Browsing by Author "Stockmeyer, Edgardo"
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- ItemBallistic dynamics of Dirac particles in electro-magnetic fields(2015) Mehringer, Josef; Stockmeyer, Edgardo
- ItemConfinement-deconfinement transitions for two-dimensional Dirac particles(2014) Stockmeyer, Edgardo
- ItemDirac Operators Coupled to the Quantized Radiation Field: Essential Self-adjointness à la Chernoff(2008) Stockmeyer, Edgardo; Zenk, H.
- ItemDynamical localization of Dirac particles in electromagnetic fields with dominating magnetic potentials(2016) Barbaroux, Jean-Marie; Mehringer, Josef; Stockmeyer, Edgardo; Taarabt, Amal
- ItemExistence of ground states of hydrogen-like atoms in relativistic QED I: The semi-relativistic Pauli-Fierz operator(2011) Könenberg, M.; Matte, O.; Stockmeyer, Edgardo
- ItemExistence of ground states of hydrogen-like atoms in relativistic quantum electrodynamics. II. The no-pair operator(2011) Könenberg, M.; Matte, O.; Stockmeyer, Edgardo
- ItemExponential localization of hydrogen-like atoms in relativistic quantum electrodynamics(2010) Matte, O.; Stockmeyer, Edgardo
- ItemInfinite mass boundary conditions for Dirac operators(2019) Stockmeyer, Edgardo; Vugalter, SemjonWe study a self-adjoint realization of a massless Dirac operator on a bounded connected domain Omega subset of R-2 which is frequently used to model graphene. In particular, we show that this operator is the limit, as M -> infinity, of a Dirac operator defined on the whole plane, with a mass term of size M supported outside Omega.
- ItemLocalization of two-dimensional massless Dirac fermions in a magnetic quantum dot(2012) Könenberg, Martin; Stockmeyer, Edgardo
- ItemMultiparticle equations for interacting Dirac fermions in magnetically confined graphene quantum dots(2010) Egger, Reinhold; De Martino, Alessandro; Siedentop, Heinz; Stockmeyer, Edgardo
- ItemOn the Asymptotic Dynamics of 2-D Magnetic Quantum Systems(2021) Cardenas, Esteban; Hundertmark, Dirk; Stockmeyer, Edgardo; Vugalter, SemjonIn this work, we provide results on the long-time localization in space (dynamical localization) of certain two-dimensional magnetic quantum systems. The underlying Hamiltonian may have the form H=H-0+W, where H-0 is rotationally symmetric and has dense point spectrum and W is a perturbation that breaks the rotational symmetry. In the latter case, we also give estimates for the growth of the angular momentum operator in time.
- ItemOn the convergence of eigenfunctions to threshold energy states(2008) Østergaard, Sørensen T.; Stockmeyer, Edgardo
- ItemOn the eigenfunctions of no-pair operators in classical magnetic fields(2009) Matte, Oliver; Stockmeyer, Edgardo
- ItemOn the spectral stability of the nonlinear Dirac equation of Soler type(2020) Aldunate Bascuñán, Danko; Stockmeyer, Edgardo; Pontificia Universidad Católica de Chile. Instituto de FísicaWe study the spectral stability of the solitary wave solutions to the nonlin- ear Dirac equation in (1+1) dimension. We focus on a Soler type nonlinear model, where the nonlinearity is given by (ψψ)^p. The method we use con- sists in perturbe the solutions with a sufficiently small function ρ, finding a time evolution equation for this perturbation where this equation depends on the spectrum of the linearized operator Hμ. We will say that the solitary wave solutions are stable if the spectrum of Hμ does not have eigenvalues with imaginary part other than zero. We were only able to provide bounds for the real and imaginary part of the discrete spectrum of Hμ. In the end, we summarize what is known about σ(Hμ).
- ItemON THE TWO-DIMENSIONAL QUANTUM CONFINED STARK EFFECT IN STRONG ELECTRIC FIELDS(2022) Cornean, Horia; Krejcirik, David; Pedersen, Thomas G.; Raymond, Nicolas; Stockmeyer, EdgardoWe consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the low-lying eigenvalues. This shows that the excitation frequencies are proportional to the square root of the boundary curvature at a certain point determined by the direction of the electric field.
- ItemReal analyticity away from the nucleus of pseudorelativistic hartree-fock orbitals(2012) Dall'Acqua, A.; Fournais, S.; Østergaard Sørensen, T.; Stockmeyer, Edgardo
- ItemResolvent Convergence to Dirac Operators on Planar Domains(2019) Barbaroux, Jean-Marie; Cornean, Horia; Le Treust, Loic; Stockmeyer, EdgardoConsider a Dirac operator defined on the whole plane with a mass term of size m supported outside a domain . We give a simple proof for the norm resolvent convergence, as m goes to infinity, of this operator to a Dirac operator defined on with infinite-mass boundary conditions. The result is valid for bounded and unbounded domains and gives estimates on the speed of convergence. Moreover, the method easily extends when adding external matrix-valued potentials.
- ItemResults on the Spectral Stability of Standing Wave Solutions of the Soler Model in 1-D(2023) Aldunate, Danko; Ricaud, Julien; Stockmeyer, Edgardo; van den Bosch, HanneWe study the spectral stability of the nonlinear Dirac operator in dimension 1 + 1, restricting our attention to nonlinearities of the form f ((psi, beta psi)C-2)beta. We obtain bounds on eigenvalues for the linearized operator around standing wave solutions of the form e(-i omega t) phi(0). For the case of power nonlinearities f (s) = s|s|(p-1), p > 0, we obtain a range of frequencies omega such that the linearized operator has no unstable eigenvalues on the axes of the complex plane. As a crucial part of the proofs, we obtain a detailed description of the spectra of the self-adjoint blocks in the linearized operator. In particular, we show that the condition (phi(0), beta phi(0))C-2 > 0 characterizes groundstates analogously to the Schrodinger case.
- ItemSelf-Adjointness of Two-Dimensional Dirac Operators on Domains(2017) Benguria Donoso, Rafael; Fournais, Soren; Stockmeyer, Edgardo; Bosch, Hanne van den
- ItemSpectral analysis of Dirac operators in waveguides with magnetic field(2025) Rodríguez Toro, Joaquín; Stockmeyer, Edgardo; Pontificia Universidad Católica de Chile. Instituto de FísicaEstudiamos el operador de Dirac en una guía de onda recta bidimensional con un campo magnético uniforme perpendicular a ella. Consideramos condiciones de frontera locales generales que aseguran que no fluya corriente a través de la frontera. Las correspondientes realizaciones autoadjuntas del operador de Dirac pueden ser parametrizadas por $\gamma\in\mathbb{R}\cup\{+\infty\}$. Identificamos los casos $\gamma=\pm1$ como la condición de frontera de masa infinita, mientras que $\gamma=0$ y $\gamma=\infty$ se relacionan con los casos de zigzag. Además, introducimos la razón $\beta>0$ entre el cuadrado de la mitad del ancho de la guía de onda y el cuadrado de la longitud magnética. El sistema puede ser descrito completamente en términos de $\gamma$ y $\beta$. La simetría translacional en la dirección longitudinal da lugar al operador autoadjunto y unidimensional transversal $\mathcal{T}_\gamma(\beta,\xi)$, donde $\xi$ es el momento longitudinal.Proporcionamos soluciones explícitas para las energías y funciones propias en términos de funciones de Weber, lo que nos permite estudiar las curvas de dispersión de energía $\lambda_n(\xi)$. Encontramos que las energías negativas exhiben un comportamiento diferente al de las positivas. Por un lado, la primera energía positiva del sistema se acumula, en el límite $\beta\to\infty$, hacia la energía cero. Las energías positivas restantes se acumulan hacia el respectivo nivel de Dirac-Landau, un comportamiento que recuerda a los sistemas descritos por un Laplaciano magnético con condición de frontera de Dirichlet. Por otro lado, mostramos que para cualquier $\gamma$ (excepto para zigzag) existe un valor crítico $\beta_c$ tal que, para $\beta$ por debajo de este valor, la primera curva de dispersión de energía negativa tiene un máximo en $\xi=0$, mientras que por encima de él, la curva tiene dos máximos en puntos simétricos alejados de $\xi=0$. Además, para $\gamma=\pm1$ la primera energía negativa se acumula, en el límite $\beta\to\infty$, hacia $1.312\sqrt{\beta}$, por encima del primer nivel de Dirac-Landau negativo.Presentamos una fórmula trascendental para $\beta_c(\gamma)$ que muestra que este mapeo es convexo y tiene un mínimo, calculado para $\gamma=1.3$, para el cual $\beta_c\approx2.9411$. Para el caso importante de $\gamma=\pm1$, tenemos $\beta_c\approx3.0118$. Hasta donde sabemos, estos resultados no han sido reportados en la literatura antes.