealed in the calculation of the heat capacity and of the internal energy. These inconsistencies are removed in our formulation. The purpose of our paper is not to adjust the theory to better describe the phenomenology of superconductivity, but to reevaluate and amend the BCS formalism.

cond-mat.supr-con↗

arXiv2014

Fractional exclusion statistics in disordered interacting particle systems

We develop a model based on the fractional exclusion statistics (FES) applicable to non-homogeneous interacting particle systems. Here the species represent elementary volumes in an (s+1)-dimensional space, formed by the direct product between the s-dimensional space of positions and the quasiparticle energy axis. The model is particularly suitable for systems with localized states. We prove the feasibility of our method by applying it to systems of different degrees of complexities. We first apply the formalism on simpler systems, formed of two sub-systems, and present numerical and analytical thermodynamic calculations, pointing out the quasiparticle population inversion and maxima in the heat capacity, in contrast to systems with only diagonal (direct) FES parameters. Further we investigate larger, non-homogeneous systems with repulsive screened Coulomb interactions, indicating accumulation and depletion effects at the interfaces. Finally, we consider systems with several degrees of disorder, which are prototypical for models with glassy behavior. We find that the disorder produces a spatial segregation of quasiparticles at low energies which significantly affects the heat capacity and the entropy of the system.

cond-mat.dis-nn↗

arXiv2013

Equivalence between fractional exclusion statistics and self-consistent mean-field theory in interacting particle systems in any number of dimensions

We describe a mean field interacting particle system in any number of dimensions and in a generic external potential as an ideal gas with fractional exclusion statistics (FES). We define the FES quasiparticle energies, we calculate the FES parameters of the system and we deduce the equations for the equilibrium particle populations. The FES gas is "ideal", in the sense that the quasiparticle energies do not depend on the other quasiparticle levels populations and the sum of the quasiparticle energies is equal to the total energy of the system. We prove that the FES formalism is equivalent to the semi-classical or Thomas Fermi limit of the self-consistent mean-field theory and the FES quasiparticle populations may be calculated from the Landau quasiparticle populations by making the correspondence between the FES and the Landau quasiparticle energies. The FES provides a natural semi-classical ideal gas description of the interacting particle gas.

cond-mat.stat-mech↗

arXiv2013

From Fractional Exclusion Statistics Back to Bose and Fermi Distributions

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this paper I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.

cond-mat.stat-mech↗