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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory (Paperback, 1st ed. 2017)
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Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory (Paperback, 1st ed. 2017)
Series: SpringerBriefs in Mathematical Physics, 13
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Lieb-Robinson bounds for multi-commutators are effective
mathematical tools to handle analytic aspects of infinite volume
dynamics of non-relativistic quantum particles with short-range,
possibly time-dependent interactions.In particular, the existence
of fundamental solutions is shown for those (non-autonomous)
C*-dynamical systems for which the usual conditions found in
standard theories of (parabolic or hyperbolic) non-autonomous
evolution equations are not given. In mathematical physics, bounds
on multi-commutators of an order higher than two can be used to
study linear and non-linear responses of interacting particles to
external perturbations. These bounds are derived for lattice
fermions, in view of applications to microscopic quantum theory of
electrical conduction discussed in this book. All results also
apply to quantum spin systems, with obvious modifications. In order
to make the results accessible to a wide audience, in particular to
students in mathematics with little Physics background, basics of
Quantum Mechanics are presented, keeping in mind its algebraic
formulation. The C*-algebraic setting for lattice fermions, as well
as the celebrated Lieb-Robinson bounds for commutators, are
explained in detail, for completeness.
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