arXiv subjects

Luis Inzunza

Publications and source records attributed to Luis Inzunza.

At least 19 recordsLinked to original sources

arXiv2026

Super-Klein tunneling in 2D Lorentzian-type barriers in graphene

We introduce a two-dimensional model of spin-1/2 Dirac fermions in graphene subjected to a highly tunable electric field, which exhibits super-Klein tunneling. The electric field can be continuously interpolated between two limiting configurations: a uniform electrostatic Lorentzian barrier with translational invariance and a chain of well-separated electrostatic scatterers. We demonstrate that super-Klein tunneling arises naturally as a direct consequence of the intrinsic connection of the model to free-particle dynamics, a relation that is established through methods of supersymmetric quantum mechanics, which provide an elegant and analytically tractable framework. Besides the mentioned super-Klein tunneling, scale invariance of the model and invisibility of the potential for particles of specific energy are revealed, and possible routes toward experimental realization are discussed.

cond-mat.mes-hall↗

arXiv2026

The soliton nature of the super-Klein tunneling effect

We establish a relationship between the Davey--Stewartson II (DS II) integrable system in $(2{+}1)$ dimensions and quasi-exactly solvable planar interacting Dirac Hamiltonians that exhibit the super-Klein tunneling (SKT) effect. The Dirac interactions are constructed from the real and imaginary parts of breather solutions of the DS II system. In this framework, the SKT effect arises when the energy is tuned to match the constant background of the soliton, while the resulting Dirac Hamiltonians simultaneously support bound states embedded in the continuum. By imposing the SKT boundary conditions, we employ Darboux transformations to construct a general three-parameter family of DS II breather solutions that can be mapped to Dirac Hamiltonians. At the initial soliton time, the corresponding Dirac systems form a massless two-parameter family of Hermitian models with nontrivial electrostatic potentials. As the soliton time evolves, the systems become $\mathcal{PT}$-symmetric and develop a nontrivial imaginary mass term. Finally, when the soliton time is taken to be imaginary, the construction yields Hermitian Dirac systems that lack time-reversal symmetry. In all cases, we identify the emergence of quasi-symmetry transformations that preserve the SKT subspace of states while not commuting with the full Hamiltonian.

hep-th↗

arXiv2025

Confining kinks. $\zeta$-regularized one-loop kink mass shifts in exotic field theories

By combining stability analysis of scalar field theories with the Darboux transformation technique, we create models featuring kink-like solutions whose quantum perturbations are all bounded. On the one hand, the stability analysis relates scalar theories with Schr\"odinger equations, whose solutions serve as quantum perturbation modes. On the other hand, the Darboux transformation allows for constructing new exotic but solvable Schr\"odinger equations. This framework relates the quantum harmonic oscillator and its rational deformations to exotic scalar theories featuring non-trivial potentials. Depending on the structure of the spectrum of perturbation frequencies, these potentials may have various local maximums, minimums, and inflection points. The stationary solutions take the form of the definite integral over a finite interval of a function times the Gaussian bell distribution, including the Error and the Owen $T$ functions. Such models do not propagate quantum perturbations around the respective vacuums, so zero-point renormalization does not take place. However, Riemann$-\zeta$ function regularization allows us to achieve finite one-loop quantum corrections to the classical mass.

hep-th↗

arXiv2025

Coupling and particle number intertwiners in the Calogero model

It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as ``horizontal'' and construct new ``vertical'' intertwiners, which \emph{change the number of interacting particles} for a fixed but integer value of the coupling constant. The emerging structure of a grid of intertwiners exists only in the algebraically integrable situation (integer coupling) and allows one to obtain each Liouville charge from the free power sum in the particle momenta by iterated intertwining either horizontally or vertically. We present recursion formul\ae\ for the intertwiners as a factorization problem for partial differential operators and prove their existence for small values of particle number and coupling. As a byproduct, a new basis of non-symmetric Liouville integrals appears, algebraically related to the standard symmetric one.

hep-th↗

arXiv2025

SUSY design of smooth quantum rings in graphene

We develop a suitable technique to design zero-energy graphene models with radial electrostatic potentials capable of achieving electrostatic confinement. Using the Gaussian law for electrostatics, we derive the charge density associated with these potentials that correspond to concentric electrostatic rings. The technique is based on a modified supersymmetric transformation that allows to design time-reversal invariant interaction terms and to find the corresponding zero-energy bound states in analytical form. Consequently, solutions with the same probability density but different angular momentum are characterized by circular probability currents flowing in opposite directions. The energies of the systems defined in two Dirac valleys (one-valley) have a fourfold (twofold) degeneracy. As an example of the technique, we construct a ring-decorated Coulomb potential that exhibits zero energy collapse and bound states together.

cond-mat.mes-hall↗

arXiv2024

Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping

Confining Dirac fermions in graphene by electrostatic fields is a challenging task. Electric quantum dots created by a scanning tunneling microscope (STM) tip can trap zero-energy quasi-particles. The Lorentzian quantum well provides a faithful, exactly solvable, approximation to such a potential, hosting zero-energy bound states for certain values of the coupling constant. We show that in this critical configuration, the system can be related to the free particle model by means of a supersymmetric transformation. The revealed shape invariance of the model greatly simplifies the calculation of the zero modes and naturally explains the degeneracy of the zero energy.

cond-mat.mes-hall↗

arXiv2023

Non-Hermitian superintegrable systems

A non-Hermitian generalisation of the Marsden--Weinstein reduction method is introduced to construct families of quantum $\mathcal{PT}$-symmetric superintegrable models over an $n$-dimensional sphere $S^n$. The mechanism is illustrated with one- and two-dimensional examples, related to $u(2)$ and $u(3)$ Lie algebras respectively, providing new quantum models with real spectra and spontaneous $\mathcal{PT}$-symmetric breaking. In certain limits, the models reduce to known non-Hermitian systems and complex extensions of previously studied real superintegrable systems.

math-ph↗

arXiv2022

Conformal bridge transformation, $\mathcal{PT}$- and super- symmetry

Supersymmetric extensions of the 1D and 2D Swanson models are investigated by applying the conformal bridge transformation (CBT) to the first order Berry-Keating Hamiltonian multiplied by $i$ and its conformally neutral enlargements. The CBT plays the role of the Dyson map that transforms the models into supersymmetric generalizations of the 1D and 2D harmonic oscillator systems, allowing us to define pseudo-Hermitian conjugation and a suitable inner product. In the 1D case, we construct a $\mathcal{PT}$-invariant supersymmetric model with $N$ subsystems by using the conformal generators of supersymmetric free particle, and identify its complete set of the true bosonic and fermionic integrals of motion. We also investigate an exotic $N=2$ supersymmetric generalization, in which the higher order supercharges generate nonlinear superalgebras. We generalize the construction for the 2D case to obtain the $\mathcal{PT}$-invariant supersymmetric systems that transform into the spin-1/2 Landau problem with and without an additional Aharonov-Bohm flux, where in the latter case, the well-defined integrals of motion appear only when the flux is quantized. We also build a 2D supersymmetric Hamiltonian related to the "exotic rotational invariant harmonic oscillator" system governed by a dynamical parameter $γ$. The bosonic and fermionic hidden symmetries for this model are shown to exist for rational values of $γ$.

hep-th↗

arXiv2022

Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the equations of motion are found by employing a local canonical transformation, that leads to their natural interpretation in terms of Riemann surfaces. The cone parameter $α$ and the angular velocity $Ω$ of the background determine the existence of hidden symmetries. Globally defined higher order integrals associated with perihelion of geodesic orbits appear at rational values of $α$. For the harmonic oscillator system with frequency $ω$, the integrals responsible for the trajectory closure arise only for rational values of $α$ and $|γ|=|Ω/ω|$, with $|γ|=1$ corresponding to the Landau problem. We face a quantum anomaly problem since the hidden symmetry operators can only be constructed when $α$ is integer. Such operators are non-local in the case of the free particle. For the harmonic oscillator, the symmetry generators are obtained with the help of the conformal bridge transformation. We also study a multi-particle version of the harmonic oscillator system with $|γ|=1$ using the mean-field theory and find that the emerging vortex structure respects a singular point of the background.

hep-th↗

arXiv2021

Conformal bridge transformation and PT symmetry

The conformal bridge transformation (CBT) is reviewed in the light of the $\mathcal{PT}$ symmetry. Originally, the CBT was presented as a non-unitary transformation (a complex canonical transformation in the classical case) that relates two different forms of dynamics in the sense of Dirac. Namely, it maps the asymptotically free form into the harmonically confined form of dynamics associated with the $\mathfrak{so}(2,1)\cong \mathfrak{sl}(2,{\mathbb R})$ conformal symmetry. However, as the transformation relates the non-Hermitian operator $i\hat{D}$, where $\hat{D}$ is the generator of dilations, with the compact Hermitian generator $\hat{\mathcal{J}}_0$ of the $\mathfrak{sl}(2,{\mathbb R})$ algebra, the CBT generator can be associated with a $\mathcal{PT}$-symmetric metric. In this work we review the applications of this transformation for one- and two-dimensional systems, as well as for systems on a cosmic string background, and for a conformally extended charged particle in the field of Dirac monopole. We also compare and unify the CBT with the Darboux transformation. The latter is used to construct $\mathcal{PT}$-symmetric solutions of the equations of the KdV hierarchy with the properties of extreme waves. As a new result, by using a modified CBT we relate the one-dimensional $\mathcal{PT}$-regularized asymptotically free conformal mechanics model with the $\mathcal{PT}$-regularized version of the de Alfaro, Fubini and Furlan system.

hep-th↗

arXiv2021

Conformal bridge in a cosmic string background

Hidden symmetries of non-relativistic $\mathfrak{so} (2,1)\cong \mathfrak{sl}(2, {\mathbb R})$ invariant systems in a cosmic string background are studied using the conformal bridge transformation. Geometric properties of this background are analogous to those of a conical surface with a deficiency/excess angle encoded in the "geometrical parameter" $α$, determined by the linear positive/negative mass density of the string. The free particle and the harmonic oscillator on this background are shown to be related by the conformal bridge transformation. To identify the integrals of the free system, we employ a local canonical transformation that relates the model with its planar version. The conformal bridge transformation is then used to map the obtained integrals to those of the harmonic oscillator on the cone. Well-defined classical integrals in both models exist only at $α=q/k$ with $q,k=1,2,\ldots,$ which for $q>1$ are higher-order generators of finite nonlinear algebras. The systems are quantized for arbitrary values of $α$; however, the well-defined hidden symmetry operators associated with spectral degeneracies only exist when $α$ is an integer, that reveals a quantum anomaly.

hep-th↗

arXiv2021

Conformal generation of an exotic rotationally invariant harmonic oscillator

An exotic rotationally invariant harmonic oscillator (ERIHO) is constructed by applying a non-unitary isotropic conformal bridge transformation (CBT) to a free planar particle. It is described by the isotropic harmonic oscillator Hamiltonian supplemented by a Zeeman type term with a real coupling constant $g$. The model reveals the Euclidean ($|g|<1$) and Minkowskian ($|g|>1$) phases separated by the phases $g=+1$ and $g=-1$ of the Landau problem in the symmetric gauge with opposite orientation of the magnetic field. A hidden symmetry emerges in the system at rational values of $g$. Its generators, together with the Hamiltonian and angular momentum produce non-linearly deformed $\mathfrak{u}(2)$ and $\mathfrak{gl}(2,{\mathbb R})$ algebras in the cases of $0<|g|<1$ and $\infty>|g|>1$, which transmute one into another under the inversion $g\rightarrow -1/g$. Similarly, the true, $\mathfrak{u}(2)$, and extended conformal, $\mathfrak{gl}(2,{\mathbb R})$, symmetries of the isotropic Euclidean oscillator ($g=0$) interchange their roles in the isotropic Minkowskian oscillator ($|g|=\infty$), while two copies of the $\mathfrak{gl}(2,{\mathbb R})$ algebra of analogous symmetries mutually transmute in Landau phases. We show that the ERIHO system is transformed by a peculiar unitary transformation into the anisotropic harmonic oscillator generated, in turn, by anisotropic CBT. The relationship between the ERIHO and the subcritical phases of the harmonically extended Landau problem, as well as with a plane isotropic harmonic oscillator in a uniformly rotating reference frame, is established.

quant-ph↗

arXiv2020

Hidden symmetries and nonlinear (super)algebras

Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and superconformal invariance.

hep-th↗

arXiv2020

Conformal bridge between asymptotic freedom and confinement

We construct a nonunitary transformation that relates a given "asymptotically free" conformal quantum mechanical system $H_f$ with its confined, harmonically trapped version $H_c$. In our construction, Jordan states corresponding to the zero eigenvalue of $H_f$, as well as its eigenstates and Gaussian packets are mapped into the eigenstates, coherent states and squeezed states of $H_c$, respectively. The transformation is an automorphism of the conformal $\mathfrak{sl}(2,{\mathbb R})$ algebra of the nature of the fourth-order root of the identity transformation, to which a complex canonical transformation corresponds on the classical level being the fourth-order root of the spatial reflection. We investigate the one- and two-dimensional examples that reveal, in particular, a curious relation between the two-dimensional free particle and the Landau problem.

hep-th↗

arXiv2020

Hidden symmetry and (super)conformal mechanics in a monopole background

We study classical and quantum hidden symmetries of a particle with electric charge $e$ in the background of a Dirac monopole of magnetic charge $g$ subjected to an additional central potential $V(r)=U(r) +(eg)^2/2mr^{2}$ with $U(r)=\tfrac{1}{2}mω^2r^2$, similar to that in the one-dimensional conformal mechanics model of de Alfaro, Fubini and Furlan (AFF). By means of a non-unitary conformal bridge transformation, we establish a relation of the quantum states and of all symmetries of the system with those of the system without harmonic trap, $U(r)=0$. Introducing spin degrees of freedom via a very special spin-orbit coupling, we construct the $\mathfrak{osp}(2,2)$ superconformal extension of the system with unbroken $\mathcal{N}=2$ Poincaré supersymmetry and show that two different superconformal extensions of the one-dimensional AFF model with unbroken and spontaneously broken supersymmetry have a common origin. We also show a universal relationship between the dynamics of a Euclidean particle in an arbitrary central potential $U(r)$ and the dynamics of a charged particle in a monopole background subjected to the potential $V(r)$.

hep-th↗

arXiv2019

Klein four-group and Darboux duality in conformal mechanics

We study the Klein four-group $(K_4)$ symmetry of the time-dependent Schrödinger equation for the conformal mechanics model of de Alfaro-Fubini-Furlan (AFF) with confining harmonic potential and coupling constant $g=ν(ν+1)\geq -1/4$. We show that it undergoes a complete or partial (at half-integer $ν$) breaking on eigenstates of the system, and is the automorphism of the $\mathfrak{osp}(2,2)$ superconformal symmetry in super-extensions of the model by inducing a transformation between the exact and spontaneously broken phases of $\mathcal{N}=2$ Poincaré supersymmetry. We exploit the $K_4$ symmetry and its relation with the conformal symmetry to construct the dual Darboux transformations which generate spectrally shifted pairs of the rationally deformed AFF models. Two distinct pairs of intertwining operators originated from Darboux duality allow us to construct complete sets of the spectrum generating ladder operators that identify specific finite-gap structure of a deformed system and generate three distinct related versions of nonlinearly deformed $\mathfrak{sl}(2,{\mathbb R})$ algebra as its symmetry. We show that at half-integer $ν$, the Jordan states associated with confluent Darboux transformations enter the construction, and the spectrum of rationally deformed AFF systems undergoes structural changes.

hep-th↗

arXiv2019

Hidden symmetries of rationally deformed superconformal mechanics

We study the spectrum generating closed nonlinear superconformal algebra that describes $\mathcal{N}=2$ super-extensions of rationally deformed quantum harmonic oscillator and conformal mechanics models with coupling constant $g=m(m+1)$, $m\in {\mathbb N}$. It has a nature of a nonlinear finite $W$ superalgebra being generated by higher derivative integrals, and generally contains several different copies of either deformed superconformal $\mathfrak{osp}(2|2)$ algebra in the case of super-extended rationally deformed conformal mechanics models, or deformed super-Schrodinger algebra in the case of super-extension of rationally deformed harmonic oscillator systems.

hep-th↗

arXiv2018

Rational deformations of conformal mechanics

We study deformations of the quantum conformal mechanics of De Alfaro-Fubini-Furlan with rational additional potential term generated by applying the generalized Darboux-Crum-Krein-Adler transformations to the quantum harmonic oscillator and by using the method of dual schemes and mirror diagrams. In this way we obtain infinite families of isospectral and non-isospectral deformations of the conformal mechanics model with special values of the coupling constant $g=m(m+1)$, $m\in {\mathbb N}$, in the inverse square potential term, and for each completely isospectral or gapped deformation given by a mirror diagram, we identify the sets of the spectrum-generating ladder operators which encode and coherently reflect its fine spectral structure. Each pair of these operators generates a nonlinear deformation of the conformal symmetry, and their complete sets pave the way for investigation of the associated superconformal symmetry deformations.

math-ph↗