Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
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 …