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Alex E. Bernardini

Publications and source records attributed to Alex E. Bernardini.

At least 73 records · Page 4Linked to original sources
arXiv2014

Maximal correlation between flavor entanglement and oscillation damping due to localization effects

Localization effects and quantum decoherence driven by the mass-eigenstate wave packet propagation are shown to support a statistical correlation between quantum entanglement and damped oscillations in the scenario of three-flavor quantum mixing for neutrinos. Once the mass-eigenstates that support flavor oscillations are identified as three-{\em qubit} modes, a decoherence scale can be extracted from correlation quantifiers, namely the entanglement of formation and the logarithmic negativity. Such a decoherence scale is compared with the coherence length of damped oscillations. Damping signatures exhibited by flavor transition probabilities as an effective averaging of the oscillating terms are then explained as owing to loss of entanglement between mass modes involved in the relativistic propagation.

hep-ph↗
arXiv2014

Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors

Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner formalism. Besides reproducing the magnetic field aspect of a Zeeman-like effect, the momentum space NC parameter introduces mutual information properties quantified by the quantum purity related to the relevant coordinates of the corresponding Hilbert space. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified.

quant-ph↗
arXiv2014

Entanglement and separability in the noncommutative phase-space scenario

Quantumness and separability criteria for continuous variable systems are discussed for the case of a noncommutative (NC) phase-space. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are examined. Two families of covariance matrices describing standard quantum mechanics (QM) separable states are deformed into a NC QM configuration and then investigated through the positive partial transpose criterium for identifying quantum entanglement. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the NC deformation. Extensions of some preliminary results are presented.

quant-ph↗
arXiv2014

Chiral oscillations in terms of the zitterbewegung effect

We seek the {\em immediate} description of chiral oscillations in terms of the trembling motion described by the velocity (Dirac) operator {\boldmath$α$}. By taking into account the complete set of Dirac equation solutions which results in a free propagating Dirac wave packet composed by positive and negative frequency components, we report about the well-established {\em zitterbewegung} results and indicate how chiral oscillations can be expressed in terms of the well know quantum oscillating variables. We conclude with the interpretation of chiral oscillations as position very rapid oscillation projections onto the longitudinally decomposed direction of the motion.

hep-th↗
arXiv2014

Phase-space noncommutative formulation of Ozawa's uncertainty principle

Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature amplifiers and for noiseless quadrature transducers. Several distinctive features appear as a consequence of the noncommutative extension: measurement interactions which are noiseless, and observables which are undisturbed by a measurement, or of independent intervention in ordinary quantum mechanics, may acquire noise, become disturbed by the measurement, or no longer be an independent intervention in noncommutative quantum mechanics. It is also found that there can be states which violate Ozawa's universal noise-disturbance trade-off relation, but verify its noncommutative deformation.

quant-ph↗
arXiv2014

C$ν$B damping of primordial gravitational waves and the fine-tuning of the C$γ$B temperature anisotropy

Damping of primordial gravitational waves due to the anisotropic stress contribution owing to the cosmological neutrino background (C$ν$B) is investigated in the context of a radiation-to-matter dominated Universe. Besides its inherent effects on the gravitational wave propagation, the inclusion of the C$ν$B anisotropic stress into the dynamical equations also affects the tensor mode contribution to the anisotropy of the cosmological microwave background (C$γ$B) temperature. Given that the fluctuations of the C$ν$B temperature in the (ultra)relativistic regime are driven by a multipole expansion, the mutual effects on the gravitational waves and on the C$γ$B are obtained through a unified prescription for a radiation-to-matter dominated scenario. The results are confronted with some preliminary results for the radiation dominated scenario. Both scenarios are supported by a simplified analytical framework, in terms of a scale independent dynamical variable, $k η$, that relates cosmological scales, $k$, and the conformal time, $η$. The background relativistic (hot dark) matter essentially works as an effective dispersive medium for the gravitational waves such that the damping effect is intensified for the Universe evolving to the matter dominated era. Changes on the temperature variance owing to the inclusion of neutrino collision terms into the dynamical equations result into spectral features that ratify that the multipole expansion coefficients $C_{l}^{T}$'s die out for $l \sim 100$.

astro-ph.CO↗
arXiv2014

Relativistic dynamics compels a thermalized Fermi gas to a unique intrinsic parity eigenstate

Dirac equation describes the dynamics of a relativistic spin-1/2 particle regarding its spatial motion and intrinsic degrees of freedom. Here we adopt the point of view that the spinors describe the state of a massive particle carrying two qubits of information: helicity and intrinsic parity. We show that the density matrix for a gas of free fermions, in thermal equilibrium, correlates helicity and intrinsic parity. Our results introduce the basic elements for discussing the spin-parity correlation for a Fermi gas: (1) at the ultra-relativistic domains, when the temperature is quite high, $T > 10^{10}\ K$, the fermions have no definite intrinsic parity (50% : 50%), which is maximally correlated with the helicity; (2) at very low temperature, $T \approx 3 \ K$, a unique parity dominates (conventionally chosen positive), by $10^{20}$ to $1$, while the helicity goes into a mixed state for spin up and down, and the quantum correlation decoheres. For the anti-fermions we get the opposite behavior. In the framework of quantum information, our result could be considered as a plausible explanation of why we do accept, as a fact (consistent with the experimental observation), that fermions (and anti-fermions), in our present epoch of a cool universe, have a unique intrinsic parity. The framework for constructing spin-parity entangled states is established.

quant-ph↗
arXiv2013

Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle

In this work we derive a matrix formulation of a noise-disturbance uncertainty relation, which is akin to the Robertson-Schrödinger uncertainty principle. Our inequality is stronger than Ozawa's uncertainty principle and takes noise-disturbance correlations into account. Moreover, we show that, for certain types of measurement interactions, it is covariant with respect to linear symplectic transformations of the noise and disturbance operators.

quant-ph↗
arXiv2013

Equivalence between Born-Infeld tachyon and effective real scalar field theories for brane structures in warped geometry

An equivalence between Born-Infeld and effective real scalar field theories for brane structures is built in some specific warped space-time scenarios. Once the equations of motion for tachyon fields related to the Born-Infeld action are written as first-order equations, a simple analytical connection with a particular class of real scalar field superpotentials can be found. This equivalence leads to the conclusion that, for a certain class of superpotentials, both systems can support identical thick brane solutions as well as brane structures described through localized energy densities, $T_{00}(y)$, in the $5^{th}$ dimension, $y$. Our results indicate that thick brane solutions realized by the Born-Infeld cosmology can be connected to real scalar field brane scenarios which can be used to effectively map the tachyon condensation mechanism.

hep-th↗
arXiv2013

The Hamiltonian formalism for scalar fields coupled to gravity in a cosmological background

A novel routine to investigate the scalar fields in a cosmological context is discussed in the framework of the Hamiltonian formalism. Starting from the Einstein-Hilbert action coupled to a Lagrangian density that contains two components - one corresponding to a scalar field Lagrangian, ${\mathcal{L}}_ϕ$, and another that depends on the scale parameter, ${\mathcal{L}}_{a}$ - one can identify a generalized Hamiltonian density from which first-order dynamical equations can be obtained. This set up corresponds to the dynamics of Friedmann-Robertson-Walker models in the presence of homogeneous fields embedded into a generalized cosmological background fluid in a system that evolves all together isentropically. Once the generalized Hamiltonian density is properly defined, the constraints on the gravity-matter-field system are straightforwardly obtained through the first-order Hamilton equations. The procedure is illustrated for three examples of cosmological interest for studies of the dark sector: real scalar fields, tachyonic fields and generalized Born-Infeld tachyonic fields. The inclusion of some isentropic fluid component into the Friedmann equation allows for identifying an exact correspondence between the dark sector underlying scalar field and an ordinary real scalar field dynamics. As a final issue, the Hamiltonian formulation is used to set the first-order dynamical equations through which one obtains the exact analytical description of the cosmological evolution of a generalized Chaplygin gas (GCG) with dustlike matter, radiation or curvature contributions. Model stability in terms of the square of the sound velocity, $c_{s}^{2}$, cosmic acceleration, $q$, and conditions for inflation are discussed.

gr-qc↗
arXiv2013

Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit

In this work we examine the effect of phase-space noncommutativity on some typically quantum properties such as quantum beating, quantum information, and decoherence. To exemplify these issues we consider the two-dimensional noncommutative quantum harmonic oscillator whose components behavior we monitor in time. This procedure allows us to determine how the noncommutative parameters are related to the missing information quantified by the linear quantum entropy and by the mutual information between the relevant Hilbert space coordinates. Particular questions concerning the thermodynamic limit of some relevant properties are also discussed in order to evidence the effects of noncommutativity. Finally, through an analogy with the Zeeman effect, we identify how some aspects of the axial symmetry of the problem suggest the possibility of decoupling the noncommutative quantum perturbations from unperturbed commutative well-known solutions.

quant-ph↗
arXiv2013

Entanglement due to noncommutativity in the phase-space

The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative (NC) phase-space. The quantum nature and the separability of NC two-mode Gaussian states are examined. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the noncommutative deformation.

quant-ph↗
arXiv2013

Cyclically deformed defects and topological mass constraints

A systematic procedure for obtaining defect structures through cyclic deformation chains is introduced and explored in detail. The procedure outlines a set of rules for analytically constructing constraint equations that involve the finite localized energy of cyclically generated defects. The idea of obtaining cyclically deformed defects concerns the possibility of regenerating a primitive (departing) defect structure through successive, unidirectional, and eventually irreversible, deformation processes. Our technique is applied on kink-like and lump-like solutions in models described by a single real scalar field, such that extensions to quantum mechanics follow the usual theory of deformed defects. The preliminary results show that the cyclic device supports simultaneously kink-like and lump-like defects into 3- and 4-cyclic deformation chains with topological mass values closed by trigonometric and hyperbolic deformations. In a straightforward generalization, results concerning with the analytical calculation of $N$-cyclic deformations are obtained and lessons regarding extensions from more elaborated primitive defects are depicted.

hep-th↗
arXiv2013

Cosmological neutrino entropy changes due to flavor statistical mixing

Entropy changes due to delocalization and decoherence effects should modify the predictions for the cosmological neutrino background (C$ν$B) temperature when one treats neutrino flavors in the framework of composite quantum systems. Assuming that the final stage of neutrino interactions with the $γe^{-}e^{+}$ radiation plasma before decoupling works as a measurement scheme that projects neutrinos into flavor quantum states, the resulting free-streaming neutrinos can be described as a statistical ensemble of flavor-mixed neutrinos. Even not corresponding to an electronic-flavor pure state, after decoupling the statistical ensemble is described by a density matrix that evolves in time with the full Hamiltonian accounting for flavor mixing, momentum delocalization and, in case of an open quantum system approach, decoherence effects. Since the statistical weights, $w$, shall follow the electron elastic scattering cross section rapport given by $0.16\,w_{e} = w_μ = w_τ$, the von-Neumann entropy will deserve some special attention. Depending on the quantum measurement scheme used for quantifying the entropy, mixing associated to dissipative effects can lead to an increasing of the flavor associated von-Neumann entropy for free-streaming neutrinos. The production of von-Neumann entropy mitigates the constraints on the predictions for energy densities and temperatures of a cosmologically evolving isentropic fluid, in this case, the cosmological neutrino background. The effects of entropy changes on the cosmological neutrino temperature are quantified, and the {\em constraint} involving the number of neutrino species, $N_ν \approx 3$, in the phenomenological confront with Big Bang nucleosynthesis parameters is consistently relieved.

astro-ph.CO↗
arXiv2013

Dynamics of chiral oscillations - A comparative analysis with spin-flipping

Chiral oscillation as well as spin flipping effects correspond to quantum phenomena of fundamental importance in the context of particle physics and, in particular, of neutrino physics. From the point of view of first quantized theories, we are specifically interested in appointing the differences between chirality and helicity by obtaining their dynamic equations for a fermionic Dirac-type particle (neutrino). We also identify both effects when the non-minimal coupling with an external (electro)magnetic field in the neutrino interacting Lagrangian is taken into account. We demonstrate that, however, there is no constraint between chiral oscillations, when it takes place in vacuum, and the process of spin flipping related to the helicity quantum number, which does not take place in vacuum. To conclude, we show that the origin of chiral oscillations (in vacuum) can be interpreted as position very rapid oscillation projections onto the longitudinal direction of momentum.

hep-ph↗
arXiv2012

The C$ν$B energy density through the quantum measurement theory

We apply concepts from the quantum measurement theory to obtain some cosmological neutrino background (C$ν$B) properties and discuss their relevance in defining theoretical bounds on cosmological neutrino energy density. Describing three neutrino generations as a composite quantum system through the generalized theory of quantum measurement provides us with the probabilistic correlation between observable energies and neutrino flavor eigenstates. By observing that flavor-averaged and flavor-weighted energies are the quantum observables respectively generated by selective and non-selective quantum measurement schemes, it is possible to identify the constraints on the effective mass value expression that determines the neutrino contribution to the energy density of the cosmic inventory. Our results agree with the quantum mechanics viewpoint that asserts that the cosmological neutrino energy density is obtained from a coherent sum of mass eigenstate energies, for normal and inverted mass hierarchies.

hep-ph↗
arXiv2012

Dynamical dispersion relation for ELKO dark spinor fields

An intrinsic mass generation mechanism for exotic ELKO dark matter fields is scrutinized, in the context of the very special relativity (VSR). Our results are reported on unraveling inequivalent spin structures that educe an additional term on the associated Dirac operator. Contrary to the spinor fields of mass dimension 3/2, this term is precluded to be absorbed as a shift of some gauge vector potential, regarding the equations for the dark spinor fields. It leads to some dynamical constraints that can be intrinsically converted into a dark spinor mass generation mechanism, with the encoded symmetries maintained by the VSR. The dynamical mass is embedded in the VSR framework through a natural coupling to the kink solution of a λϕ^{4} theory for a scalar field ϕ. Our results evince the possibility of novel effective scenarios, derived from exotic couplings among dark spinor fields and scalar field topological solutions.

hep-th↗