SciPost Phys. 9, 004 (2020) ·
published 8 July 2020

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We study the equilibration properties of isolated ergodic quantum systems initially prepared in a cat state, i.e a macroscopic quantum superposition of states. Our main result consists in showing that, even though decoherence is at work in the mean, there exists a remnant of the initial quantum coherences visible in the strength of the fluctuations of the steady state. We backup our analysis with numerical results obtained on the XXX spin chain with a random field along the zaxis in the ergodic regime and find good qualitative and quantitative agreement with the theory. We also present and discuss a framework where equilibrium quantities can be computed from general statistical ensembles without relying on microscopic details about the initial state, akin to the eigenstate thermalization hypothesis.
SciPost Phys. 6, 045 (2019) ·
published 16 April 2019

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We introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. We focus on periodic boundary conditions and derive the complete stationary distribution of the system. It is proven that the generating function of the latter is provided by the HarishChandraItzyksonZuber integral which allows us to access all fluctuations of the system state. The steady state is characterized by non trivial correlations which have a topological nature. Diagrammatic tools appropriate for the study of these correlations are presented. In the thermodynamic large system size limit, the system approaches a non random equilibrium state plus occupancy and coherence fluctuations of magnitude scaling proportionally with the inverse of the square root of the volume. The large deviation function for those fluctuations is determined. Although decoherence is effective on the mean steady state, we observe that subleading fluctuating coherences are dynamically produced from the inhomogeneities of the initial occupancy profile.
SciPost Phys. 5, 037 (2018) ·
published 24 October 2018

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We revisit aspects of monitoring observables with continuous spectrum in a
quantum system subject to dissipative (Lindbladian) or conservative
(Hamiltonian) evolutions. After recalling some of the salient features of the
case of pure monitoring, we deal with the case when monitoring is in
competition with a Lindbladian evolution. We show that the strong measurement
limit leads to a diffusion on the spectrum of the observable. For the case with
competition between observation and Hamiltonian dynamics, we exhibit a scaling
limit in which the crossover between the classical regime and a diffusive
regime can be analyzed in details.
SciPost Phys. 3, 033 (2017) ·
published 4 November 2017

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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.
Mr Jin: "I thank the referee for very u..."
in Report on Equilibration of quantum cat states