Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum-Classical Transition of the Escape Rate of a Uniaxial Spin
  System in an Arbitrarily Directed Field   The escape rate \Gamma of the large-spin model described by the Hamiltonian H
= -DS_z^2 - H_zS_z - H_xS_x is investigated with the help of the mapping onto a
particle moving in a double-well potential U(x). The transition-state method
yields $\Gamma$ in the moderate-damping case as a Boltzmann average of the
quantum transition probabilities. We have shown that the transition from the
classical to quantum regimes with lowering temperature is of the first order
(d\Gamma/dT discontinuous at the transition temperature T_0) for h_x below the
phase boundary line h_x=h_{xc}(h_z), where h_{x,z}\equiv H_{x,z}/(2SD), and of
the second order above this line. In the unbiased case (H_z=0) the result is
h_{xc}(0)=1/4, i.e., one fourth of the metastability boundary h_{xm}=1, at
which the barrier disappears. In the strongly biased limit \delta\equiv 1-h_z
<< 1, one has h_{xc} \cong (2/3)^{3/4}(\sqrt{3}-\sqrt{2})\delta^{3/2}\cong
0.2345 \delta^{3/2}, which is about one half of the boundary value h_{xm} \cong
(2\delta/3)^{3/2} \cong 0.5443 \delta^{3/2}.The latter case is relevant for
experiments on small magnetic particles, where the barrier should be lowered to
achieve measurable quantum escape rates.

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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-alg