Quantum dynamics and relaxation in comb turbulent diffusion
- URL: http://arxiv.org/abs/2010.06490v1
- Date: Tue, 13 Oct 2020 15:50:49 GMT
- Title: Quantum dynamics and relaxation in comb turbulent diffusion
- Authors: Alexander Iomin
- Abstract summary: Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered.
Operators of the form $hatcal H=hatA+ihatB$ are described.
Rigorous analytical analysis is performed for both wave and Green's functions.
- Score: 91.3755431537592
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Continuous time quantum walks in the form of quantum counterparts of
turbulent diffusion in comb geometry are considered. The interplay between the
backbone inhomogeneous advection $\delta(y)x\partial_x$ along the $x$ axis,
which takes place only at the $y=0$, and normal diffusion inside fingers
$\partial_y^2$ along the $y$ axis leads to turbulent diffusion. This
geometrical constraint of transport coefficients due to comb geometry and
properties of a dilatation operator lead to consideration of two possible
scenarios of quantum mechanics. These two variants of continuous time quantum
walks are described by non-Hermitian operators of the form $\hat{\cal
H}=\hat{A}+i\hat{B}$. Operator $\hat{A}$ is responsible for the unitary
transformation, while operator $i\hat{B}$ is responsible for quantum/classical
relaxation. At the first quantum scenario, the initial wave packet can move
against the classical streaming. This quantum swimming upstream is due to the
dilatation operator, which is responsible for the quantum (not unitary)
dynamics along the backbone, while the classical relaxation takes place in
fingers. In the second scenario, the dilatation operator is responsible for the
quantum relaxation in the form of an imaginary optical potential, while the
quantum unitary dynamics takes place in fingers. Rigorous analytical analysis
is performed for both wave and Green's functions.
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