Complex density of continuum states in resonant quantum tunneling

Abstract

We introduce a complex-extended continuum level density and apply it to one-dimensional scattering problems involving tunneling through finite-range potentials. We show that the real part of the density is proportional to a real "time shift" of the transmitted particle, while the imaginary part reflects the imaginary time of an instanton-like tunneling trajectory. We confirm these assumptions for several potentials using the complex scaling method. In particular, we show that stationary points of the potentials give rise to specific singularities of both real and imaginary densities which represent close analogues of excited-state quantum phase transitions in bound systems.

arXiv comment6 pages, 3 figures

References in corpus (18)

• Resonant tunnelling and negative differential conductance in graphene transistors
• Excited state quantum phase transitions in many-body systems
• Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
• Reversible quantum information spreading in many-body systems near criticality
• Quantum criticality and dynamical instability in the kicked top
• Level Density in the Complex Scaling Method
• Classification of excited-state quantum phase transitions for arbitrary number of degrees of freedom
• Excited-state quantum phase transitions in systems with two degrees of freedom: III. Interacting boson systems
• Relaxation, chaos, and thermalization in a three-mode model of a BEC
• Calculation of Transition State Energies in the HCN-HNC Isomerization with an Algebraic Model
• Instantons revisited: dynamical tunnelling and resonant tunnelling
• Time delayed control of excited state quantum phase transitions in the Lipkin-Meshkov-Glick model
• Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential
• Interatomic Coulombic Decay in two coupled Quantum Wells
• NOON state of Bose atoms in the double-well potential via an excited state quantum phase transition
• Excited State Quantum Phase Transitions Studied from a Non-Hermitian Perspective
• Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models
• Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes

Cited by in corpus (5)

• Excited-state quantum phase transitions
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Continuum analogues of excited-state quantum phase transitions
• Avoided level crossings in quasi-exact approach
• Stabilization of product states and excited-state quantum phase transitions in a coupled qubit-field system