arXiv subjects

A. Martín-Ruiz

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

At least 19 recordsLinked to original sources

arXiv2026

Magnetic-field-activated transport from band geometry in gapped nodal-line semimetals

We develop a nonperturbative semiclassical theory of magnetotransport in gapped nodal-line semimetals, retaining the full magnetic-field dependence of Berry-curvature and orbital-magnetic-moment corrections. Starting from a minimal two-band model, we derive exact expressions for both the intrinsic Hall response and the dissipative Fermi-surface conductivity, valid to all orders in the magnetic field within the semiclassical regime. We show that the orbital magnetic moment reconstructs the geometrically active Fermi surface, breaking the azimuthal cancellation imposed by the nodal-line geometry and thereby activating an intrinsic Hall current that is absent at zero magnetic field. The Hall response exhibits a pronounced nonmonotonic dependence on the chemical potential and a strongly nonlinear magnetic-field evolution, reflecting the redistribution of geometrically active states around the nodal ring. We further demonstrate that the Fermi-surface conductivities recover the conventional Drude behavior in the weak-field limit, while acquiring quadratic and ultimately nonperturbative magnetic-field corrections together with a field-induced transport anisotropy that gives rise to a measurable planar Hall effect at intermediate fields. Both the intrinsic and dissipative responses are strongly enhanced when the Fermi level lies close to the nodal ring, where Berry curvature and orbital magnetic moment are largest. Our results identify magnetic-field-activated geometric transport as a characteristic signature of nodal-line semimetals and provide a unified framework for describing magnetotransport beyond perturbative magnetic-field expansions, together with experimentally accessible signatures of orbital-magnetic-moment physics.

cond-mat.mes-hall↗

arXiv2026

Linear and nonlinear transport responses of topological nodal-line semimetals

Topological nodal-line semimetals are three-dimensional quantum materials characterized by band crossings that form closed loops in momentum space. In $\mathcal{PT}$-symmetric realizations, these nodal rings are stabilized in the absence of spin-orbit coupling, giving rise to drumhead surface states and unconventional transport responses. In this work, we study charge transport across a nodal-line semimetal containing a finite electrostatic barrier, with both leads described by the same equilibrium material. By solving the corresponding scattering problem, we show that the transmission across the barrier exhibits {Klein-tunneling behavior protected at normal incidence by the nodal topology}, despite the extended nodal-line dispersion, which can be traced back to Berry-curvature-induced momentum locking. Using the Landauer-Büttiker formalism, we derive general expressions for the linear and nonlinear conductances, including both longitudinal and Hall components, and evaluate them at zero and finite temperature. Our analytical and numerical results elucidate the dependence of the conductance on barrier height and width, as well as on a $\mathcal{PT}$-breaking mass term. We identify distinct transport regimes in which nonlinear contributions are strongly enhanced and transverse Hall currents emerge, providing clear transport signatures of nodal-line topology and suggesting potential routes toward device applications.

cond-mat.mes-hall↗

arXiv2026

Fermionic Casimir effect in an axial Lorentz-violating background

We investigate the fermionic Casimir effect for a Dirac field confined between two parallel plates with MIT bag boundary conditions in the presence of CPT-odd Lorentz-symmetry violation described by a constant axial background vector $b_μ$. The exact mode quantization is derived from the modified Dirac equation in the planar geometry, and the vacuum energy is formulated through a phase-shift representation. For spacelike backgrounds we show that the components parallel to the plates can be absorbed into a shift of the transverse momenta and therefore do not affect the renormalized Casimir energy, while the component normal to the plates modifies the longitudinal spectrum and produces a genuine Lorentz-violating correction. Both the timelike component $b_{0}$ and the normal spacelike component $b_{z}$ can thus be treated within a unified framework characterized by a single effective spectral parameter. A closed logarithmic integral representation for the Casimir energy is obtained and its behavior is analyzed in the Lorentz-symmetric, weak-background, and strong-background regimes.

hep-th↗

arXiv2026

Non-Hermitian impurity scattering in graphene: Boltzmann transport and thermoelectric response

We investigate charge and thermoelectric transport in monolayer graphene containing a dilute distribution of finite-range non-Hermitian scattering centers. The impurities are modeled as circular complex potentials, whose imaginary component describes local carrier loss or gain. By solving the Dirac scattering problem exactly within a partial-wave approach, we obtain the nonunitary scattering matrix and derive the transport and absorption cross sections, which separately characterize momentum relaxation and net carrier exchange with the environment. To connect the microscopic scattering problem with stationary transport, we formulate a semiclassical Boltzmann description in which an external reservoir compensates the equilibrium particle loss or gain. This leads to an effective relaxation time governed by both elastic momentum scattering and non-Hermitian flux exchange. Using the full energy-dependent relaxation time, we evaluate the Onsager coefficients and the resulting electrical conductivity, electronic thermal conductivity, Seebeck coefficient, Lorenz ratio, and electronic thermoelectric figure of merit. We find that weak gain increases the effective carrier lifetime and enhances both charge and heat conductivities, while absorption produces the opposite behavior. More importantly, gain enhances the magnitude of the thermopower and the electronic figure of merit, whereas loss suppresses them. The Lorenz ratio remains close to the Sommerfeld value, with non-Hermiticity mainly modifying its finite-temperature corrections. Our results show that non-Hermitian scattering provides an additional mechanism for controlling the energy dependence of carrier relaxation and, consequently, the thermoelectric response of graphene.

cond-mat.mes-hall↗

arXiv2026

Disorder-induced modulation of the nonlinear Hall effect in Weyl semimetals

We study the effects of impurity scattering on the nonlinear Hall response of Weyl semimetals within the semiclassical Boltzmann approach. We derive the rectified and second-harmonic conductivity tensors for a general momentum-dependent transport relaxation time and evaluate this quantity microscopically for short-range, Gaussian, screened Coulomb, and magnetic impurities. For scalar disorder, the relaxation time is isotropic and chirality independent. The nonlinear Hall response is then determined by the anomalous velocity associated with the Berry curvature, and a finite net response requires energetically inequivalent Weyl nodes to avoid cancellation between opposite chiralities. Polarized magnetic impurities lead to a qualitatively different behavior. We find that interference between the first- and second-order Born amplitudes generates a helicity-dependent anisotropic correction to the relaxation time. This anisotropy changes the tensor structure of the nonlinear Hall conductivity and gives rise to a finite second-harmonic current for suitable orientations of the electric field relative to the impurity polarization. For representative parameters, however, the anisotropic contribution is several orders of magnitude smaller than the dominant isotropic response. These results establish how the microscopic form of impurity scattering enters the nonlinear Hall response of Weyl semimetals through the transport relaxation time.

cond-mat.mes-hall↗

arXiv2026

Newton geometry of Bogdanov-Takens degeneracies in integrable dilatonic models: invariant divisors and boundary multiplicity

The Kantowski--Sachs interior of Grumiller's two-dimensional dilaton gravity model reduces to $\dot H=\tfrac12(Λ-3H^2-u^2)+Qu$, $\dot u=-Hu$, where $H$ is the expansion rate of the orbit two-spheres, $u$ their inverse areal radius, and $Q$ is minus twice the Rindler acceleration. For $Q\neq0$ it has two distinct rank-one nilpotent equilibria with complementary Bogdanov--Takens (BT) degeneracies: $(a,b)=(0,\neq0)$ with multiplicity $μ=3$, and $(a,b)=(\neq0,0)$ with $μ=2$. We show that this complementarity is forced by a single divisor-organized structure. The system is Darboux integrable, $X=\tfrac12u^4X_I$, where $I$ is the mass function and $u^4$ is an inverse integrating factor whose zero divisor is the invariant axis $\{u=0\}$. Off the divisor, every nilpotent equilibrium of $RX_I$ with $R(p)\neq0$ has $b=0$, from $b=D_{q_0}\operatorname{tr}DX$. On the divisor, invariance of the coordinate axis forces $a=0$ because $\det DX|_{u=0}=Φ_xG$ and both factors vanish at the corner. Hence $ab=0$ throughout the class, so a versal two-parameter BT unfolding is impossible. The Bernstein--Kushnirenko bound fails at both points; instead, the exact local identity $μ_0=m_1\ell_y+m_2\ell_x$ gives $μ=3,2$ without a nondegeneracy hypothesis. Both multiplicities have a mixed-covolume interpretation, with $\operatorname{Covol}=\sum_{k,i}\min(p_kq_i',p_i'q_k)$ on convenient diagrams; the corresponding general theorem for the non-convenient diagrams arising here remains open. For $\dot H=\tfrac{1-m}{2}H^2+ψ(u)$, $\dot u=-Hu$, with $ψ(0)=0$, $ψ'(0)\neq0$, $m\neq1$, the vacuum always has $μ=3$, $a=0$, $b=-m$. Its Dumortier--Llibre--Artés discriminant is $b_1^2+8a_3=(m-2)^2$, so for every $m>1$ it has one hyperbolic and one elliptic sector, independently of $ψ$.

math.DS↗

arXiv2026

Symmetric Nonlinear Cellular Automata as Algebraic References for Rule 30

A comparative algebraic framework for elementary cellular automata is developed, centered on the role of spatial symmetry. The primary object of study is Rule 22, the elementary cellular automaton with algebraic normal form $g(a,b,c)=a\oplus b\oplus c\oplus abc$ over $\mathrm{F}_2$, the simplest rule combining full $S_3$ symmetry with genuine nonlinearity. It is proved that the single-seed orbit of Rule 22 admits the closed form $Q_{2j}(x)=(x^2+x^{-2})^j$ and $Q_{2j+1}(x)=(x^{-1}+1+x)(x^2+x^{-2})^j$ for the row generating polynomials over $\mathrm{F}_2$. Three consequences follow: an exact support-set cardinality $|S_m|=2^{\mathrm{popcount}(\lfloor m/2\rfloor)}\cdot 3^{m\bmod 2}$, a two-step recursive construction of the support sets, and, in a formal continuum approximation, a parabolic reaction--diffusion equation $\partial_m u=u_{xx}+2u+u^3$. Rule~22 is then used as a symmetric reference for Rule 30. The symmetry-breaking deviation $ε(m)=|S_m^{(30)}|-|S_m^{(22)}|$ between full-row support cardinalities is empirically consistent with a power law $m^b$ ($b\approx 1.11$), and is non-positive exactly at the Mersenne indices $m=2^k-1$. A mechanism for the apparent randomness of Rule~30's center column is identified through the left-permutive structure and asymmetric Boolean sensitivity profile.

math-ph↗

arXiv2026

Matrix bordering structure of the Faddeev-Jackiw algorithm: kernel reduction and symbolic automation

We show that the iterative Faddeev-Jackiw (FJ) reduction for singular Lagrangian systems constitutes a geometrically constrained instance of the Matrix Bordering Technique (MBT). Since the initial pre-symplectic matrix is singular, the classical Schur determinantal identity cannot be applied. Instead, regularity is governed by the interaction of the bordering block with the kernel of the initial matrix. Writing N for an orthonormal basis of this kernel, we introduce the reduced constraint matrix $Γ= N^T B$ and derive an exact determinant factorization showing that the extended symplectic matrix is nondegenerate precisely when the generated constraints span the kernel and $Γ$ is nonsingular. We further identify $Γ$ with the Hessian of the symplectic potential restricted to the kernel and with the corresponding Faddeev-Jackiw constraint matrix. This establishes that, for independent generated constraints, termination of the FJ algorithm in a nondegenerate symplectic form is equivalent to nondegeneracy of the constraint algebra, characterizing a second-class system in the Dirac-Bergmann sense. These results provide the algebraic foundation for a fully symbolic implementation in the Wolfram Language. The resulting BorderedFJReduction engine preserves parametric dependencies throughout the reduction and is validated on representative constrained mechanical systems.

math-ph↗

arXiv2026

Nullcline geometry constrains the location of oscillatory instabilities in planar predator--prey systems

We prove that the critical structure of the prey nullcline governs where oscillatory instabilities can emerge in planar predator--prey systems. For a broad class of Gause--type models, we establish a general geometric localization theorem: the prey coordinate of every Hopf bifurcation point is confined between consecutive critical points of the prey nullcline. The mechanism is purely geometric. Along the nullcline, the diagonal Jacobian entry $J_{11}$ is proportional to the nullcline slope $g'(x)$, independently of the bifurcation parameter, while $J_{22}\le 0$ at any coexistence equilibrium. At critical points of the nullcline ($g'=0$), the Jacobian trace becomes strictly negative, creating a spectral barrier that precludes oscillatory instability. This barrier partitions the state space into dynamically distinct regions, confining the onset of limit--cycle oscillations to the ascending branches of the nullcline. We illustrate the principle in three canonical families---Bazykin's model (quadratic nullcline), a Leslie--Holling type~IV system with harvesting (cubic nullcline), and the Crowley--Martin model with predator interference (rational nullcline)---for which we obtain closed--form Hopf bifurcation loci. The same geometric mechanism extends to discrete time: for the forward Euler map with step size $τ$, an exact identity $\det(J^G)-1=τ[\operatorname{tr}(J)+τ\det(J)]$ shows that the Neimark--Sacker locus is strictly disjoint from the continuous Hopf locus yet tracks it on the same ascending branch at an $O(τ)$ distance, crossing the spectral barrier only in the coarse--step regime. The results demonstrate that the functional responses responsible for predator saturation and interference not only bound the efficiency of interactions but also imprint a geometric architecture on the bifurcation landscape.

math.DS↗

arXiv2026

Casimir effect in Plebański nonlinear electrodynamics with spontaneously Lorentz-breaking magnetic vacua

We study the Casimir effect in a class of gauge-invariant nonlinear electrodynamics models designed to admit spontaneously Lorentz-breaking magnetic vacua. The theory is formulated in the Plebański first-order representation, with a single-invariant Hamiltonian potential $\widehat V(P)$ as the fundamental nonlinear object. In this formulation, nontrivial magnetic vacua are stationary points of the reduced effective Hamiltonian. The symmetry-breaking condition is controlled by $\Sm(P)\equiv\widehat V_P(P)+2P\widehat V_{PP}(P)$, which also controls the rank of the longitudinal magnetic response and of the Hamiltonian constraint structure. Taking this Lorentz-breaking nonlinear electrodynamics as the model under study, we analyze how the distinction between the regular constant-rank sector and the degenerate magnetic vacuum enters the parallel-plate Casimir spectrum. Linearization around a regular magnetic background $\bar P$, with $\Sm(\bar P)\neq0$, yields an ordinary Maxwell-like branch and an extraordinary anisotropic branch controlled by $α(\bar P)=\widehat V_P(\bar P)/\Sm(\bar P)$. We compute the regularized Casimir energy for magnetic backgrounds perpendicular and parallel to the plates. In the regular-sector limit $\bar P\to P_\star$, with $\Sm(P_\star)=0$, the extraordinary branch becomes singular and the parallel-configuration energy diverges. This divergence is not an infinite physical Casimir force; it signals that the regular two-branch optical description cannot be continued uniformly to the rank-changing magnetic vacuum. Direct analysis on the degenerate surface shows that the extraordinary branch does not survive as an independent propagating mode for generic momenta. Thus, quantizing the regular theory and then taking $\Sm\to0$ is not equivalent to imposing $\Sm(P_\star)=0$ before quantization.

hep-th↗

arXiv2026

Nonperturbative magnetotransport from band geometry in Weyl semimetals

We develop a nonperturbative semiclassical theory of magnetotransport in Weyl semimetals, retaining the full magnetic-field dependence of the Fermi-surface conductivity in the presence of Berry curvature and orbital magnetic moment effects. We obtain closed-form expressions valid to all orders in the magnetic field within the semiclassical regime. We show that the exact continuum formulation exhibits an intrinsic infrared sensitivity associated with the singular behavior of the orbital magnetic moment, requiring a physically motivated regularization. While the full conductivity tensor reduces to the standard quadratic magnetoconductivity, we demonstrate that magnetic-field expansion and momentum integration do not commute, leading to nonanalytic contributions at the level of scalar transport coefficients. Our results identify a regime, relevant for low carrier densities or moderate magnetic fields, where magnetotransport becomes intrinsically nonperturbative and cannot be captured by conventional weak-field expansions.

cond-mat.mes-hall↗

arXiv2026

Electromagnetic response of two interacting topological insulator spheres in external fields

We study the static electromagnetic response of two spherical topological insulators embedded in a dielectric medium and subjected to a uniform external electric field. The gapped surface states are described by a piecewise constant axion field, which induces a topological magnetoelectric coupling localized at the spherical interfaces. {More generally, the same formalism applies to isotropic magnetoelectric media characterized by an effective scalar magnetoelectric response.} The electrostatic problem is solved at zeroth order using bispherical coordinates, allowing for an exact treatment of both parallel and perpendicular orientations of the external field relative to the center-to-center axis. The resulting mode expansions are determined by three-term recurrence relations, which are solved perturbatively for nonoverlapping spheres. The { magnetoelectric}-induced response is then computed to leading order in the fine-structure constant {(or, more generally, in the effective coupling strength)}. The induced sources are purely interfacial and generate distinct magnetostatic field configurations in the parallel and perpendicular geometries. Closed-form series representations for the induced vector potential and magnetic field are obtained in terms of the zeroth-order electrostatic coefficients. These results provide an analytically controlled description of {interaction-induced magnetostatics in coupled spherical magnetoelectric systems}.

cond-mat.other↗

arXiv2026

A supersymmetric study of charge and spin transport in Weyl semimetals under axionic electrodynamic response

We investigate the charge and spin transport properties of a Weyl semimetal under an external magnetic field using a low-energy effective theory. By performing a chiral transformation, we remove the axial term from the fermionic Lagrangian, while its physical effects are retained through the system's electromagnetic response. This response, derived from integrating out the fermionic degrees of freedom, takes the form of axionic electrodynamics and enters the Dirac equation via minimal coupling. The resulting dynamics separate naturally into magnetic and electric components: the magnetic sector admits a supersymmetric factorization, while the electric part exhibits a PT-supersymmetric structure. Robin boundary conditions are applied to the spinor, setting the energy spectrum and defining exact spinor solutions. We obtain the chiral projections of probability and current densities, exhibiting a chiral imbalance in the material. We show that in the x-direction, only one chirality contributes to the chiral current ($j^x_l = 0$). Spin density and currents where also computed. Our results demonstrate how the interplay between axionic response and supersymmetry governs transport phenomena in our specific setup, offering novel insights into the effective field theory description of Weyl semimetals.

cond-mat.mes-hall↗

arXiv2026

Spontaneous persistent currents and time-reversal symmetry breaking in thick-walled Weyl semimetal cylinders

We theoretically investigate the Aharonov-Bohm effect in a thick-walled Weyl semimetal (WSM) cylinder subject to an external axial magnetic field. By employing a low-energy effective Hamiltonian, we analytically solve the eigenvalue problem for both infinite and finite-length cylindrical geometries. We apply infinite-mass boundary conditions at the radial walls and MIT bag boundary conditions at the cylinder caps to properly account for intra-node confinement and inter-valley scattering, respectively. Our numerical results demonstrate that the spatial separation of the Weyl nodes acts as an internal chiral gauge field. This geometric field intrinsically breaks time-reversal (TR) symmetry, lifting the chiral degeneracy even at zero external flux. This symmetry breaking manifests as spontaneous persistent currents and the unfolding of conductance channels. Furthermore, longitudinal confinement induces propagation-direction-dependent energy splitting, altering the partial density of states and causing spatio-chiral current imbalances.

cond-mat.mes-hall↗

arXiv2026

Anomalous Hall effect in anisotropic type-II Weyl semimetals

We extend our previous analysis [Phys. Rev. D 109, 065005 (2024)] of CPT-odd electromagnetic response in tilted, anisotropic Weyl semimetals to the overtilted (type-II) regime, where electron and hole pockets coexist at the Fermi level. Starting from the minimal QED sector of the Standard-Model Extension matched to a lattice-motivated anisotropic Dirac Hamiltonian with tilt, we compute the zero-temperature finite-density effective action nonperturbatively from the vacuum polarization tensor, and corroborate the result using a complementary chiral kinetic theory formulation that consistently incorporates both Fermi-sea and Fermi-surface contributions. In the type-II regime the unbounded linear dispersion necessitates a physical ultraviolet regularization. Implementing a hard momentum cutoff tied to the lattice bandwidth, we show that the CPT-odd, axion-like response remains finite across the type-I to type-II Lifshitz transition, while acquiring tilt- and anisotropy-dependent renormalizations together with nonuniversal, cutoff-sensitive terms governed by the geometry of the electron and hole pockets. As a concrete application, we evaluate the anomalous Hall conductivity in the prototypical type-II Weyl semimetal WTe$_2$, using parameters extracted from first-principles calculations and experiments, and find that Fermi-sea and Fermi-surface contributions are comparable and partially cancel, yielding a finite and strongly anisotropic Hall response characteristic of the overtilted regime.

hep-th↗

arXiv2026

Non-Hermitian thermoelectric transport in graphene: Tunable anomalous transmission through complex barriers

We investigate thermoelectric transport in monolayer graphene across a finite complex barrier within a Landauer scattering framework. Solving the Dirac-Weyl problem exactly, we show that the imaginary part of the barrier renders the scattering matrix nonunitary and replaces the usual Hermitian flux conservation by a generalized flux-balance relation determined by the net gain or loss inside the barrier. In the Hermitian limit, the standard graphene $n$-$p$-$n$ barrier behavior is recovered, including perfect transmission at normal incidence and Fabry-Perot-type resonances. For a finite imaginary part, however, the same resonant channels are selectively attenuated or amplified, which significantly modifies both the angular response and the conductance profile. We further show that the lead-resolved conductances become dependent on the bias partition, providing a direct signature of the breakdown of gauge invariance in the effective two-terminal response. At finite temperature, the exact linear-response coefficients reveal a clear trade-off controlled by the imaginary part of the barrier: gain enhances both the electrical and thermal conductances, whereas loss suppresses the thermal conductance more efficiently and yields the largest thermoelectric figure of merit within the parameter range considered. These results demonstrate that complex barriers extend the range of transport behaviors accessible in graphene beyond the usual Hermitian $n$-$p$-$n$ junction. They also suggest a practical interpretation of the imaginary potential as an effective reduced description of unresolved source-sink channels or additional probes coupled to the device, particularly when a fully microscopic model of the environment is not available.

cond-mat.mes-hall↗

arXiv2026

Exact classical emergence from high-energy quantum superpositions

We examine the correspondence principle for an equiprobable superposition of high-energy eigenstates of the infinite square well using a fully analytical Fourier-based approach. We derive a closed-form asymptotic expression for the interference terms $ρ_α^{\text{a}}(x)$ by expanding them into a geometric series of quantum Fourier coefficients. We show these terms act as functional envelopes that do not vanish individually but become asymptotically equivalent in the large-$n$ limit. Furthermore, we prove the total probability density for a superposition of $2Δ+1$ states converges exactly to the uniform classical distribution as $Δ\to \infty$. Dynamically, the expectation value of position reproduces the classical triangular trajectory asymptotically. Residual quantum deviations remain confined to boundary layers whose relative width vanishes under macroscopic resolution. These results establish a rigorous asymptotic realization of the classical limit for isolated bound systems in both static and dynamical contexts.

quant-ph↗

arXiv2026

Landauer-based study of transport in Chern insulator heterostructures

We study charge transport through a trivial-topological-trivial junction described by the continuous Qi-Wu-Zhang model, which realizes a two-dimensional Chern-insulating phase. The central region is tuned into the topological regime, while the adjoining leads remain trivial, and an electrostatic barrier of tunable height and width is applied exclusively to the topological slab. By matching wave functions across the interfaces, we obtain the angle- and energy-resolved transmission probability and demonstrate the occurrence of Klein tunneling despite the presence of a bulk spectral gap. Within the continuum Dirac description, this perfect transmission originates from the inversion of the Dirac mass across the junction, which reflects the band inversion of the central layer relative to the trivial leads. In the Qi-Wu-Zhang model considered here, this mass inversion coincides with the transition between trivial and Chern-insulating phases and is accompanied by finite Berry curvature that governs the nonlinear transport response. The resulting transmission function is then incorporated into a Landauer-Büttiker framework to analyze both linear and nonlinear transport. Closed-form expressions for the linear and nonlinear conductances are derived at zero and finite temperatures. In addition, we investigate the role of dephasing, showing how partial loss of coherence suppresses Fabry-Pérot oscillations while leaving the overall transport trends intact. Finally, we map out the interplay between barrier height, slab thickness, and topological mass parameter, identifying optimal regimes that yield enhanced rectification in the nonlinear response.

cond-mat.mes-hall↗