arXiv subjects

J. Gamboa

Publications and source records attributed to J. Gamboa.

At least 37 records · Page 2Linked to original sources

arXiv2018

Meissner Effect from Landau Problem

The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen-Olesen vortices are established. Firstly we show that the Landau problem with non-homogeneous magnetic fields exhibits Meissner effect that is unstable unless two-body interactions are added and vortices emerge. Using the scaling freedom we can write the Schrödinger equation in terms of the scales ratio $κ={ E}/{ m }\propto 1- T/T_c $ where the last identification is realised simply by using the Gizburg-Landau theory. We find our equations are valid in the superconducting regime, and it is not possible for the Cooper pairs amplitude to reach to a constant, non-zero value, and therefore the theory is unstable. The supersymmetric quantum mechanics version, by completeness, is also considered.

hep-th↗

arXiv2018

Magnetic Seed and Cosmology as Quantum Hall Effect

In the framework of a bimetric model, we discuss a relation between the (modified) Friedmann equations and a mechanical system similar to the quantum Hall effect problem. Firstly, we show how these modified Friedmann equations are mapped to an anisotropic two-dimensional charged harmonic oscillator in the presence of a constant magnetic field, with the frequencies of the oscillator playing the role of the cosmological constants. This problem has two energy scales leading to the identification of two different regimes, namely, one dominated by the cosmological constants, with exponential expansions for the scale factors, and the other dominated by a magnetic seed, which would be responsible for both a component of dark energy and a primordial magnetic field. The latter regime would be described by a (nonperturbative) mapping between the cosmological evolution and the quantum Hall effect.

hep-th↗

arXiv2018

Classical Noncommutative Bicosmology Model

We propose a bicosmology model which is the classical analog of noncommutative quantum mechanics. From this point of view the sources of the modified FRW equations are dark energy ones governed by a Chapligyn's equation state. The parameters of noncommutativity $θ$ and $B$ are interpreted in terms of the Planck area and a like-magnetic field, presumably the magnetic seed of magnetogenesis.

hep-th↗

arXiv2018

The twin paradox: the role of acceleration

The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The question can be asked: "Is there anything more to say?" It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view of the twin that undergoes the acceleration, then the role of the acceleration is crucial and cannot be dismissed. In the resolution of the twin paradox, the role of the acceleration has been denigrated to the extent that it has been treated as a red-herring. This is a mistake and shows a clear misunderstanding of the twin paradox.

gr-qc↗

arXiv2017

Inflation without Inflaton: A Model for Dark Energy

The interaction between two initially causally disconnected regions of the universe is studied using analogies of non-commutative quantum mechanics and deformation of Poisson manifolds. These causally disconnect regions are governed by two independent Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) metrics with scale factors $a$ and $b$ and cosmological constants $Λ_a$ and $Λ_b$, respectively. The causality is turned on by positing a non-trivial Poisson bracket $[ {\cal P}_α, {\cal P}_β ] =ε_{αβ}\fracκ{G}$, where $G$ is Newton's gravitational constant and $κ$ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of $κ$. In this model the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for $κ\ll1 $ is also studied.

gr-qc↗

arXiv2016

Generalized Dirac duality and CP violation in a two photon theory

A kinetic mixing term, which generalizes the duality symmetry of Dirac, is studied in a theory with two photons (visible and hidden). This theory can be either CP conserving or CP violating depending on the transformation of fields in the hidden sector. However if CP is violated, it necessarily occurs in the hidden sector. This opens up an interesting possibility of new sources of CP violation.

hep-ph↗

arXiv2016

Non-Abelian Monopoles as the Origin of Dark Matter

We suggest that dark matter may be partially constituted by a dilute 't Hooft-Polyakov monopoles gas. We reach this conclusion by using the Georgi-Glashow model coupled to a dual kinetic mixing term $ F{\tilde {\cal G}}$ where $F$ is the electromagnetic field and ${\cal G}$ the 't Hooft tensor. We show that these monopoles carry both (Maxwell) electric and (Georgi-Glashow) magnetic charges and the electric charge quantization condition is modified in terms of a dimensionless real parameter. This parameter could be determined from milli-charged particle experiments.

hep-th↗

arXiv2015

Dark and Visible Photons as Source of CP Violation

The problem of excess gamma radiation in the center of galaxy is discussed assuming that the photon's production is dominated by two kinds of processes, the first one due to the conventional kinetic mixing term and, secondly, due to a kinetic mixing term violating the CP symmetry between dark and visible photons. The CP violation symmetry between dark and visible sectors is not forbidden and, in principle, could be considered as an additional source of CP violation. The conversion probability between dark and visible photons is calculated and compared between both processes. The processes violating CP are less significant but contribute non-trivially to the excess gamma radiation.

hep-ph↗

arXiv2014

U'(1) Neutrino Interaction at Very Low Energies

A procedure for studying low energy neutrinos processes using hadronic physics ideas is proposed. We describe how the neutrino-neutrino interactions can be modelled using massive gauge theories. The mass of the gauge bosons is created by spontaneous symmetry breaking and we show that relationship between mass, currents and potential gauge is through vector dominance, i.e. $J_μ= M^2 A_μ$. A tiny charge $U(1)$ for neutrinos is turned on for energies around the temperature of the cosmic neutrinos background which allow the interaction between neutrinos, above this temperature this interaction disappears. The magnetic flux is quantized in terms of the hidden charge. We found an approximate relation between the order parameter and neutrino condensate $\langle{\bar ν} ν\rangle_{\tiny{0}}$. The relation between the neutrino magnetic moment and hidden photons bounds are also discussed.

hep-ph↗

arXiv2012

Particle-antiparticle asymmetry from magnetogenesis through the Landau mechanism

Motivated by string theory an extension of the Landau problem to quantum field theory is considered. We show that the commutator between momenta of the fields violates Lorentz and CPT invariance leading to an alternative method of understanding the question of particle-antiparticle asymmetry. The presence of magnetic field at very early moments of the universe would then suggest that the particle-antiparticle asymmetry can be understood as a consequence of magnetogenesis.

hep-th↗

arXiv2012

Noncommutativity in (2+1)-dimensions and the Lorentz group

In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of the Lorentz group. The Hilbert space gets the structure of a direct product with the representation space, where we are able to construct operators which realize the algebra of Lorentz transformations. We study the modified Landau problem for both Schrödinger and Dirac particles, whose Hamiltonians are obtained through a kind of non-Abelian Bopp's shift of the dynamical variables from the ones of the usual problem in the normal space. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters. We find no constraint between the parameters referring to no-commutativity in coordinates and momenta but they rather play similar roles. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension.

hep-th↗

arXiv2012

Dynamics determines geometry

The inverse problem of calculus of variations and $s$-equivalence are re-examined by using results obtained from non-commutative geometry ideas. The role played by the structure of the modified Poisson brackets is discussed in a general context and it is argued that classical $s$-equivalent systems may be non-equivalent at the quantum mechanical level. This last fact is explicitly discussed comparing different approaches to deal with the Nair-Polychronakos oscillator.

math-ph↗

arXiv2012

Graphene and non-Abelian quantization

In this article we employ a simple nonrelativistic model to describe the low energy excitation of graphene. The model is based on a deformation of the Heisenberg algebra which makes the commutator of momenta proportional to the pseudo-spin. We solve the Landau problem for the resulting Hamiltonian which reduces, in the large mass limit while keeping fixed the Fermi velocity, to the usual linear one employed to describe these excitations as massless Dirac fermions. This model, extended to negative mass, allows to reproduce the leading terms in the low energy expansion of the dispersion relation for both nearest and next-to-nearest neighbor interactions. Taking into account the contributions of both Dirac points, the resulting Hall conductivity, evaluated with a $ζ$-function approach, is consistent with the anomalous integer quantum Hall effect found in graphene. Moreover, when considered in first order perturbation theory, it is shown that the next-to-leading term in the interaction between nearest neighbor produces no modifications in the spectrum of the model while an electric field perpendicular to the magnetic field produces just a rigid shift of this spectrum. PACS: 03.65.-w, 81.05.ue, 73.43.-f

math-ph↗

arXiv2011

Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator

A three-dimensional harmonic oscillator with spin non-commutativity in the phase space is considered. The system has a regular symplectic structure and by using supersymmetric quantum mechanics techniques, the ground state is calculated exactly. We find that this state is infinitely degenerate and it has explicit spontaneous broken symmetry. Analyzing the Heisenberg equations, we show that the total angular momentum is conserved.

hep-th↗

arXiv2011

Aharonov-Bohm effect in a Class of Noncommutative Theories

The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $θ$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schrödinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of $θ$.

hep-th↗

arXiv2010

Spin Triplet Pairing for Superconductivity

A generalization of the Cooper pairing mechanism is proposed which allows for a triplet state of lower energy. This is achieved by incorporating spin into the canonical commutation relations and by modifying the $δ$ potential contact interaction. The gap equation contain as solutions both singlet and triplet states. It is shown that the triplet state is lower in energy than the singlet state which may explain the spin-triplet superconductivity observed in heavy fermion compound UPt3 and in Sr$_2$RuO$_4$.

cond-mat.supr-con↗

arXiv2009

Bose-Einstein condensation theory for any integer spin: approach based in noncommutative quantum mechanics

A Bose-Einstein condensation theory for any integer spin using noncommutative quantum mechanics methods is considered. The effective potential is derived as a multipolar expansion in the non-commutativity parameter ($θ$) and, at second order in $θ$, our procedure yields to the standard dipole-dipole interaction with $θ^2$ playing the role of the strength interaction parameter. The generalized Gross-Pitaevskii equation containing non-local dipolar contributions is found. For $^{52}$Cr isotopes $θ= C_{dd}/4π$ becomes $\sim 10^{-11}$ cm and, thus for this value of $θ$ one cannot distinguish interactions coming from non-commutativity or those of dynamical origin.

hep-th↗

arXiv2009

Neutrino Oscillations in a Minimal CPT Violation Frame

The oscillation neutrino problem in the extended standard model with minimal number of parameters is considered. The dispersion relations with explicit neutrino-antineutrino asymmetry are discussed and an explanation to the MINIBooNE and solar neutrino controversy is offered. Bounds for the CPT violation symmetry are also found.

hep-ph↗