This article is available for purchase or by subscription. See below.
Abstract
|
We consider the Bloch–Torrey operator in
, where
. After normalization, this
operator takes the form
,
where
and
represents a magnetic
vector field. For
we give
natural conditions under which this operator can be defined as a maximally accretive operator, characterize
its domain and obtain its spectral properties in some special cases where we manage to show that the essential
spectrum is
. This result
lies in contrast with the
case considered in previous works.
In the asymptotic limit
and for
,
assuming that
is an affine function, we give accurate estimates for the location of the discrete spectrum in
the cases
or when
is a finite interval. Resolvent estimates are established as well.
|
PDF Access Denied
We have not been able to recognize your IP address
18.191.181.231
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
Bloch–Torrey, Schrödinger, matrix potential
|
Mathematical Subject Classification
Primary: 35P05
|
Milestones
Received: 1 December 2020
Revised: 23 November 2021
Accepted: 5 January 2022
Published: 29 April 2022
|
|