Perturbatively deformed defects in Pöschl-Teller-driven scenarios for quantum mechanics

Abstract

Pöschl-Teller-driven solutions for quantum mechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties concerning the quantum fluctuations in one-dimension, zero-mode states, first- and second- excited states, and energy density profiles are all obtained from deformed topological and non-topological structures supported by real scalar fields. Results are firstly derived from an integrated $\lambda {\varphi }^4$ theory, with corresponding generalizations applied to starting $\lambda {\chi }^4$ and {\em sine}-Gordon theories. By focusing our calculations on structures supported by the $\lambda {\varphi }^4$ theory, the outcome of our study suggests an exact quantitative correspondence to Pöschl-Teller-driven systems. Embedded into the perturbative quantum mechanics framework, such a correspondence turns into a helpful tool for computing excited states and continuous mode solutions, as well as their associated energy spectrum, for quantum fluctuations of perturbatively deformed structures. Perturbative deformations create distinct physical scenarios in the context of exactly solvable quantum systems and may also work as an analytical support for describing novel braneworld universes embedded into a $5$-dimensional gravity bulks.

arXiv comment20 pages, 5 figures

References in corpus (36)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• Modeling the fifth dimension with scalars and gravity
• Universal Aspects of Gravity Localized on Thick Branes
• Tachyon Dynamics in Open String Theory
• Gravitational Stability and Renormalization-Group Flow
• Four-dimensional gravity on a thick domain wall
• Opening up extra dimensions at ultra-large scales
• Topological Inflation
• Supergravity Domain Walls
• Static Domain Walls in N=1 Supergravity
• Thick brane solutions
• Thick Brane Worlds and Their Stability
• New Global Defect Structures
• Critical phenomena of thick branes in warped spacetimes
• Entropic Measure for Localized Energy Configurations: Kinks, Bounces, and Bubbles
• Fermions on Thick Branes in the Background of Sine-Gordon Kinks
• Hidden supersymmetry in quantum bosonic systems
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Dynamical dispersion relation for ELKO dark spinor fields
• Deformed defects with applications to braneworlds
• A Note on Asymmetric Thick Branes
• New Lump-like Structures in Scalar-field Models
• Classical behavior of deformed sine-Gordon models
• Information-Entropic Measure of Energy-Degenerate Kinks in Two-Field Models
• Study of models of the sine-Gordon type in flat and curved spacetime
• Gravitating multidefects from higher dimensions
• Study of field fluctuations and their localization in a thick braneworld generated by gravity non-minimally coupled to a scalar field with the Gauss-Bonnet term
• Equivalence between Born-Infeld tachyon and effective real scalar field theories for brane structures in warped geometry
• Exact solutions for a Maxwell-Kalb-Ramond action with dilaton: Localization of massless and massive modes in a sine-Gordon brane-world
• Non-topological solitons in brane world models
• Generalized Morse and Poschl-Teller potentials : The connection via Schrodinger equation
• Gravity effects on thick brane formation from scalar field dynamics
• The Spectrum of Sl(2, R)/U(1) Black Hole Conformal Field Theory
• Charge varying sine-Gordon deformed defects
• Thick Braneworlds and the Gibbons-Kallosh-Linde No-go Theorem in the Gauss-Bonnet Framework

Cited by in corpus (6)

• The nuclear configurational entropy approach to dynamical QCD effects
• Configurational entropy and $\rho$ and $\varphi$ mesons production in QCD
• The nuclear configurational entropy impact parameter dependence in the Color-Glass Condensate
• Fine-tuning the Color-Glass Condensate with the nuclear configurational entropy
• Phase-space quantum profile of Pöschl-Teller two-level systems
• Topological view of quantum tunneling coherent destruction