Recent zbMATH articles in MSC 82Dhttps://zbmath.org/atom/cc/82D2022-09-13T20:28:31.338867ZWerkzeugLandau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaronhttps://zbmath.org/1491.353622022-09-13T20:28:31.338867Z"Leopold, Nikolai"https://zbmath.org/authors/?q=ai:leopold.nikolai"Mitrouskas, David"https://zbmath.org/authors/?q=ai:mitrouskas.david"Rademacher, Simone"https://zbmath.org/authors/?q=ai:rademacher.simone"Schlein, Benjamin"https://zbmath.org/authors/?q=ai:schlein.benjamin"Seiringer, Robert"https://zbmath.org/authors/?q=ai:seiringer.robertSummary: We consider the Fröhlich Hamiltonian with large coupling constant \(\alpha \). For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm-approximation of the evolution, valid up to times of order \(\alpha^2\). The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order \(\alpha^2\).Spin generalizations of the Benjamin-Ono equationhttps://zbmath.org/1491.353902022-09-13T20:28:31.338867Z"Berntson, Bjorn K."https://zbmath.org/authors/?q=ai:berntson.bjorn-k"Langmann, Edwin"https://zbmath.org/authors/?q=ai:langmann.edwin"Lenells, Jonatan"https://zbmath.org/authors/?q=ai:lenells.jonatanSummary: We present new soliton equations related to the \(A\)-type spin Calogero-Moser (CM) systems introduced by Gibbons and Hermsen. These equations are spin generalizations of the Benjamin-Ono (BO) equation and the recently introduced non-chiral intermediate long-wave (ncILW) equation. We obtain multi-soliton solutions of these spin generalizations of the BO equation and the ncILW equation via a spin-pole ansatz where the spin-pole dynamics is governed by the spin CM system in the rational and hyperbolic cases, respectively. We also propose physics applications of the new equations, and we introduce a spin generalization of the standard intermediate long-wave equation which interpolates between the matrix Korteweg-de Vries equation, the Heisenberg ferromagnet equation, and the spin BO equation.Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulushttps://zbmath.org/1491.354112022-09-13T20:28:31.338867Z"Jang, Jin Woo"https://zbmath.org/authors/?q=ai:jang.jin-woo"Strain, Robert M."https://zbmath.org/authors/?q=ai:strain.robert-m"Wong, Tak Kwong"https://zbmath.org/authors/?q=ai:wong.tak-kwongSummary: Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to be relatively insufficient. This paper deals with the mathematical analysis of the magnetic confinement of the plasma via kinetic equations. We prove the global wellposedness of the \textit{Vlasov-Maxwell} system in a two-dimensional annulus when a huge (\textit{but finite-in-time}) external magnetic potential is imposed near the boundary. We assume that the solution is axisymmetric. The authors hope that this work is a step towards a more generalized work on the three-dimensional Tokamak structure. The highlight of this work is the physical assumptions on the external magnetic potential well which remains finite \textit{within a finite time interval} and from that, we prove that the plasma never touches the boundary. In addition, we provide a sufficient condition on the magnitude of the external magnetic potential to guarantee that the plasma is confined in an annulus of the desired thickness which is slightly larger than the initial support. Our method uses the cylindrical coordinate forms of the \textit{Vlasov-Maxwell} system.Nonlinear approximation of 3D smectic liquid crystals: sharp lower bound and compactnesshttps://zbmath.org/1491.490112022-09-13T20:28:31.338867Z"Novack, Michael"https://zbmath.org/authors/?q=ai:novack.michael-r"Yan, Xiaodong"https://zbmath.org/authors/?q=ai:yan.xiaodongSummary: We consider the 3D smectic energy
\[
\mathcal{E}_\varepsilon(u) = \frac{1}{2}\int_\Omega \frac{1}{\varepsilon} \left( \partial_z u-\frac{(\partial_x u)^2+(\partial_y u)^2}{2}\right)^2 +\varepsilon \left(\partial_x^2u + \partial_y^2u\right)^2dx\,dy\,dz.
\]
The model contains as a special case the well-known 2D Aviles-Giga model. We prove a sharp lower bound on \(\mathcal{E}_\varepsilon\) as \(\varepsilon \rightarrow 0\) by introducing 3D analogues of the Jin-Kohn entropies [\textit{W. Jin} and \textit{R. V. Kohn}, J. Nonlinear Sci. 10, No. 3, 355--390 (2000; Zbl 0973.49009)]. The sharp bound corresponds to an equipartition of energy between the bending and compression strains and was previously demonstrated in the physics literature only when the approximate Gaussian curvature of each smectic layer vanishes. Also, for \(\varepsilon_n\rightarrow 0\) and an energy-bounded sequence \(\{u_n\}\) with \(\Vert\nabla u_n\Vert_{L^p(\Omega)}\), \(\Vert \nabla u_n\Vert_{L^2(\partial\Omega)}\le C\) for some \(p>6\), we obtain compactness of \(\nabla u_n\) in \(L^2\) assuming that \(\Delta_{xy}u_n\) has constant sign for each \(n\).Two-temperatures overlap distribution for the 2D discrete Gaussian free fieldhttps://zbmath.org/1491.600532022-09-13T20:28:31.338867Z"Pain, Michel"https://zbmath.org/authors/?q=ai:pain.michel"Zindy, Olivier"https://zbmath.org/authors/?q=ai:zindy.olivierSummary: In this paper, we prove absence of temperature chaos for the two-dimensional discrete Gaussian free field using the convergence of the full extremal process, which has been obtained recently by Biskup and Louidor. This means that the overlap of two points chosen under Gibbs measures at different temperatures has a nontrivial distribution. Whereas this distribution is the same as for the random energy model when the two points are sampled at the same temperature, we point out here that they are different when temperatures are distinct: more precisely, we prove that the mean overlap of two points chosen under Gibbs measures at different temperatures for the DGFF is strictly smaller than the REM's one. Therefore, although neither of these models exhibits temperature chaos, one could say that the DGFF is more chaotic in temperature than the REM.Nonhomogeneous Euclidean first-passage percolation and distance learninghttps://zbmath.org/1491.601782022-09-13T20:28:31.338867Z"Groisman, Pablo"https://zbmath.org/authors/?q=ai:groisman.pablo"Jonckheere, Matthieu"https://zbmath.org/authors/?q=ai:jonckheere.matthieu"Sapienza, Facundo"https://zbmath.org/authors/?q=ai:sapienza.facundoSummary: Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of the manifold and the underlying density. We define such a sample distance and prove the convergence, as the sample size goes to infinity, to a macroscopic one that we call \textit{Fermat distance} as it minimizes a path functional, resembling Fermat principle in optics. The proof boils down to the study of geodesics in Euclidean first-passage percolation for nonhomogeneous Poisson point processes.Influence of disorder on DNA denaturation: the disordered generalized Poland-Scheraga modelhttps://zbmath.org/1491.601802022-09-13T20:28:31.338867Z"Legrand, Alexandre"https://zbmath.org/authors/?q=ai:legrand.alexandreSummary: The Poland-Scheraga model is a celebrated model for the denaturation transition of DNA, which has been widely used in the bio-physical literature to study, and investigated by mathematicians. In the original model, only opposite bases of the two strands can be paired together, but a generalized version of this model has recently been introduced, and allows for mismatches in the pairing of the two strands, and for different strand lengths. This generalized Poland-Scheraga (gPS) model has only been studied recently in the case of homogeneous interactions, then with disordered interactions perturbed by an i.i.d. field. The present paper considers a disordered version of the gPS model which is more appropriate to depict the inhomogeneous composition of the two strands (in particular interactions are perturbed in a strongly dependent manner): we study the question of the influence of disorder on the denaturation transition, and our main results provide criteria for disorder (ir)-relevance, both in terms of critical points and of order of the phase transition. Surprisingly, we find that criteria for disorder relevance depend on the law of the disorder field. We discuss this with regards to Harris' prediction for disordered systems.Thermal-piezoelectric problem of a semiconductor medium during photo-thermal excitationhttps://zbmath.org/1491.740162022-09-13T20:28:31.338867Z"Khamis, Alaa. K."https://zbmath.org/authors/?q=ai:khamis.alaa-k"Lotfy, Kh."https://zbmath.org/authors/?q=ai:lotfy.khaled|lotfy.kh"El-Bary, A. A."https://zbmath.org/authors/?q=ai:el-bary.alla-a|el-bary.alaa-a"Mahdy, Amr M. S."https://zbmath.org/authors/?q=ai:mahdy.amr-m-s"Ahmed, M. H."https://zbmath.org/authors/?q=ai:ahmed.marwa-h|ahmed.mohammad-helal-uddin|ahmed.mohamed-h|ahmed.mousa-khalifaSummary: The main goal of this paper is to develop a mathematical model for the piezoelectric elastic-semiconductor medium. The medium is homogeneous and isotropic that is exposed to photothermal excitation processes. Gauss's law of electrostatics is used to obtain the effect of the piezoelectric phenomenon. The governing equations with the electric potential are expressed in terms of thermoelasticity theory and photothermal theory. One-dimensional Laplace transform is used to get the solution of some physical quantities when the heat sources and body forces are absent. The mechanical forces and thermal loads are used to get the analytical solution of physical quantities under investigation. The inverse Laplace technique with a numerical method is employed to obtain the solution in the time-physical domain. A novel parameter depends on pyro-electric moduli is presented. Some numerical results are illustrated and shown graphically.Free vibration of a piezoelectric semiconductor platehttps://zbmath.org/1491.740382022-09-13T20:28:31.338867Z"Guo, Jianyu"https://zbmath.org/authors/?q=ai:guo.jianyu"Nie, Guoquan"https://zbmath.org/authors/?q=ai:nie.guoquan"Liu, Jinxi"https://zbmath.org/authors/?q=ai:liu.jinxi"Zhang, Lele"https://zbmath.org/authors/?q=ai:zhang.leleSummary: We analyze free vibration of a piezoelectric semiconductor (PSC) plate taking account of the coupling between deformation, polarization and carriers within the framework of the first-order shear deformation theory. The PSC plate is subjected to a biaxial force and an external electric voltage. The governing equations and corresponding boundary conditions are derived using Hamilton principle. An analytical solution for a simply supported PSC plate is obtained. A detailed parametric study is conducted to discuss the effects of steady-state carrier density, axial force, external electric voltage, length-to-thickness ratio and length-to-width ratio on the free vibration characteristics of the PSC plate. The numerical results show that the steady-state carrier density has a significantly influence on natural frequency of the PSC plate in a certain range. The vibration frequency decreases when the plate is subjected to the axial compression and the positive external voltage. The vibration frequency increases with the increase of length-width ratio of and also increases with the decrease of length-thickness ratio of the PSC plate. This work may be useful for the analysis and design of electron devices made from PSC materials.Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responseshttps://zbmath.org/1491.740542022-09-13T20:28:31.338867Z"Mondal, Sudip"https://zbmath.org/authors/?q=ai:mondal.sudip"Sur, Abhik"https://zbmath.org/authors/?q=ai:sur.abhikSummary: This article highlights on the study of coupled plasma, thermal and elastic waves within an orthotropic infinite semiconducting medium in context of photothermal transport process having a spherical cavity under two-temperature theory. The memory-dependent heat transport equation for the present problem is involving the two-temperature dual-phase (DP) lag model of generalized thermoelasticity. The inner boundary of the cavity is stress free and is subjected to an exponentially decaying pulse. Moreover, the carrier density is prescribed on the boundary in terms of the recombination velocity. Employing the Laplace transform as tool, the analytical results for the distributions of the thermophysical quantities have been derived. The numerical inversion of the Laplace transform is carried out using a suitable scheme based on the Riemann-sum approximation technique. Numerical computations for an orthotropic semiconductor are performed and have been demonstrated graphically. The results also demonstrate the effect of coupling between plasma, thermal and elastic waves due to the presence of several kernel functions and response of memory effect. Also, significant differences on the thermophysical quantities are revealed due to the influence of two-temperature parameter, memory effect and time-delay parameter.Multiscale modelling and splitting approaches for fluids composed of Coulomb-interacting particleshttps://zbmath.org/1491.760082022-09-13T20:28:31.338867Z"Geiser, Jürgen"https://zbmath.org/authors/?q=ai:geiser.jurgenSummary: We consider fluids composed of Coulomb-interacting particles, which are modelled by the Fokker-Planck equation with a collision operator. Based on modelling the transport and collision of the particles, we propose new, computationally efficient, algorithms based on splitting the equations of motion into a global Newtonian transport equation, where the effects of an external electric field are considered, and a local Coulomb interaction stochastic differential equation, which determines the new velocities of the particle. Two different numerical schemes, one deterministic and the other stochastic, as well as an Hamiltonian splitting approach, are proposed for coupling the interactionand transport equations. Results are presented for two- and multi-particle systems with different approximations for the Coulomb interaction. Methodologically, the transport part is modelled by the kinetic equations and the collision part is modelled by the Langevin equations with Coulomb collisions. Such splitting approaches allow concentrating on different solver methods for each different part. Further, we solve multiscale problems involving an external electrostatic field. We apply a multiscale approach so that we can decompose the different time-scales of the transport and the collision parts. We discuss the benefits of the different splitting approaches and their numerical analysis.Floquet engineering of electric polarization with two-frequency drivehttps://zbmath.org/1491.780132022-09-13T20:28:31.338867Z"Ikeda, Yuya"https://zbmath.org/authors/?q=ai:ikeda.yuya"Kitamura, Sota"https://zbmath.org/authors/?q=ai:kitamura.sota"Morimoto, Takahiro"https://zbmath.org/authors/?q=ai:morimoto.takahiroSummary: Electric polarization is a geometric phenomenon in solids and has a close relationship to the symmetry of the system. Here we propose a mechanism to dynamically induce and manipulate electric polarization by using an external light field. Specifically, we show that application of bicircular lights controls the rotational symmetry of the system and can generate electric polarization. To this end, we use Floquet theory to study a system subjected to a two-frequency drive. We derive an effective Hamiltonian with high-frequency expansions, for which the electric polarization is computed with the Berry phase formula. We demonstrate the dynamical control of polarization for a one-dimensional Su-Shrieffer-Heeger chain, a square lattice model, and a honeycomb lattice model.Basic space plasma physicshttps://zbmath.org/1491.820012022-09-13T20:28:31.338867Z"Baumjohann, Wolfgang"https://zbmath.org/authors/?q=ai:baumjohann.wolfgang"Treumann, Rudolf A."https://zbmath.org/authors/?q=ai:treumann.rudolf-aPublisher's description: This textbook describes Earth's plasma environment from single particle motion in electromagnetic fields, with applications to Earth's magnetosphere, up to plasma wave generation and wave-particle interaction. The origin and effects of collisions and conductivities are discussed in detail, as is the formation of the ionosphere, the origin of magnetospheric convection and magnetospheric dynamics in solar wind-magnetosphere coupling, the evolution of magnetospheric storms, auroral substorms, and auroral phenomena of various kinds.
The second half of the book presents the theoretical foundation of space plasma physics, from kinetic theory of plasma through the formation of moment equations and derivation of magnetohydrodynamic theory of plasmas. The validity of this theory is elucidated, and two-fluid theory is presented in more detail. This is followed by a brief analysis of fluid boundaries, with Earth's magnetopause and bow shock as examples. The main emphasis is on the presentation of fluid and kinetic wave theory, deriving the relevant wave modes in a high temperature space plasma. Plasma instability is the most important topic in all applications and is discussed separately, including a section on thermal fluctuations. These theories are applied to the most interesting problems in space plasma physics, collisionless reconnection and collisionless shock waves with references provided. The Appendix includes the most recent developments in the theory of statistical particle distributions in space plasma, the Kappa distribution, etc, also including a section on space plasma turbulence and emphasizing on new observational developments with a dimensional derivation of the Kolmogorov spectrum, which might be instructive for the student who may worry about its origin.
The book ends with a section on space climatology, space meteorology and space weather, a new application field in space plasma physics that is of vital interest when considering the possible hazards to civilization from space.
See the reviews of the first and second editions in [Zbl 0971.82040; Zbl 1252.82001].The Parisi formula is a Hamilton-Jacobi equation in Wasserstein spacehttps://zbmath.org/1491.820122022-09-13T20:28:31.338867Z"Mourrat, Jean-Christophe"https://zbmath.org/authors/?q=ai:mourrat.jean-christopheSummary: The Parisi formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We showthat this quantity can be recast as the solution of a Hamilton-Jacobi equation in the Wasserstein space of probability measures on the positive half-line.Chaotic discrete breathers and their effect on macroscopic properties of triangular latticehttps://zbmath.org/1491.820202022-09-13T20:28:31.338867Z"Upadhyaya, A."https://zbmath.org/authors/?q=ai:upadhyaya.arpita"Semenova, M. N."https://zbmath.org/authors/?q=ai:semenova.m-n"Kudreyko, A. A."https://zbmath.org/authors/?q=ai:kudreyko.a-a"Dmitriev, S. V."https://zbmath.org/authors/?q=ai:dmitriev.sergey-vSummary: The localization of energy on chaotic discrete breathers (DBs) arising in a two- dimensional triangular lattice due to the modulation instability of delocalized nonlinear vibrational modes (DNVMs) is analyzed. Three DNVMs with frequencies above the phonon band and demonstrating hard-type anharmonicity (an increase in the vibration frequency with amplitude) are considered. Chaotic DBs have long lifetime, slowly radiate their energy and eventually disappear. The evolution of the macroscopic characteristics of the lattice is observed during the transition from the regime with chaotic DBs to thermal equilibrium. It is established that chaotic DBs with a hard type of anharmonicity reduce the ratio of the total energy to the kinetic energy (and, consequently, reduce the heat capacity). They also reduce lattice pressure at constant area (and therefore reduce thermal expansion). The tensile rigidity of the lattice also decreases due to DBs with a hard type of anharmonicity. The most sensitive to the presence of DBs is the pressure, which in the presence of DBs is approximately 30\% less than in thermal equilibrium. The ratio of the total energy to the kinetic energy in the regime of chaotic DBs decreases by about 3\%, and the tensile rigidity by only 0.1\%.Gamma-convergence results for nematic elastomer bilayers: relaxation and actuationhttps://zbmath.org/1491.820212022-09-13T20:28:31.338867Z"Cesana, Pierluigi"https://zbmath.org/authors/?q=ai:cesana.pierluigi"León Baldelli, Andrés A."https://zbmath.org/authors/?q=ai:leon-baldelli.andres-aSummary: We compute effective energies of thin bilayer structures composed of soft nematic elastic liquid crystals in various geometrical regimes and functional configurations. Our focus is on elastic foundations composed of an isotropic layer attached to a nematic substrate where order-strain interaction results in complex opto-mechanical instabilities activated \textit{via} coupling through the common interface. Allowing out-of-plane displacements, we compute Gamma-limits for vanishing thickness which exhibit spontaneous stress relaxation and shape-morphing behaviour. This extends the plane strain modelling of the authors [Math. Models Methods Appl. Sci. 28, No. 14, 2863--2904 (2018; Zbl 1411.49008)], and shows the asymptotic emergence of fully coupled active macroscopic nematic foundations. Subsequently, we focus on actuation and compute asymptotic configurations of an active plate on nematic foundation interacting with an applied electric field. From the analytical standpoint, the presence of an electric field and its associated electrostatic work turns the total energy non-convex and non-coercive. We show that equilibrium solutions are min-max points of the system, that min-maximising sequences pass to the limit and, that the limit system can exert mechanical work under applied electric fields.Regular solution for the compressible Landau-Lifshitz-Bloch equation in a bounded domain of \(\mathbb{R}^3\)https://zbmath.org/1491.820222022-09-13T20:28:31.338867Z"Ayouch, C."https://zbmath.org/authors/?q=ai:ayouch.chahid"Benmouane, M."https://zbmath.org/authors/?q=ai:benmouane.m"Essoufi, E. H."https://zbmath.org/authors/?q=ai:essoufi.el-hassanSummary: In this paper, we prove a local in time existence of regular solution for the compressible Landau-Lifshitz-Bloch equation in a bounded domain of \(\mathbb{R}^3 \). The uniqueness of the solution is also established.Evidence of superfluidity in a dipolar supersolid from nonclassical rotational inertiahttps://zbmath.org/1491.820232022-09-13T20:28:31.338867Z"Tanzi, L."https://zbmath.org/authors/?q=ai:tanzi.l"Maloberti, J. G."https://zbmath.org/authors/?q=ai:maloberti.j-g"Biagioni, G."https://zbmath.org/authors/?q=ai:biagioni.g"Fioretti, A."https://zbmath.org/authors/?q=ai:fioretti.a"Gabbanini, C."https://zbmath.org/authors/?q=ai:gabbanini.c"Modugno, G."https://zbmath.org/authors/?q=ai:modugno.gSummary: A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Nonclassical rotational effects have also been considered in the context of the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here, we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. Using a dipolar gas of dysprosium atoms, we studied a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, previously investigated in ordinary superfluids. From the measured moment of inertia, we deduced a superfluid fraction that is different from zero and of order of unity, providing direct evidence of the superfluid nature of the dipolar supersolid.Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev stateshttps://zbmath.org/1491.820242022-09-13T20:28:31.338867Z"Valentini, Marco"https://zbmath.org/authors/?q=ai:valentini.marco"Peñaranda, Fernando"https://zbmath.org/authors/?q=ai:penaranda.fernando"Hofmann, Andrea"https://zbmath.org/authors/?q=ai:hofmann.andrea"Brauns, Matthias"https://zbmath.org/authors/?q=ai:brauns.matthias"Hauschild, Robert"https://zbmath.org/authors/?q=ai:hauschild.robert"Krogstrup, Peter"https://zbmath.org/authors/?q=ai:krogstrup.peter"San-Jose, Pablo"https://zbmath.org/authors/?q=ai:san-jose.pablo"Prada, Elsa"https://zbmath.org/authors/?q=ai:prada.elsa"Aguado, Ramón"https://zbmath.org/authors/?q=ai:aguado.ramon"Katsaros, Georgios"https://zbmath.org/authors/?q=ai:katsaros.georgiosSummary: A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magnetic field dependence of the Andreev levels, through both the Zeeman and Little-Parks effects, may result in robust zero-bias peaks -- features that could be easily misinterpreted as originating from Majorana zero modes but are unrelated to topological superconductivity.Thermoelectric effects in self-similar multibarrier structure based on monolayer graphenehttps://zbmath.org/1491.820252022-09-13T20:28:31.338867Z"Miniya, M."https://zbmath.org/authors/?q=ai:miniya.m"Oubram, O."https://zbmath.org/authors/?q=ai:oubram.o"Reynaud-Morales, A. G."https://zbmath.org/authors/?q=ai:reynaud-morales.a-g"Rodríguez-Vargas, I."https://zbmath.org/authors/?q=ai:rodriguez-vargas.i"Gaggero-Sager, L. M."https://zbmath.org/authors/?q=ai:gaggero-sager.l-m