Supercriticality and Transmission Resonances in the Dirac equation

Abstract

It is shown that a Dirac particle of mass $m$ and arbitrarily small momentum will tunnel without reflection through a potential barrier $V=U_c(x)$ of finite range provided that the potential well $V=-U_c(x)$ supports a bound state of energy $E=-m.$ This is called a supercritical potential well.

Submitted to Physical Review Letters

References in corpus (1)

• Positron Tunnelling through the Coulomb Barrier of Superheavy Nuclei

Cited by in corpus (28)

• Quasi-exact solution to the Dirac equation for the hyperbolic secant potential
• The Woods-Saxon Potential in the Dirac Equation
• Scattering of a Klein-Gordon particle by a Woods-Saxon potential
• Relativistic quantum effects of Dirac particles simulated by ultracold atoms
• Macroscopic Klein Tunneling in spin-orbit coupled Bose-Einstein Condensates
• New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case
• Transmission resonances and supercritical states in a one dimensional cusp potential
• Two-dimensional Dirac particles in a Pöschl-Teller waveguide
• Scattering of a relativistic scalar particle by a cusp potential
• Low Momentum Scattering in the Dirac Equation
• Effective-Mass Dirac Equation for Woods-Saxon Potential: Scattering, Bound States and Resonances
• Scattering, bound and quasi-bound states of the generalized symmetric Woods-Saxon potential
• The Strong Levinson Theorem for the Dirac Equation
• Scattering state of Klein-Gordon Particles by q-parameter hyperbolic Poschl-Teller potential
• Scattering of a spinless particle by an asymmetric Hulth{é}n potential within the effective mass formalism
• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• Resonant states in an attractive one dimensional cusp potential
• Tunneling and transmission resonances of a Dirac particle by a double barrier
• Space-time resolved quantum field approach to Klein tunneling dynamics across a finite barrier
• Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections
• Solution of the spin and pseudo-spin symmetric Dirac equation in 1+1 space-time using the tridiagonal representation approach
• Relativistic Double Barrier Problem with Three Sub-Barrier Transmission Resonance Regions
• Refined comparison theorems for the Dirac equation in d dimensions
• Nodal theorems for the Dirac equation in d >= 1 dimensions
• Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump
• Relativistic particles in super-periodic potentials: exploring graphene and fractal systems
• Perfect transmission of a Dirac particle in one-dimension double square barrier
• Full transmission within a wide energy range and super-criticality in relativistic barrier scattering