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Landau-Lifshitz damping from Lindbladian dissipation in quantum magnets
by Götz Silvester Uhrig
Submission summary
| Authors (as registered SciPost users): | Götz Uhrig |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2406.10613v3 (pdf) |
| Date submitted: | 2025-04-08 10:37 |
| Submitted by: | Uhrig, Götz |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
As of now, the phenomenological classical Landau-Lifshitz (LL) damping of magnetic order is not conceptually linked to the quantum theory of dissipation of the Lindbladian formalism which is unsatisfactory for the booming research on magnetic dynamics. Here, it is shown that LL dynamics can be systematically derived from Lindbladian dynamics in a local mean-field theory for weak external fields. The derivation also extends the LL dynamics beyond the orientation →m/|→m| to the length |→m| of the magnetization. A key assumption is that the Lindbladian dissipation adapts to the non-equilibrium H(t) instantaneously to lower its expectation value.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
to avoid inaccuracies. For details please see the comprehensive replies to the two reports.
This has improved the manuscript and strengthend the advocated link between two
well-established formalisms which even allowed to extend the Landau-Lifshitz equation.
For these reasons, I am resubmitting the manuscript herewith.
List of changes
1)
Paragraph added on the direction of relaxation and
how the bath can know about the direction of the (effective)
magnetic field.
2)
Reformulation of the motivation to look for a link
between the Landau-Lifshitz and the Lindblad formalism
3)
Justifications added for the equations where appropriate;
Hamiltonians specified and the discussion of the coupling J
postponed to where it has been introduced.
Stating that the approximation on the direction of the magnetization
to be almost parallel to the total field is justified only a posteriori.
4)
Pointing out that the structure of the Lindblad equation
does not depend on the weak-coupling limit.
5)
Instability of the extended equation is now related to the one of
the LL equations.
6)
Discussion of the value of C: no sign change occurs.
7)
Clarification that a local mean-field theory does not
per se imply quantum effects. But the possibility that the
length of the order parameter changes does represent
a quantum effect.
8)
Sect. 5 with Fig. 2 is added to discuss generic solution
for the length changes of the order parameter due to relaxation.
9)
All smaller typos and spotted formulation errors are removed.