Hidden supersymmetry in quantum bosonic systems

Abstract

We show that some simple well studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Poschl-Teller potential problems, in which the unbroken and broken N=2 supersymmetry of linear and nonlinear (polynomial) forms is revealed.

4 pages; refs and comments added, to appear in Ann. Phys

References in corpus (11)

• Supersymmetry and Quantum Mechanics
• Structure of Resonance in Preheating after Inflation
• Black Holes and Superconformal Mechanics
• Higher-Derivative Supersymmetry and the Witten Index
• Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
• Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics
• Hidden nonlinear supersymmetry of finite-gap Lame equation
• AB and Berry phases for a quantum cloud of charge
• Three aspects of bosonized supersymmetry and linear differential field equation with reflection
• On hidden broken nonlinear superconformal symmetry of conformal mechanics and nature of double nonlinear superconformal symmetry
• Mass Gap in Kaluza-Klein Spectrum in a Network of Brane Worlds

Cited by in corpus (73)

• Theta, Time Reversal, and Temperature
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Bosonization, Singularity Analysis, Nonlocal Symmetry Reductions and Exact Solutions of Supersymmetric KdV Equation
• Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics II:Painleve transcendent potentials
• Domain wall brane in squared curvature gravity
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials
• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Spectral singularities in PT-symmetric periodic finite-gap systems
• The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit
• Bosonization of Supersymmetric KdV equation
• The origin of the hidden supersymmetry
• Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry
• Hidden nonlinear su(2|2) superunitary symmetry of N=2 superextended 1D Dirac delta potential problem
• Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation
• Supersymmetric twisting of carbon nanotubes
• Matrix superpotentials
• Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
• Twisted kinks, Dirac transparent systems and Darboux transformations
• Higgs algebraic symmetry in the two-dimensional Dirac equation
• Wronskian differential formula for k-confluent SUSY QM
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• Supersymmetry, PT-symmetry and Spectral Bifurcation
• Landau levels, self-adjoint extensions and Hall conductivity on a cone
• Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
• Extended supersymmetry of the self-isospectral crystalline and soliton chains
• Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields
• Hidden superconformal symmetry: Where does it come from?
• Generic matrix superpotentials
• Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• Bosonized supersymmetry of anyons and supersymmetric exotic particle on the non-commutative plane
• Hidden superconformal symmetry of spinless Aharonov-Bohm system
• Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation
• Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons
• Carbon nanotubes in almost homogeneous transverse magnetic field: exactly solvable model
• The structure of invariants in conformal mechanics
• Conserved Correlation in PT -symmetric Systems: Scattering and Bound States
• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons
• Quantum Mechanics and Hidden Superconformal Symmetry
• Pöschl-Teller Hamiltonian: Gazeau-Klauder type coherent states, related statistics and geometry
• Hierarchy of QM SUSYs on a Bounded Domain
• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
• Spectral Signatures of Non-Trivial Topology in a Superconducting Circuit
• Hidden symmetries for transparent de Sitter space
• Perturbatively deformed defects in Pöschl-Teller-driven scenarios for quantum mechanics
• Quantum fluctuations around low-dimensional topological defects
• Nonlinear supersymmetry as a hidden symmetry
• Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
• Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• Supersymmetry Transformations for Delta Potentials
• Conformal bridge in a cosmic string background
• Color Superconductivity, Fermionic Quasinormal Modes in Reissner-Nordström-anti-de Sitter Spacetimes and Supersymmetry
• De Sitter Cosmic Strings and Supersymmetry
• Double complex SUSY-transformations: deformations of real potentials and their spectral characteristics
• Algebraic Shape Invariant Potentials as the Generalized Deformed Oscillator
• Supersymmetric relativistic quantum mechanics in time-domain
• A Note on Shape Invariant Potentials for Discretized Hamiltonians
• Rotational Symmetry of Classical Orbits, Arbitrary Quantization of Angular Momentum and the Role of Gauge Field in Two-Dimensional Space
• Exotic nonlinear supersymmetry and integrable systems
• Fractional supersymmetry algebra and lacunary Hermite polynomials
• Quasi-isospectral higher-order Hamiltonians via a reversed Lax pair construction
• The soliton nature of the super-Klein tunneling effect
• Hidden symmetries and nonlinear (super)algebras
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry