Searcharxiv⌕ Search

arXiv subjects

J. Guerrero

Publications and source records attributed to J. Guerrero.

At least 19 recordsLinked to original sources
arXiv2022

Hilbert space structure of the low energy sector of U(N) quantum Hall ferromagnets and their classical limit

Using the Lieb-Mattis ordering theorem of electronic energy levels, we identify the Hilbert space of the low energy sector of U($N$) quantum Hall/Heisenberg ferromagnets at filling factor $M$ for $L$ Landau/lattice sites with the carrier space of irreducible representations of U($N$) described by rectangular Young tableaux of $M$ rows and $L$ columns, and associated with Grassmannian phase spaces U($N$)/U($M$)$\times$U($N-M$). We embed this $N$-component fermion mixture in Fock space through a Schwinger-Jordan (boson and fermion) representation of U($N$)-spin operators. We provide different realizations of basis vectors using Young diagrams, Gelfand-Tsetlin patterns and Fock states (for an electron/flux occupation number in the fermionic/bosonic representation). U($N$)-spin operator matrix elements in the Gelfand-Tsetlin basis are explicitly given. Coherent state excitations above the ground state are computed and labeled by complex $(N-M)\times M$ matrix points $Z$ on the Grassmannian phase space. They adopt the form of a U($N$) displaced/rotated highest-weight vector, or a multinomial Bose-Einstein condensate in the flux occupation number representation. Replacing U($N$)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy (long wavelength) U($N$)-spin-wave coherent excitations (skyrmions) of U($N$) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.

cond-mat.mes-hall↗
arXiv2021

Role of mixed permutation symmetry sectors in the thermodynamic limit of critical three-level Lipkin-Meshkov-Glick atom models

We introduce the notion of Mixed Symmetry Quantum Phase Transition (MSQPT) as singularities in the transformation of the lowest-energy state properties of a system of identical particles inside each permutation symmetry sector $μ$, when some Hamiltonian control parameters $λ$ are varied. We use a three-level Lipkin-Meshkov-Glick (LMG) model, with $U(3)$ dynamical symmetry, to exemplify our construction. After reviewing the construction of $U(3)$ unirreps using Young tableaux and Gelfand basis, we firstly study the case of a finite number $N$ of three-level atoms, showing that some precursors (fidelity-susceptibility, level population, etc.) of MSQPTs appear in all permutation symmetry sectors. Using coherent (quasi-classical) states of $U(3)$ as variational states, we compute the lowest-energy density for each sector $μ$ in the thermodynamic $N\to\infty$ limit. Extending the control parameter space by $μ$, the phase diagram exhibits four distinct quantum phases in the $λ$-$μ$ plane that coexist at a quadruple point. The ground state of the whole system belongs to the fully symmetric sector $μ=1$ and shows a four-fold degeneracy, due to the spontaneous breakdown of the parity symmetry of the Hamiltonian. The restoration of this discrete symmetry leads to the formation of four-component Schrödinger cat states.

quant-ph↗
arXiv2016

Revisiting the optical $PT$-symmetric dimer

Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.

physics.optics↗
arXiv2015

Optical finite representation of the Lorentz group

We present a class of photonic lattices with an underlying symmetry given by a finite-dimensional representation of the 2+1D Lorentz group. In order to construct such a finite-dimensional representation of a non-compact group, we have to design a $\mathcal{PT}$-symmetric optical structure. Thus, the array of coupled waveguides may keep or break $\mathcal{PT}$-symmetry, leading to a device that behaves like an oscillator or directional amplifier, respectively. We show that the so-called linear $\mathcal{PT}$-symmetric dimer belongs to this class of photonic lattices.

physics.optics↗
arXiv2012

Symmetries of the quantum damped harmonic oscillator

For the non-conservative Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg-Weyl algebra can be found. The inclusion of the standard time evolution generator (which is not a symmetry) as a symmetry in this algebra, in a unitary manner, requires a non-trivial extension of this basic algebra and hence of the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman dual system, which now includes a new particle acting as an energy reservoir. In addition, the Caldirola-Kanai dissipative system can be retrieved by imposing constraints. The algebra of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. As opposed to other approaches, where it is claimed that the spectrum of the Bateman Hamiltonian is complex and discrete, we obtain that it is real and continuous, with infinite degeneracy in all regimes.

math-ph↗
arXiv2012

Flapping states of an el astically anchored wing in a uniform flow

Linear stability analysis of an elastically anchored wing in a uniform flow is investigated both analytically and numerically. The analytical formulation explicitly takes into account the effect of the wake on the wing by means of Theodorsen's theory. Three different parameters non-trivially rule the observed dynamics: mass density ratio between wing and fluid, spring elastic constant and distance between the wing center of mass and the spring anchor point on the wing. We found relationships between these parameters which rule the transition between stable equilibrium and fluttering. The shape of the resulting marginal curve has been successfully verified by high Reynolds number direct numerical simulations. Our findings are of interest in applications related to energy harvesting by fluid-structure interaction, a problem which has recently attracted a great deal of attention. The main aim in that context is to identify the optimal physical/geometrical system configuration leading to large sustained motion, which is the source of energy we aim to extract.

physics.flu-dyn↗
arXiv2011

A symmetry trip from Caldirola to Bateman damped systems

For the Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg algebra can be found. The inclusion of the standard time evolution symmetry in this algebra for damped systems, in a unitary manner, requires a non-trivial extension of this basic algebra and hence the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman's dual system, which now includes a new particle acting as an energy reservoir. The group of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schr\"odinger equation. The usual second-order equation and the inclusion of the original Caldirola-Kanai model in Bateman's system are also discussed.

math-ph↗
arXiv2010

Symmetries of Non-Linear Systems: Group Approach to their Quantization

We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically non-perturbative, is primarily intended for non-linear systems, although needless to say that finding the basic symmetry associated with a given (quantum) physical problem is in general a difficult task, which many times nearly emulates the complexity of finding the actual (classical) solutions. Apart from some interesting examples related to the electromagnetic and gravitational particle interactions, where an algebraic version of the equivalence principle naturally arises, we attempt to the quantum description of non-linear sigma models. In particular, we present the actual quantization of the partial-trace non-linear SU(2) sigma model as a representative case of non-linear quantum field theory.

math-ph↗
arXiv2008

Group-quantization of non-linear sigma models: particle on S^2 revisited

We present the quantum mechanics of "partial-trace" non-linear sigma models, on the grounds of a fully symmetry-based procedure. After the general scheme is sketched, the particular example of a particle on the two-sphere is explicitly developed. As a remarkable feature, no explicit constraint treatment is required nor ordering ambiguities do appear. Moreover, the energy spectrum is recovered without extra terms in the curvature of the sphere.

hep-th↗
arXiv2004

Gravitational wave radiation from the coalescence of white dwarfs

We compute the emission of gravitational radiation from the merging of a close white dwarf binary system. This is done for a wide range of masses and compositions of the white dwarfs, ranging from mergers involving two He white dwarfs, mergers in which two CO white dwarfs coalesce to mergers in which a massive ONe white dwarf is involved. In doing so we follow the evolution of binary system using a Smoothed Particle Hydrodynamics code. Even though the coalescence process of the white dwarfs involves considerable masses, moving at relatively high velocities with a high degree of asymmetry we find that the signature of the merger is not very strong. In fact, the most prominent feature of the coalescence is that in a relatively small time scale (of the order of the period of the last stable orbit, typically a few minutes) the sources stop emitting gravitational waves. We also discuss the possible implications of our calculations for the detection of the coalescence within the framework of future space-borne interferometers like LISA.

astro-ph↗
arXiv2004

Group Approach to the Quantization of the Pöschl-Teller dynamics

The quantum dynamics of a particle in the Modified Pöschl-Teller potential is derived from the group $SL(2,R)$ by applying a Group Approach to Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder operators is found in the enveloping algebra of this basic symmetry group. The present algorithm provides a physical realization of the non-unitary, finite-dimensional, irreducible representations of the $SL(2,R)$ group. The non-unitarity manifests itself in that only half of the states are normalizable, in contrast with the representations of SU(2) where all the states are physical.

quant-ph↗
arXiv2003

Group-cohomology refinement to classify $G$-symplectic manifolds

``Pseudo-cohomology'', as a refinement of Lie group cohomology, is soundly studied aiming at classifying of the symplectic manifolds associated with Lie groups. In this study, the framework of symplectic cohomology provides fundamental new insight, which enriches the analysis previously developed in the setting of Cartan-Eilenberg $H^2(G,U(1))$ cohomology.

math-ph↗
arXiv2002

Revisited gauge principle: towards a unification of space-time and internal gauge interactions

The minimal coupling principle is revisited under the quantum perspectives of the space-time symmetry. This revision is better realized on a Group Approach to Quantization (GAQ) where group cohomology and extensions of groups play a preponderant role. We firstly consider the case of the electromagnetic potential; the Galilei and/or Poincare group is (non-centrally) extended by the "local" U(1) group. This group can also be seen as a central extension, parametrized by both the mass and the electric charge, of an infinite-dimensional group, on which GAQ leads to the dynamics of a particle moving in the presence of an electromagnetic field. Then we try the gravitational interaction of a particle by turning into "local" the space-time translations. However, promoting to "local" the space-time subgroup of the true symmetry of the quantum free relativistic particle, i.e. the centrally extended by U(1) Poincare group, results in a new electromagnetic-like force of pure gravitational origin. This is a consequence of the space-time translations not being an invariant subgroup of the extended Poincare group and constitutes a preliminary attempt to a non-trivial mixing of space-time and internal gauge interactions.

math-ph↗
arXiv2002

New insights in particle dynamics from group cohomology

The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a group which is obtained from a centrally extended kinematical group (Poincare or Galilei) by making local some subgroup. The corresponding dynamics is generated by a vector field inside the kernel of a presymplectic form which is derived from the canonical left-invariant one-form on the extended group. A non-relativistic limit is derived from the geodesic motion via an Inonu-Wigner contraction. A deeper analysis of the cohomological structure reveals the possibility of a new force associated with a non-trivial mixing of gravity and electromagnetism leading to in principle testable predictions.

hep-th↗
arXiv2001

Modular Invariance on the Torus and Abelian Chern-Simons Theory

The implementation of modular invariance on the torus as a phase space at the quantum level is discussed in a group-theoretical framework. Unlike the classical case, at the quantum level some restrictions on the parameters of the theory should be imposed to ensure modular invariance. Two cases must be considered, depending on the cohomology class of the symplectic form on the torus. If it is of integer cohomology class $n$, then full modular invariance is achieved at the quantum level only for those wave functions on the torus which are periodic if $n$ is even, or antiperiodic if $n$ is odd. If the symplectic form is of rational cohomology class $\frac{n}{r}$, a similar result holds --the wave functions must be either periodic or antiperiodic on a torus $r$ times larger in both direccions, depending on the parity of $nr$. Application of these results to the Abelian Chern-Simons is discussed.

hep-th↗
arXiv2000

Invariant Measures on Polarized Submanifolds in Group Quantization

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict invariance of the measures and, accordingly, the unitarity of the quantization of coadjoint orbits. As an example, the representations of $SL(2,\Real)$ are recovered.

math-ph↗