On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains

Abstract

We investigate spectral and asymptotic properties of the particular Schrödinger operator (also known as the Bloch-Torrey operator), $-\Delta +igx$, in infinite periodically perforated domains of ${\mathbb{R}}^d$. We consider Dirichlet realizations of this operator and formalize a numerical approach proposed in [J. Phys. A: Math. Theor. 53, 325201 (2020)] for studying such operators. In particular, we discuss the existence of the spectrum of this operator and its asymptotic behavior as $g\to \infty$.

References in corpus (9)

• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Theoretical energies of low-lying states of light helium-like ions
• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• Testing fundamental interactions on the helium atom
• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Diffusion MRI/NMR at high gradients: challenges and perspectives
• On spectral properties of the Bloch-Torrey operator in two dimensions
• The complex Airy operator with a semi-permeable barrier
• Helium-like and Lithium-like ions: Ground state energy

Cited by in corpus (7)

• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
• Detecting continuous variable entanglement in phase space with the $Q$-distribution
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Contractive inequalities for mixed norm spaces and the Beta function
• On a variational problem related to the Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities
• Information and majorization theory for fermionic phase-space distributions