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J. Socorro

Publications and source records attributed to J. Socorro.

At least 73 records · Page 4Linked to original sources
arXiv1999

Simple supersymmetric methods in neutron diffusion

We present the supersymmetric Witten and double Darboux (strictly isospectral) constructions as applied to the diffusion of thermal neutrons from an infinitely long line source. While the Witten construction is just a mathematical scheme, the double Darboux method introduces a one-parameter family of diffusion solutions which are strictly isospectral to the stationary solution. They correspond to a Darboux-transformed diffusion length which is flux dependent

math-ph↗
arXiv1999

Supersymmetric strictly isospectral FRW models for zero factor ordering

We apply the strictly isospectral technique of standard supersymmetric quantum mechanics to the Q=0 factor ordered Wheeler-DeWitt equation for the Friedmann-Robertson-Walker (FRW) minisuperspace model. The resulting strictly isospectral one-parameter families of both FRW cosmological potentials and "wavefunctions of the universe" are exhibited with relevant plots

gr-qc↗
arXiv1998

Supersymmetric one-parameter strict isospectrality for the attractive delta potentials

The Schrödinger equation with attractive delta potential has been previously studied in the supersymmetric quantum mechanical approach by a number of authors, but they all used only the particular superpotential solution. Here, we introduce a one-parameter family of strictly isospectral attractive delta function potentials, which is based on the general superpotential (general Riccati) solution, we study the problem in some detail and suggest possible applications

quant-ph↗
arXiv1998

The wave function of the universe and spontaneaus breaking of supersymmetry

In this work we define a scalar product ``weighted'' with the scalar factor $R$ and show how to find a normalized wave function for the supersymmetric quantum FRW cosmological model using the idea of supersymmetry breaking selection rules under local n=2 conformal supersymmetry. We also calculate the expectation value of the scalar factor R in this model and its corresponding behaviour.

hep-th↗
arXiv1998

Dual symmetry and the vacuum energy

In this work we present a new hidden symmetry in gravity for the scale factor in the FRW model, for $k=0$. This exact symmetry vanishes the cosmological constant. We interpret this hidden symmetry as a dual symmetry in the sense that appears in the string theory.

hep-th↗
arXiv1998

Supersymmetric FRW model and the ground state of supergravity

In this work we construct the vacuum configuration of supergravity interacting with homogeneous complex scalar matter fields. The corresponding configuration is of the FRW model invariant under the $n=2$ local conformal time supersymmetry, which is a subgroup of the four dimensional space-time supersymmetry. We show, that the potential of the scalar matter fields is a function of the Kähler potential and of the arbitrary parameter $α$. This parameter enumerates the vacuum states. The scalar matter potential induces the spontaneous breaking of supersymmetry in supergravity. On the quantum level our model is a specific supersymmetric quantum mechanics, which admits quantum states in supergravity, and the states with zero energy are described by the wave function of the FRW universe.

hep-th↗
arXiv1998

General scalar interaction in the supersymmetric FRW model

In this work we have constructed the most general action for a set of complex homogeneous scalar supermultiplets interacting with the scale factor in the supersymmetric FRW model. It is shown, that local conformal time supersymmetry leads to the scalar fields potential, which is defined in the same combination: Kähler potential and superpotential as in supergravity (or effective superstring) theories. This scalar fields potential depends on arbitrary parameter $α$, which is not fixed by conformal time supersymmetry.

hep-th↗
arXiv1998

Double Darboux method for the Taub continuum

The strictly isospectral double Darboux method is applied to the quantum Taub model in order to generate a one-parameter family of strictly isospectral potentials for this case. The family we build is based on a scattering Wheeler-DeWitt solution first discussed by Ryan and collaborators that we slightly modified according to a suggestion due to Dunster. The strictly isospectral Taub potentials possess different (attenuated) scattering states with respect to the original Taub potential

gr-qc↗
arXiv1998

Supersymmetric partner chirping of Newtonian free damping

We connect the classical free damping cases by means of Rosner's construction in supersymmetric quantum mechanics. Starting with the critical damping, one can obtain in the underdamping case a chirping of instantaneous physical frequency ω^{2}(t) \propto ω_{u}^{2}sech^2(ω_{u}t), whereas in the overdamped case the "chirping" is of the (unphysical) type ω^{2}(t)\proptoω_{o}^{2}sec^{2}(ω_{o}t), where ω_{u}$ and $ω_{o} are the underdamped and overdamped frequency parameters, respectively

math-ph↗
arXiv1998

Note on the Demkov-Ostrovsky nodeless sector

We briefly tackle the following concepts in the Demkov-Ostrovsky (DO) nodeless sector: (i) orbital impedance, (ii) orbital capacity, (iii) closeness to reflectionlessness. Moreover, using previous supersymmetric results for the DO problem, a strictly isospectral effect in the DO orbital impedances is discussed and explicit plots are displayed for the Maxwell fisheye lens. This effect, though rather small, is general, that is, it may apply to any focusing structure.

quant-ph↗
arXiv1998

Supersymmetric double Darboux method in quantum cosmology

We briefly present the supersymmetric double Darboux method and next apply it to the continuum of the quantum Taub cosmological model as a toy model in order to generate a one-parameter family of bosonic Taub potentials and the corresponding wavefunctions

gr-qc↗
arXiv1998

Whittaker quantum universes

We show that closed, radiation-filled Friedmann-Robertson-Walker quantum universes of arbitrary factor ordering obey the Whittaker equation. We also present the formal Witten factorization as well as the double Darboux strictly isospectral scheme for the Whittaker equation

gr-qc↗
arXiv1996

Is nonsymmetric gravity related to string theory?

In this work we raise the question whether nonsymmetric gravity and string theory are related. We start making the observation, that the gravitational field $ g_{μν}$ and the nonsymmetric gauge field $ A_{μν}$ arising in the low energy limit in the string theory are exactly the same two basic fields used in four dimensions in nonsymmetric gravity. We argue, that this connection between nonsymmetric gravity and string theory at the level of the gauge fields $ g_{μν}$ and $ A_{μν}$ is not, however, reflected at the level of the corresponding associated actions. In an effort to find a connection between such an actions we discover a new gravitational action, which suggests an alternative version of the bosonic string in which the target and the world-volume metrics are unified.

hep-th↗
arXiv1996

Classical solutions in five dimensional induced matter theory and its relation to an imperfect fluid

We study five dimensional cosmological models with four dimensional hypersufaces of the Bianchi type I and V. In this way the five dimensional vacuum field equations $\rm G_{AB} = 0$, led us to four dimensional matter equations $\rm G_{μν}=T_{μν}$ and the matter is interpreted as a purely geometrical property of a fifth dimension. Also, we find that the energy-momentum tensor induced from the fifth dimension has the structure of an imperfect fluid that has dissipative terms.

gr-qc↗
arXiv1996

Two-dimensional Fokker-Planck solutions and Grassmann variables

After a short outline of the factorization and Grassmann picture of the one-dimensional (1D) Fokker-Planck (FP) equation, we consider a class of spatially-inhomogeneous solutions of the 2D FP equation with symmetric 2D (super)potentials. We show that the spatial inhomogeneities of that class of solutions can be attributed to underlying Grassmannian pseudo-degrees of freedom. Such an interpretation may also be applied to FP solutions in three and more dimensions.

cond-mat↗
arXiv1995

$\rm Ψ= W e^{\pm Φ}$ quantum cosmological solutions for Class A Bianchi Models

We find solutions for quantum Class A Bianchi models of the form $\rm Ψ=W e^{\pm Φ}$ generalizing the results obtained by Moncrief and Ryan in standard quantum cosmology. For the II and IX Bianchi models there are other solutions $\rm \tildeΦ_2$, $\rm \tildeΦ_9$ to the Hamilton-Jacobi equation for which $\rm Ψ$ is necessarely zero, in contrast with solutions found in supersymmetric quantum cosmology.

gr-qc↗