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‎L3-demon.html

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‎L3-phys.html

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‎L3-qinfo.html

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‎L3-qphase.html

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‎L3-skyrm.html

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‎L3-telep.html

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‎archives.html

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‎author/alberto-verga.html

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‎author/alberto-verga2.html

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‎authors.html

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‎categories.html

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‎category/blog.html

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‎category/blog2.html

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‎category/teaching.html

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‎cirm2020.html

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‎cp.html

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identical to a cluster Hamiltonian in a symmetry preserving&nbsp;field <span class="math">\(\bar{g}/2\)</span>. The expression&nbsp;of <span class="math">\(M_n\)</span> contains the&nbsp;number <span class="math">\(|n_+|\)</span> of 1 in the binary expansion of the&nbsp;integer <span class="math">\(n = 0,\ldots,2^L - 1\)</span> (<span class="math">\(n_+\)</span> is the set of 1 positions in this expansion): This corresponds to the number of simultaneous&nbsp;&#8220;errors&#8221; <span class="math">\(Y_x\)</span>. To obtain&nbsp;(<span class="math">\(\ref{e:Mn}\)</span>) we assumed a limit of&nbsp;small <span class="math">\(J\)</span> (<span class="math">\(\bar{g}\)</span> can be of order one, and in our&nbsp;units <span class="math">\(J=J\Delta t\)</span>), and, in this limit, we assumed that at each time step the density matrix separates between the two subsystems, leading to the usual Markov form in which the actual state of the system only depends on its preceding&nbsp;state.</p>
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<p>Usually, in the Lindblad approximation, one consider stochastic processes in which the probability of simultaneous errors are negligible. In our model, at variance, the relevant term is the one in which we&nbsp;have <span class="math">\(L\)</span> simultaneous <span class="math">\(Y\)</span> flips of the environment spins: This ensures perfect synchronization of the homogeneous environment state. In this case the Markov equation simplifies&nbsp;to
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<p>Usually, in the Lindblad approximation, one considers stochastic processes in which the probability of simultaneous errors are negligible. In our model, at variance, the relevant term is the one in which we&nbsp;have <span class="math">\(L\)</span> simultaneous <span class="math">\(Y\)</span> flips of the environment spins: This ensures perfect synchronization of the homogeneous environment state. In this case the Markov equation simplifies&nbsp;to
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‎hexa2023.html

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