Abstract
Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in quantum stochastic differential equations. They induce dissipative friction on the spin chain currents. We show that, as the friction becomes stronger, the noise induced dissipative effects localize the spin chain states on a slow mode manifold, and we determine the effective stochastic quantum dynamics of these slow modes. We illustrate this approach by studying the quantum stochastic Heisenberg spin chain.
Highlights
Non-equilibrium dynamics, classical and quantum, is one of the main current focuses of both theoretical and experimental condensed matter physics
In a way similar to classical Langevin equations of the type considered in the introduction which codes for the interaction between a classical system with memoryless noise, quantum stochastic equations [19] code for the interaction between a quantum system and an infinitely large memoryless quantum reservoir representing quantum noise
As we argued in the Introduction, we aim at taking the large friction limit η → ∞ in order to recover the quantum analogue of the macroscopic fluctuation theory
Summary
Non-equilibrium dynamics, classical and quantum, is one of the main current focuses of both theoretical and experimental condensed matter physics. Motivated by the previous discussion, we look at the large friction limit η → ∞ In this limit, the on-site random dephasing produces strong decoherence which induces a transmutation of the coherent hopping process generated by the XXZ hamiltonian into an incoherent jump process along the chain. We extract the relevant slow modes of those quantum stochastic systems and we describe their effective stochastic dynamics by taking the large friction limit of the previously defined quantum stochastic spin chain models.
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