arXiv subjects

L. E. Oxman

Publications and source records attributed to L. E. Oxman.

At least 37 records · Page 2Linked to original sources

arXiv2017

Two-qudit topological phase evolution under dephasing

In this work, we study a bipartite system composed by a pair of entangled qudits coupled to an environment. Initially, we derive a master equation and show how the dynamics can be restricted to a "diagonal" sector that includes a maximally entangled state (MES). Next, we solve this equation for mixed qutrit pairs and analyze the $I$-concurrence $C(t)$ for the effective state, which is needed to compute the geometric phase when the initial state is pure. Unlike (locally operated) isolated systems, the coupled system leads to a nontrivial time-dependence, with $C(t)$ generally decaying to zero at asymptotic times. However, when the initial condition gets closer to a MES state, the effective concurrence is more protected against the effects of decoherence, signaling a transition to an effective two-qubit MES state at asymptotic times. This transition is also observed in the geometric phase evolution, computed in the kinematic approach. Finally, we explore the system-environment coupling parameter space and show the existence of a Weyl symmetry among the various physical quantities.

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arXiv2016

Exploring center vortices in SU(2) and SU(3) relativistic Yang-Mills-Higgs models

We develop numerical tools and apply them to solve the relativistic Yang--Mills--Higgs equations in a model where the SU(N) symmetry is spontaneously broken to its center. In SU(2) and SU(3), we obtain the different field profiles for infinite and finite center vortices, with endpoints at external monopole sources. Exploration of parameter space permits the detection of a region where the equations get Abelianized. Finally, a general parametrization of the color structure of SU(2) fields leads us to a reference point where an Abelian-like BPS bound is reconciled with N-ality.

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arXiv2015

BPS center vortices in nonrelativistic SU(N) gauge models with adjoint Higgs fields

In this work, we propose a class of SU(N) Yang-Mills models, with adjoint Higgs fields, that accept BPS center vortex equations. The lack of a local magnetic flux that could serve as an energy bound is circumvented by including a new term in the energy functional. This term tends to align, in the Lie algebra, the magnetic field and one of the adjoint Higgs fields. Finally, a reduced set of equations for the center vortex profile functions is obtained (for N=2,3). In particular, Z(3) BPS vortices come in three colours and three anticolours, obtained from an ansatz based on the defining representation and its conjugate.

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arXiv2015

Detecting topological sectors in continuum Yang-Mills theory and the fate of BRST symmetry

In this work, motivated by Laplacian type center gauges in the lattice, designed to avoid the Gribov problem, we introduce a new family of gauge fixings for pure Yang-Mills theories in the continuum. This procedure separates the partition function into partial contributions associated with different sectors, containing center vortices and correlated monopoles. We show that, on each sector, the gauge fixed path-integral displays a BRST symmetry, however, it cannot be globally extended due to sector dependent boundary conditions on the ghost fields. These are nice features as they would permit to discuss the independence of the partial contributions on gauge parameters,, while opening a window for the space of quantum states to be different from the perturbative one, which would be implied if topological configurations were removed.

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arXiv2015

Hybrid mesons as systems of confined monopoles

We review some recent ideas regarding classical topological objects in dual superconductor models that could represent different confining states of the gluon field. We also comment about natural components in (magnetic) ensembles that could effectively originate these models at large distances.

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arXiv2014

Vacuum fluctuations in the presence of nonlinear boundary conditions

We consider a system consisting of a quantum, massless, real scalar field, in the presence of nonlinear mirrors: infinite parallel planes, upon which the field satisfies nonlinear boundary conditions. The latter are implemented by non-quadratic interaction vertices, strictly localized on the mirrors. By using the appropriate perturbative expansions, we obtain approximate expressions for the Casimir energy corresponding to weak coupling, regarding the strength of the interaction terms. We also comment on an alternative expansion scheme that may be useful when the weak coupling expansion is not justified.

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arXiv2014

Coloured loops in 4D and their effective field representation

Gaining insight about ensembles of magnetic configurations, that could originate the confining string tension between quarks, constitutes a major concern in current lattice investigations. This interest also applies to a different approach, where gauge models with spontaneous symmetry breaking are constructed to describe the confining string as a smooth vortex solution. In this article, we initially show how to incorporate non Abelian information into an ensemble of monopoles in $4D$, characterized by phenomenological parameters. Next, using some recent techniques developed for polymers, we were able to relate the coloured ensemble with a non Abelian gauge model. This could offer an interesting perspective to discuss some of the different approaches to describe confinement.

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arXiv2014

Non Abelian structures and the geometric phase of entangled qudits

In this work, we address some important topological and algebraic aspects of two-qudit states evolving under local unitary operations. The projective invariant subspaces and evolutions are connected with the common elements characterizing the su(d) Lie algebra and their representations. In particular, the roots and weights turn out to be natural quantities to parametrize cyclic evolutions and fractional phases. This framework is then used to recast the coset contribution to the geometric phase in a form that generalizes the usual monopole-like formula for a single qubit.

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arXiv2014

Topological phase structure of entangled qudits

We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions. The topological nature of the phase evolution and its restriction to fractional values are related to both the structure of the projective space of states and entanglement. For maximally entangled states of qudits with the same Hilbert space dimension, the fractional geometric phases are the only ones attainable under local SU($d$) operations, an effect that can be experimentally observed through conditional interference.

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arXiv2013

A non Abelian effective model for ensembles of magnetic defects in QCD(3)

We construct a non Abelian model for SU(2) QCD in Euclidean three-dimensional spacetime and study its different phases. The model contains a center vortex sector coupled to a dual effective field encoding information about how the vortices are paired in the ensemble. The possible phases in parameter space are interpreted in terms of the proliferation of either closed center vortices or closed chains, where the endpoints of open vortices are attached in pairs to monopole-like defects.

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arXiv2013

Fractional topological phase on spatially encoded photonic qudits

We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits encoded on photonic degrees of freedom. We show how the spatial correlations between photons generated by spontaneous parametric down conversion can be used to evidence the multiple topological phases acquired by entangled qudits and the role played by the Hilbert space dimension. A realistic experimental proposal is presented with numerical predictions of the expected results.

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arXiv2012

Confinement of quarks and valence gluons in SU(N) Yang-Mills-Higgs models

In this work, we analyze a class of Yang-Mills models containing adjoint Higgs fields, with SU(N) symmetry spontaneously broken down to Z(N), showing they contain center vortices, Y-junctions formed by them, and junctions where different center vortices are smoothly interpolated by monopole-like configurations. In the context of dual superconductors, these objects represent different states of the gluon field. Center vortices confine quarks to form normal hadron states. The interpolating monopole, which in our model cannot exist as an isolated configuration, is identified with a confined valence gluon. A junction containing a monopole can bind quarks in a color nonsinglet state to form an overall neutral object, identified with a hybrid hadron. These states, formed by quarks bound to a valence gluon, are allowed by QCD, and current experimental collaborations are aimed at identifying them. Finally, considering the general version of the model, based on a compact simple gauge group G, the picture is completed with a heuristic discussion about why it would be natural using as G the dual of the chromoelectric gauge group G_e, and external pointlike monopoles to represent the mesonic and baryonic Wilson loops.

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arXiv2011

Diagonal deformations of thin center vortices and their stability in Yang-Mills theories

The importance of center vortices for the understanding of the confining properties of SU(N) Yang-Mills theories is well established in the lattice. However, in the continuum, there is a problem concerning the relevance of center vortex backgrounds. They display the so called Savvidy-Nielsen-Olesen instability, associated with a gyromagnetic ratio $g^{(b)}_m=2$ for the off-diagonal gluons. In this work, we initially consider the usual definition of a {\it thin} center vortex and rewrite it in terms of a local color frame in SU(N) Yang-Mills theories. Then, we define a thick center vortex as a diagonal deformation of the thin object. Besides the usual thick background profile, this deformation also contains a frame defect coupled with gyromagnetic ratio $g^{(d)}_m=1$, originated from the charged sector. As a consequence, the analysis of stability is modified. In particular, we point out that the defect should stabilize a vortex configuration formed by a pair of straight components separated by an appropriate finite distance.

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arXiv2011

Derivation of an Abelian effective model for instanton chains in 3D Yang-Mills theory

In this work, we derive a recently proposed Abelian model to describe the interaction of correlated monopoles, center vortices, and dual fields in three dimensional SU(2) Yang-Mills theory. Following recent polymer techniques, special care is taken to obtain the end-to-end probability for a single interacting center vortex, which constitutes a key ingredient to represent the ensemble integration.

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arXiv2010

Large Dual Transformations and the Petrov-Diakonov Representation of the Wilson Loop

In this work, based on the Petrov-Diakonov representation of the Wilson loop average W in the SU(2) Yang-Mills theory, together with the Cho-Fadeev-Niemi decomposition, we present a natural framework to discuss possible ideas underlying confinement and ensembles of defects in the continuum. In this language we show how for different ensembles the surface appearing in the Wess-Zumino term in W can be either decoupled or turned into a variable, to be summed together with gauge fields, defects and dual fields. This is discussed in terms of the regularity properties imposed by the ensembles on the dual fields, thus precluding or enabling the possibility of performing the large dual transformations that would be necessary to decouple the initial surface.

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arXiv2010

Fractional topological phase for entangled qudits

We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly calculated in terms of the concurrence. As a main result, we predict a fractional topological phase for cyclic evolutions in the multiply connected space of maximally entangled states.

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arXiv2009

How to get rid of Dirac worldsheets in the Cho-Fadeev-Niemi representation of SU(2) Yang-Mills theory

In this paper, we present an exact procedure to deal with Dirac strings or worldsheets in gauge theories containing ensembles of monopoles interacting with charged fields. For SU(2) Yang-Mills theory, initially we construct the appropriate change of variables of the charged fields (including charged ghosts and auxiliary fields) so that the only change in the integrand of the partition function, in the Maximal Abelian gauge, is the addition of given closed Dirac worldsheets. Next, we derive our main result, namely, we show that it is always possible to choose them in such a manner that the total (open plus closed) Dirac worldsheets explicitly decouple from the charged sector, leaving only the effect of their associated gauge invariant borders (where the monopoles are placed), without missing any information about the center vortex sector. This procedure serves as a simplifying basis to deal with ensembles of monopoles and center vortices in the framework of the Cho-Faddeev-Niemi gauge field decomposition, by writing the partition function only in terms of the physical part of the defects to be integrated.

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arXiv2008

Center vortices as sources of Abelian dominance in pure SU(2) Yang-Mills theory

We argue that in the infrared regime of continuum Yang-Mills theory, the possibility of a mass gap in the charged sector is closely associated with the center vortex sector. The analysis of the possible consequences of the ensembles of defects is done by showing that the description of center vortices and monopoles is naturally unified by means of a careful treatment of Cho decomposition. If on the one hand confinement is usually associated with monopole condensation in a compact abelian model, in this scenario, the previous decoupling of the off-diagonal degrees of freedom, for the abelian model dominate at large distances, can be understood as induced by a phase where center vortices become thick objects. Other important scenarios for correlated monopoles and center vortices, observed in lattice simulations, are also accomodated in our general formulation.

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