Exponential decay in a spin bath

Spin-orbit coupled particle in a spin bath

Peter Stano,1,2 Jaroslav Fabian,3 and Igor Žutić4 1Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava, Slovakia 2Department of Physics, Klingelbergstrasse 82, University of Basel, Switzerland 3Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany 4Department of Physics, University at Buffalo, New York 14260-1500, USA (Received 28 August 2012; ...

Exponential Decay in Nonlinear Networks1

Exponential Decay in Quantum Mechanics

First of all: disregard all of so called “preliminary physical expectations”, because all these expectations are just a pseudonym for prejudices elaborated by the older generation. These words belong to Dirac, not to me. The right way of creating new physics is different: one should begin with a beautiful mathematical idea. But it should be really beautiful! No special relations to physics is c...

Domination with exponential decay

Let G be a graph and S ⊆ V (G). For each vertex u ∈ S and for each v ∈ V (G) − S, we define d(u, v) = d(v, u) to be the length of a shortest path in 〈V (G)−(S−{u})〉 if such a path exists, and∞ otherwise. Let v ∈ V (G). We define wS(v) = ∑ u∈S 1 2d(u,v)−1 if v 6∈ S, and wS(v) = 2 if v ∈ S. If, for each v ∈ V (G), we have wS(v) ≥ 1, then S is an exponential dominating set. The smallest cardinalit...

Quantum phase transition of a magnet in a spin bath.

The excitation spectrum of a model magnetic system, LiHoF4, was studied with the use of neutron spectroscopy as the system was tuned to its quantum critical point by an applied magnetic field. The electronic mode softening expected for a quantum phase transition was forestalled by hyperfine coupling to the nuclear spins. We found that interactions with the nuclear spin bath controlled the lengt...