arXiv subjects

A. Martín-Ruiz

Publications and source records attributed to A. Martín-Ruiz.

65 records · Page 4Linked to original sources

arXiv2018

Interaction of a hydrogenlike ion with a planar topological insulator

An electric charge near the surface of a topological insulator (TI) induces an image magnetic monopole. Here we study the spectra of hydrogenlike ions near the surface of a planar TI, taking into account the modifications which arise due to the presence of the image monopole magnetic fields. In fact, the atom-TI interaction provides additional contributions to the Casimir-Polder potential while the ion-TI interaction modifies the energy shifts in the spectrum, which now became distance dependent. We show that the hyperfine structure is sensitive to the image magnetic monopole fields in states with nonzero angular momentum, and that circular Rydberg ions can enhance the maximal energy shifts. We discuss in detail the energy splitting of the $n$P$_{1/2}$ and $n$P$_{3/2}$ states in hydrogen. We also analyze the Casimir-Polder potential and find that this magnetic interaction produces a large distance repulsive tail for some particular atomic states. A sizable value of the maximum of the potential requires TIs with very low values of the permittivity together with high values of the topological magnetoelectric polarization.

quant-ph↗

arXiv2017

Dynamics of a Rydberg hydrogen atom near a topologically insulating surface

We investigate the classical dynamics of a Rydberg hydrogen atom near the surface of a planar topological insulator. The system is described by a Hamiltonian consisting of the free-hydrogen part and the hydrogen-surface potential. The latter includes the interactions between the electron and both image electric charges and image magnetic monopoles. Owing to the axial symmetry, the $z$ component of angular momentum $l_{z}$ is conserved. Here we consider the $l_{z} = 0$ case. The structure of the phase space is explored extensively by means of numerical techniques and Poincaré surfaces of section for the recently discovered topological insulator TlBiSe$_{2}$. The phase space of the system is separated into regions of vibrational and rotational motion. We show that vibrational-rotational-vibrational type transitions can be tuned with the topological magnetoelectric polarizability.

nlin.CD↗

arXiv2017

Gravitational waves propagation in nondynamical Chern-Simons gravity

We investigate the propagation of gravitational waves in linearized Chern-Simons (CS) modified gravity by considering two nondynamical models for the coupling field $θ$: (i) a domain wall and (ii) a surface layer of $θ$, motivated by their relevance in condensed matter physics. We demonstrate that the metric and its first derivative become discontinuous for a domain wall of $θ$, and we determine the boundary conditions by realizing that the additional contribution to the wave equation corresponds to one of the self-adjoint extensions of the D'Alembert operator. Nevertheless, such discontinuous metric satisfies the area matching conditions introduced by Barrett. On the other hand, the propagation through a surface layer of $θ$ behaves similarly to the propagation of electromagnetic waves in CS extended electrodynamics. In both cases we calculate the corresponding reflection and transmission amplitudes. As a consequence of the distributional character of the additional terms in the equations that describe wave propagation, the results obtained for the domain wall are not reproduced when the thickness of the surface layer goes to zero, as one could naively expect.

gr-qc↗

arXiv2017

On the equivalence between bumblebee models and electrodynamics in a non-linear gauge

Bumblebee models are effective field theories describing a vector field with a nonzero vacuum expectation value that spontaneously breaks Lorentz invariance. They provide an alternative way of exploring the similarities between theories with spontaneous Lorentz symmetry breaking and gauge theories. The equivalence between bumblebee models with suitable conditions and standard electrodynamics in a non-linear gauge $A_μA^μ-b^2=0$ is taken for granted; however, this point is very subtle and has not yet been fully addressed. The main goal of this paper is to fill in this gap. More precisely, here we study the relation between a bumblebee model, with a smooth potential of the form $V(B _μ) = V (B _μ B ^μ - b ^{2})$, and standard electrodynamics in the non-linear gauge $A _μ A ^μ - b ^{2} = 0$, both at the classical and quantum levels. Using the Dirac's method we show that after introducing Dirac brackets with suitable initial conditions, the classical dynamics of the bumblebee model corresponds to that of standard electrodynamics in the aforementioned non-linear gauge. In the quantum case we demonstrate that perturbative calculations of Feynman amplitudes to any physical process in each model are indistinguishable. To do this, we show that the Feynman rules and propagators of standard electrodynamics in the non-linear gauge and those describing the bumblebee model are the same.

hep-th↗

arXiv2016

Local effects of the quantum vacuum in Lorentz-violating electrodynamics

The Casimir effect is one of the most remarkable consequences of the non-zero vacuum energy predicted by quantum field theory. In this paper we use a local approach to study the Lorentz violation effects of the minimal standard model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method similar to that used for obtaining the Born series for the scattering amplitudes in quantum mechanics, we compute, at leading order in the Lorentz-violating coefficients, the relevant Green's function which satisfies given boundary conditions. The standard point-splitting technique allow us to express the vacuum expectation value of the stress-energy tensor in terms of the Green's function. We discuss its structure in the region between the plates. We compute the renormalized vacuum stress, which is obtained as the difference between the vacuum stress in the presence of the plates and that of the vacuum. The Casimir force is evaluated in an analytical fashion by two methods: by differentiating the renormalized global energy density and by computing the normal-normal component of the renormalized vacuum stress. We compute the local Casimir energy, which is found to diverge as approaching the plates, and we demonstrate that it does not contribute to the observable force.

hep-th↗

arXiv2016

Casimir effect between ponderable media as modeled by the standard model extension

The CPT-even sector of the standard model extension amounts to extending Maxwell electrodynamics by a gauge invariant term of the form $- \frac{1}{4} (k _{F}) _{αβμν} F ^{αβ} F ^{μν}$, where the Lorentz-violating (LV) background tensor $(k _{F}) _{αβμν}$ possesses the symmetries of the Riemann tensor. The electrodynamics in ponderable media is still described by Maxwell equations in matter with modified constitutive relations which depend on the coefficients for Lorentz violation. We study the effects of this theory on the Casimir force between two semi-infinite ponderable media. The Fresnel coefficients characterizing the vacuum-medium interface are derived, and with the help of these, we compute the Casimir energy density. At leading-order in the LV coefficients, the Casimir energy density is numerically evaluated and successfully compared with the standard result. We also found a variety of intriguing effects, such as a non-trivial Kerr effect and the Casimir effect between two phases of the electromagnetic vacuum. We consider a bubble of Lorentz-symmetric (Maxwell) vacuum embedded in the infinite Lorentz-violating vacuum, and we calculate the Casimir energy at leading order, which in this case is quadratic in the LV coefficients. The Casimir force can be positive, zero, or negative, depending on the relative strengths between the LV coefficients.

hep-th↗

arXiv2016

A Green's function approach to the Casimir effect on topological insulators with planar symmetry

We investigate the Casimir stress on a topological insulator (TI) between two metallic plates. The TI is assumed to be joined to one of the plates and its surface in front of the other is covered by a thin magnetic layer, which turns the TI into a full insulator. We also analyze the limit where one of the plates is sent to infinity yielding the Casimir stress between a conducting plate and a TI. To this end we employ a local approach in terms of the stress-energy tensor of the system, its vacuum expectation value being subsequently evaluated in terms of the appropriate Green's function. Finally, the construction of the renormalised vacuum stress-energy tensor in the region between the plates yields the Casimir stress. Numerical results are also presented.

cond-mat.mes-hall↗

arXiv2015

Green's function approach to Chern-Simons extended electrodynamics: an effective theory describing topological insulators

Boundary effects produced by a Chern-Simons (CS) extension to electrodynamics are analyzed exploiting the Green's function (GF) method. We consider the electromagnetic field coupled to a $θ$-term in a way that has been proposed to provide the correct low energy effective action for topological insulators (TI). We take the $θ$-term to be piecewise constant in different regions of space separated by a common interface $Σ$, to be called the $θ$-boundary. Features arising due to the presence of the boundary, such as magnetoelectric effects, are already known in CS extended electrodynamics and solutions for some experimental setups have been found with specific configuration of sources. In this work we illustrate a method to construct the GF that allows to solve the CS modified field equations for a given $θ$-boundary with otherwise arbitrary configuration of sources. The method is illustrated by solving the case of a planar $θ$-boundary but can also be applied for cylindrical and spherical geometries for which the $θ$-boundary can be characterized by a surface where a given coordinate remains constant. The static fields of a point-like charge interacting with a planar TI, as described by a planar discontinuity in $θ$, are calculated and successfully compared with previously reported results. We also compute the force between the charge and the $θ$-boundary by two different methods, using the energy momentum tensor approach and the interaction energy calculated via the GF. The infinitely straight current-carrying wire is also analyzed.

cond-mat.other↗

arXiv2014

Tunneling of Polymer Particles

In this paper we study the tunneling using a background independent (polymer) quantization scheme. We show that at low energies, for the tunneling through a single potential barrier, the polymer transmission coefficient and the polymer tunneling time converge to its quantum-mechanical counterparts in a clear fashion. As the energy approaches the maximum these polymer quantities abruptly decrease to zero. We use the transfer matrix method to study the tunneling through a series of identical potential barriers. We obtain that the transmission coefficients (polymer and quantum-mechanical) behave qualitatively in a similar manner, as expected. Finally we show that the polymer tunneling time exhibits anomalous peaks compared with the standard result. Numerical results are also presented.

quant-ph↗

arXiv2014

Diffraction in Time of Polymer Particles

We study the quantum dynamics of a suddenly released beam of particles using a background independent (polymer) quantization scheme. We show that, in the first order of approximation, the low-energy polymer distribution converges to the standard quantum-mechanical result in a clear fashion, but also arises an additional small polymer correction term. We find that the high-energy polymer behaviour becomes predominant at short distances and short times. Numerical results are also presented. We find that particles whose wave functions satisfy the polymer wave equation do not exhibit the diffraction in time phenomena. The implementation of a lower bound to the possible resolution of times into the time-energy Heisenberg uncertainty relation is briefly discussed.

quant-ph↗

arXiv2013

Macroscopic quantum behaviour of periodic quantum systems

In this paper we introduce a simple procedure for computing the macroscopic quantum behaviour of periodic quantum systems in the high energy regime. The macroscopic quantum coherence is ascribed to a one-particle state, not to a condensate of a many-particle system; and we are referring to a system of high energy but with few degrees of freedom. We show that, in the first order of approximation, the quantum probability distributions converge to its classical counterparts in a clear fashion, and that the interference effects are strongly suppressed. The harmonic oscillator provides a testing ground for these ideas and yields excellent results.

quant-ph↗