1,195 research outputs found
An exact solution method for 1D polynomial Schr\"odinger equations
Stationary 1D Schr\"odinger equations with polynomial potentials are reduced
to explicit countable closed systems of exact quantization conditions, which
are selfconsistent constraints upon the zeros of zeta-regularized spectral
determinants, complementing the usual asymptotic (Bohr--Sommerfeld)
constraints. (This reduction is currently completed under a certain vanishing
condition.) In particular, the symmetric quartic oscillators are admissible
systems, and the formalism is tested upon them. Enforcing the exact and
asymptotic constraints by suitable iterative schemes, we numerically observe
geometric convergence to the correct eigenvalues/functions in some test cases,
suggesting that the output of the reduction should define a contractive
fixed-point problem (at least in some vicinity of the pure case).Comment: flatex text.tex, 4 file
An Introduction to Superconducting Qubits and Circuit Quantum Electrodynamics
A subset of the concepts of circuit quantum electrodynamics are reviewed as a
reference to the Axion Dark Matter Experiment (ADMX) community as part of the
proceedings of the 2nd Workshop on Microwave Cavities and Detectors for Axion
Research. The classical Lagrangians and Hamiltonians for an LC circuit are
discussed along with black box circuit quantization methods for a weakly
anharmonic qubit coupled to a resonator or cavity
A Note on Black Hole Entropy in Loop Quantum Gravity
Several recent results have hinted that black hole thermodynamics in loop
quantum gravity simplifies if one chooses an imaginary Barbero-Immirzi
parameter . This suggests a connection with
or conformal field
theories at the "boundaries" formed by spin network edges intersecting the
horizon. I present a bit of background regarding the relevant conformal field
theories, along with some speculations about how they might be used to count
black hole states. I show, in particular, that a set of unproven but plausible
assumptions can lead to a boundary conformal field theory whose density of
states matches the Bekenstein-Hawking entropy.Comment: v2: added references; v3: slight addition to discussion of 3d
gravity; v4: more references, typos fixe
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