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Full-Text Articles in Physical Sciences and Mathematics
Instantons In Quantum Mechanics And Resurgent Expansions, Ulrich D. Jentschura, Jean Zinn-Justin
Instantons In Quantum Mechanics And Resurgent Expansions, Ulrich D. Jentschura, Jean Zinn-Justin
Physics Faculty Research & Creative Works
Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical case, the eigenvalue may be expressed in terms of a generalized perturbative expansion (resurgent expansion). Modified Bohr-Sommerfeld quantization conditions lead to generalized perturbative expansions which may be expressed in terms of nonanalytic factors of the form exp(-a/g), where a>0 is the instanton action, and power series in the coupling g, as well as logarithmic factors. The ground-state energy, for …
Order-Parameter Symmetry And Mode-Coupling Effects At Dirty Superconducting Quantum Phase Transitions, Rastko Sknepnek, Thomas Vojta, Rajesh Narayanan
Order-Parameter Symmetry And Mode-Coupling Effects At Dirty Superconducting Quantum Phase Transitions, Rastko Sknepnek, Thomas Vojta, Rajesh Narayanan
Physics Faculty Research & Creative Works
We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non- s -wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior …
Extrapolation Of The Zα-Expansion And Two-Loop Bound-State Energy Shifts, Ulrich D. Jentschura
Extrapolation Of The Zα-Expansion And Two-Loop Bound-State Energy Shifts, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
Quantum electrodynamic (QED) effects that shift the binding energies of hydrogenic energy levels have been expressed in terms of a semi-analytic expansion in powers of Zα and ln[(Zα)-2], where Z is the nuclear charge number and α is the fine-structure constant. For many QED effects, numerical data are available in the domain of high Z where the Zα expansion fails. In this Letter, we demonstrate that it is possible, within certain limits of accuracy, to extrapolate the Zα-expansion from the low-Z to the high-Z domain. We also review two-loop self-energy effects and provide an estimate for the problematic …
Local Polariton Modes And Resonant Tunneling Of Electromagnetic Waves Through Periodic Bragg Multiple Quantum Well Structures, Lev I. Deych, Alexey Yamilov, Alexander A. Lisyansky
Local Polariton Modes And Resonant Tunneling Of Electromagnetic Waves Through Periodic Bragg Multiple Quantum Well Structures, Lev I. Deych, Alexey Yamilov, Alexander A. Lisyansky
Physics Faculty Research & Creative Works
We study analytically defect polariton states in Bragg multiple quantum well structures and defect-induced changes in transmission and reflection spectra. Defect layers can differ from the host layers in three ways: exciton-light coupling strength, exciton resonance frequency, and interwell spacing. We show that a single defect leads to two local polariton modes in the photonic band gap. These modes cause peculiarities in reflection and transmission spectra. Each type of defect can be reproduced experimentally, and we show that each of these plays a distinct role in the optical properties of the system. For some defects, we predict a narrow transmission …