On the Dirac oscillator in a spinning cosmic string spacetime in external magnetic fields: Investigation of energy spectrum and connection with the condensed matter physics
Márcio M. Cunha, Henrique S. Dias, Edilberto O. Silva
In this article, we study topological and noninertial effects on the motion of the two-dimensional Dirac oscillator in the presence of a uniform magnetic field and the Aharonov-Bohm potential. We obtain the Dirac equation that describes the model. Expressions for the wave functions and energy spectrum are derived. The energy spectrum of the oscillator as a function of the various physical parameters involved in the problem is rigorously studied. Finally, we present some analogies between our results and others of the condensed matter physics.
We examine the effects of gravitational fields produced by topological defects on a Dirac field and a Dirac oscillator in a spinning cosmic string spacetime. We obtain the eigenfunctions and the energy levels of the relativistic field in that background and consider the effect of various parameters, such as the frequency of the rotating frame, the oscillator's frequency, the string density and other quantum numbers.
In this article, we investigate the behavior of relativistic spin-zero bosons in the space-time generated by a spinning cosmic string. We obtain the generalized beta matrices in terms of the flat spacetime ones and rewrite the covariant form of DuffinKemmer-Petiau (DKP) equation in spinning cosmic string space-time. We find the solution of DKP oscillator and determine the energy levels. We also discuss the influence of the topology of the cosmic string on the energy levels and the DKP spinors.
Universality in Relativistic Spinning Particle Models
Walter Burke Institute for Theoretical Physics, California Institute of Technology（加州理工学院沃尔特·伯克理论物理研究所）；School of Physics, Korea Institute for Advanced Study（韩国高等科学研究院物理学院）
It is shown that the Lorentz group plays prominent roles in at least two areas in condensed matter physics, namely in the Bogoliubov transformation and optical filters. It is pointed out that the underlying symmetry of the Bogoliubov transformation is that of two coupled oscillators, and that the underlying symmetry of two coupled oscillators in that of the group $O(3,3)$. The Lorentz group is also shown to be the underlying symmetry group for the Jones matrix formalism which is standard language for optical filters.
We obtain Proca field theory from the quantisation of the $\mathcal{N}=2$ supersymmetric worldline upon supplementing the graded BRST-algebra with an extra multiplet of oscillators. The linearised theory describes the BV-extended spectrum of Proca theory, together with a Stückelberg field. When coupling the theory to background fields we derive the Proca equations, arising as consistency conditions in the BRST procedure. We also explore non-abelian modifications, complexified vector fields as well as coupling to a dilaton field. We propose a cubic action on the space of BRST-operators which re…
The semiclassical evolution of spinning particles has recently been re-examined in condensed matter physics, high energy physics, and optics, resulting in the prediction of the intrinsic spin Hall effect associated with the Berry phase. A fundamental nature of this effect is related to the spin-orbit interaction and topological monopoles. Here we report a unified theory and a direct observation of two mutual phenomena: a spin-dependent deflection (the spin Hall effect) of photons and the precession of the Stokes vector along the coiled ray trajectory of classical geometrical optics. Our measur…
The fluctuation-dissipation theorem (FDT) is very general and applies to a broad variety of different physical phenomena in condensed matter physics. With the help of the FDT and following the famous work of Caldeira and Leggett, we show that, whenever linear response theory applies, any generic bosonic or fermionic system at finite temperature $T$ can be mapped onto a fictitious system of free harmonic oscillators. To the best of our knowledge, this is the first time that such a mapping is explicitly worked out. This finding provides further theoretical support to the phenomenological harmoni…
Describing the bosonic AdS_3 x S^3 particle and string in SU(1,1) x SU(2) group variables, we provide a Hamiltonian treatment of the isometry group orbits of solutions via analysis of the pre-symplectic form. For the particle we obtain a one-parameter family of orbits parameterized by creation-annihilation variables, which leads to the Holstein-Primakoff realization of the isometry group generators. The scheme is then applied to spinning string solutions characterized by one winding number in AdS_3 and two winding numbers in S^3. We find a two-parameter family of orbits, where quantization aga…
We construct top down models for holographic d-wave superfluids in which the order parameter is a charged spin two field in the bulk. Close to the transition temperature the condensed phase can be captured by a charged spin two field in an R-charged black hole background (downstairs picture) or equivalently by specific graviton perturbations of a spinning black brane (upstairs picture). We analyse the necessary conditions on the mass and the charge of the spin two field for a condensed phase to exist and we discuss the competition of the d-wave phase with other phases such as s-wave superfluid…
A general class of rotating closed string solutions in AdS_5 x S^5 is shown to be described by a Neumann-Rosochatius one-dimensional integrable system. The latter represents an oscillator on a sphere or a hyperboloid with an additional ``centrifugal'' potential. We expect that the reduction of the AdS_5 x S^5 sigma model to the Neumann-Rosochatius system should have further generalizations and should be useful for uncovering new relations between integrable structures on the two sides of the AdS/CFT duality. We find, in particular, new circular rotating string solutions with two AdS_5 and thre…
We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $θ$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $θ$-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (à la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the $θ$-modified Pauli equation. Then, we extract $θ$-modified interaction between a nonrelativistic spin and a magnetic …
We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $θ$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $θ$-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (à la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the $θ$-modified Pauli equation. We extract $θ$-modified interaction between a nonrelativistic spin and a magnetic field …
Van Holten's covariant algorithm for deriving conserved quantities is presented, with particular attention paid to Runge-Lenz-type vectors. The classical dynamics of isospin-carrying particles is reviewed. Physical applications including non-Abelian monopole-type systems in diatoms, introduced by Moody, Shapere and Wilczek, are considered. Applied to curved space, the formalism of van Holten allows us to describe the dynamical symmetries of generalized Kaluza-Klein monopoles. The framework is extended to supersymmetry and applied to the SUSY of the monopoles. Yet another application concerns t…
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories of effective models are allowed or not by the conservation of top…
Instantons, monopoles and vortices have become paradigms of topological structures in field theory and quantum mechanics, with important applications in particle physics, astrophysics, condensed matter physics and mathematics. We have discussed here the self-dual Chern-Simons theory specially in (2+1) dimensions. we start with a relevant topological quantum mechanical model (such as Landau problem consisting of two basic chiral oscillators) and extrapolate the analysis to (2+1)dimensional vector field theory. Aspects of selfdual symmetry in topologically massive gravity model were also conside…
We present for the first time solutions in the gauged $U(1)\times U(1)$ model of Witten describing vortons -- spinning flux loops stabilized against contraction by the centrifugal force. Vortons were heuristically described many years ago, however, the corresponding field theory solutions were not obtained and so the stability issue remained open. We construct explicitly a family of stationary vortons characterized by their charge and angular momentum. Most of them are unstable and break in pieces when perturbed. However, thick vortons with small radius preserve their form in the 3+1 non-linea…
The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the Möbius domain-wall fermion formulation, in the $1+1$-, $2+1$-, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary conditio…
