A Specific N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach

By exploiting the supersymmetric invariant restrictions on the chiral and anti-chiral supervariables, we derive the off-shell nilpotent symmetry transformations for a specific (0 + 1)-dimensional N = 2 supersymmetric quantum mechanical model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables (\theta, \bar\theta). We also provide the geometrical meaning to the symmetry transformations. Finally, we show that this specific N = 2 SUSY quantum mechanical model is a model for Hodge theory.Comment: LaTeX File, 13 Pages, Minor Modifications, Advances in High Energy Physics, 2017, 1403937 (2017

A Specific N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach

By exploiting the supersymmetric invariant restrictions on the chiral and antichiral supervariables, we derive the off-shell nilpotent symmetry transformations for a specific (0 + 1)-dimensional N = 2 supersymmetric quantum mechanical model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable and a pair of Grassmannian variables ( , )). We also provide the geometrical meaning to the symmetry transformations. Finally, we show that this specific N = 2 SUSY quantum mechanical model is a model for Hodge theory

Exact Solutions of Augmented GP Equation: Solitons, Droplets and Supersolid

The augmented nonlinear Schr\"odinger equation (ANLSE), describing BEC, with the Lee-Huang-Yang (LHY) correction has exhibited a quantum droplet state, which has found experimental verification. In addition to the droplet, exact kink-antikink and supersolid phases have been recently obtained in different parameter domains. Interestingly, these solutions are associated with a constant background, unlike the form of BEC in quasi-one dimension, where dark, bright, and grey solitons have been experimentally obtained. Here, we connect a wide class of solutions of the ANLSE with the Jacobi elliptic functions using a fractional transformation method in a general scenario. The conserved energy and momentum are obtained in this general setting which differentiates and characterizes the different phases of the solution space. We then concentrate on the Jacobi-elliptic $dn(x, m^2)$ function, as the same is characterized by a non-vanishing background as compared to the other $cn$ and $sn$ functions.Comment: 10 pages, two figure

(Anti-)BRST Symmetries in FLRW Model: Supervariable Approach

We derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations corresponding to the local time-reparametrization symmetry transformation of the $(0+1)$-dimensional (1D) diffeomorphism (i.e. time-reparameterization) invariant FRLW model within the framework of supervariable approach BRST formalism. An application of (super-)diffeomorphism invariance yields horizontality conditions. The celebrated CF-type of condition which emerges as an off-shoot of the horizontality condition provides the absolute anticommutativity of the (anti-)BRST transformations. In addition, this CF-type condition is required for the derivation of coupled (but equivalent) Lagrangians. We also capture the (anti-)BRST invariance of the Lagrangians in terms of the Grassmannian translational generators and supervariables.Comment: 20 pages, 0 figur

Chiral kinetic theory from effective field theory revisited

Abstract We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the O(1/μ) expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also show that they give equivalent description of the dynamics of chiral fermions.</jats:p

PT-symmetry and supersymmetry: interconnection of broken and unbroken phases

The broken and unbroken phases of P T and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of P T -symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in P T -symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scraf potential, in P T -symmetric phase, a connection between complex isospecrtal superpotentials and modified Korteweg-de Vries equation occurs, only with certain restrictive parametric conditions. In the broken P T -symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter. </jats:p