Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

Caruso, Francisco; Helayël-Neto, J. A.; Martins, J.; Oguri, V.

doi:10.1140/epjb/e2013-40282-1

Cited by 12 publications

(21 citation statements)

References 67 publications

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“…and ψ( r) = r l e −ωnr 2 /2 y nl (r) e ±ilθ = R nl (r, ω n )e ±ilθ (22) where each ω n is a root of the respective A n . Let us now determine the wave function normalization.…”

Section: Numerical Resultsmentioning

confidence: 99%

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

2014

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The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigeinfunctions for the Schrödinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field.

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“…and ψ( r) = r l e −ωnr 2 /2 y nl (r) e ±ilθ = R nl (r, ω n )e ±ilθ (22) where each ω n is a root of the respective A n . Let us now determine the wave function normalization.…”

Section: Numerical Resultsmentioning

confidence: 99%

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

2014

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“…Additionally, we may obtain the fluctuationdissipation relation determining the corresponding fluctuating forceξ α i,BW (t) by replacing (75) in the expression (53). In the high temperature limit Γ αα ij β 1, this takes the particular form…”

Section: Example: Markovian Langevin Dynamicsmentioning

confidence: 99%

“…Moreover, the second line in the frequency domain identically coincides with the fluctuations of an antisymmetric 1/f noise of power spectrum S(ω) = (iω) −1 . The latter may be realized by paying attention to (53): the hyperbolic cotangent renders an effective inverse scaling for the power spectrum of the transversal correlations, whereas the spectral density contributes with a constant factor owning to the form (75). Interestingly, 1/f power law is characteristic of the low-frequency magnetic flux noise in superconducting circuits [57,58], which suggests that the environmental noise acting upon transversal spatial degrees of freedom originates from the fluctuations of the Chern-Simons flux carried by the harmonic oscillators.…”

Section: Example: Markovian Langevin Dynamicsmentioning

confidence: 99%

Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

Valido¹

2019

Phys. Rev. D

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Conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of two-dimensional harmonic oscillators that contains the conventional Brownian motion as a particular instance. This description is derived from first principles in the framework of the so-called Maxwell-Chern-Simons electrodynamics, or also known, Abelian topological massive gauge theory. Disregarding backreaction effects and endowing the system Hamiltonian with a suitable renormalized potential interaction, the conceived description is equivalent to a minimal-coupling theory with a gauge field giving rise to a fluctuating force that mimics the Lorentz force induced by a particle-attached magnetic flux. We show that the underlying symmetry structure of the theory (i.e. time-reverse asymmetry and parity violation) yields an interacting vortex-like Brownian dynamics for the system particles. An explicit comparison to the conventional Brownian motion in the quantum Markovian limit reveals that the proposed description represents a second-order correction to the well-known damped harmonic oscillator, which manifests that there may be dissipative phenomena intrinsic to the dimensionality of the interesting system.

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“…[17]). Note also that due to Chern-Simons gauge property [12] [18]- [20], the quark-current will rotate in a 2D manner on top of this early stage thin mass shell, generating huge magnetic field (with axis not necessarily along the L z direction) of a new born star. Such huge electromagnetic fields are observed in pulsars and magnetars.…”

Section: Formation Of New Born Stars-pulsars According To the Projectmentioning

confidence: 99%

“…We venture to suggest that those WDs having more protons and electrons than neutrons, near their surfaces become magnetic white dwarf (MWD). These electrons and protons form Chern-Simons hydrogens [18]- [20] which are pushed out quickly to the atmosphere above the surface, generating huge magnetic fields (as compared to WD).…”

Section: White Dwarfs (Wd) and Magnetic White Dwarfs (Mwd) With Mass mentioning

confidence: 99%

On the Origin of Mass and Angular Momentum of Stellar Objects

Fung¹,

Wong²

2015

JMP

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The consequence of the 5D projection theory [1] is extended beyond the Gell-Mann Standard Model for hadrons to cover astronomical objects and galaxies. The proof of Poincare conjecture by Perelman's differential geometrical techniques led us to the consequence that charged massless spinors reside in a 5D void of a galactic core, represented by either an open 5D core or a closed, time frozen, 3D × 1D space structure, embedded in massive structural stellar objects such as stars and planets. The open galactic core is obtained from Ricci Flow mapping. There exist in phase, in plane rotating massless spinors within these void cores, and are responsible for 1) the outward spiral motion of stars in the galaxy in the open core, and 2) self rotations of the massive stellar objects. It is noted that another set of eigen states pertaining to the massless charged spinor pairs rotating out of phase in 1D (out of the 5D manifold) also exist and will generate a relatively weak magnetic field out of the void core. For stars and planets, it forms the intrinsic dipole field. Due to the existence of a homogeneous 5D manifold from which we believe the universe evolves, the angular momentum arising from the rotation of the in-phase spinor pairs is proposed to be counter-balanced by the rotation of the matter in the surrounding Lorentz domain, so as to conserve net zero angular momentum. Explicit expression for this total angular momentum in terms of a number of convergent series is derived for the totally enclosed void case/core, forming in general the structure of a star or a planet. It is shown that the variables/parameters in the Lorentz spacetime domain for these stellar objects involve the object's mass M, the object's Radius R, period of rotation P, and the 5D void radius Ro, together with the Fermi energy E f and temperature T of the massless charged spinors residing in the void. We discovered three laws governing the relationships between R o /R, T, E f and the angular momentum Iω of such astronomical object of interest, from which we established two distinct regions, which we define as the First and Second Laws for the evolution of the stellar object. The Fermi energy E f was found to be that of the electron mass, as it is the lightest massive elementary particle that could be created from pure energy in the core. In fact the mid-temperature of the transition region between the First and Second Law regions for this E f value is 5.3 × 10 9 K, just about that of the Bethe fusion temperature. We then apply our P. C. W. Fung, K. W. Wong 2304 theory to analyse observed data of magnetars, pulsars, pre-main-sequence stars, the NGC 6819 group, a number of low-to-mid mass main sequence stars, the M35 members, the NGC 2516 group, brown dwarfs, white dwarfs, magnetic white dwarfs, and members of the solar system. The ρ = (R o /R) versus T, and ρ versus P relations for each representative object are analysed, with reference to the general process of stellar evolution. Our analysis leads us to the following age sequence of stell...

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Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

Cited by 12 publications

References 67 publications

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

On the Origin of Mass and Angular Momentum of Stellar Objects

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