Dynamical chaotic phases and constrained quantum dynamics

Timpanaro, André M.; Wald, Sascha; Semião, F. L.; Landi, Gabriel T.

doi:10.1103/physreva.100.012117

Cited by 9 publications

(8 citation statements)

References 56 publications

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“…These constraints render the system effectively non-linear and therefore allow for different phases to exist. The constrained oscillator possesses a regime where oscillations are centered around ⟨x⟩ = 0 and one where oscillations are displaced due to the external forcing [31,32]. An explanation of how such constraints are linked to work protocols can be found in [32].…”

Section: The Modelmentioning

confidence: 99%

“…Based on the idea of introducing transition phenomena through adequate constraints or appropriate limits of physical parameters in few body problems [29,30], we study here the case of a single SQS [31]. From the point of view of statistical mechanics, the SQS may be interpreted as a mean-field version of the spherical model, while from the point of view of quantum optics and quantum thermodynamics, it may be seen as a highly controlled quantum system subjected to work protocols, as explained in [32]. Originally introduced to overcome the lack of an analytical solution of the three dimensional Ising model [25], the spherical model has quickly proven itself as an excellent starting ground to study various transition phenomena in and out of equilibrium and routinely obtain results that go beyond mean-field statements [28,[33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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In and out of equilibrium quantum metrology with mean-field quantum criticality

Wald,

Moreira,

Semião

2020

Preprint

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We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level. First, we focus on equilibrium quantum criticality in the SQS and obtain the quantum Fisher information analytically, which is associated with the minimum lower bound for the precision of estimation of the parameter driving the phase transition. We compare it with the Fisher information for a specific experimental scenario where photoncounting-like measurements are employed. We find how quantum criticality and squeezing are useful resources in the metrological scenario. Second, we obtain the quantum Fisher information for the out of equilibrium transition in the dissipative non-equilibrium steady state (NESS), and investigate how the presence of dissipation affects the parameter estimation. In this scenario, we find that the critical point is shifted by an amount which depends on the dissipation rate. This is used here to design high precision protocols for a whole range of the transition-driving parameter in the ordered phase. In fact, for certain values of the parameter being estimated, dissipation may be used to obtain higher precision when compared to the equilibrium scenario.

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Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

In and out of equilibrium quantum metrology with mean-field quantum criticality

Wald,

Moreira,

Semião

2020

Preprint

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“…It turns out that such a constrained quantum dynamics leads to a formidable problem which has obtained a lot of attention, already since the early days of Dirac [19] and has been actively discussed recently, see e.g. [64,68,69,35] and references therein. We presented a simple scaling argument which focusses on the long-time limit where an effective constrained Langevin equation should become more easily treatable.…”

Section: Concludendum Estmentioning

confidence: 99%

“…The long-time dynamics of a disordered quantum spherical model was analysed in the mean-field limit [56]. The quantum dynamical behaviour of the open quantum spherical model quenched to temperature T = 0 as described by a Lindblad equation was recently studied [68,69,70,64] and it was shown that for quantum quenches deep into the ordered state, the long-time behaviour of several averages becomes independent of the coupling to the bath. We shall outline how the explicit solution of the quantum spherical dynamics can be considerably simplified in the long-time limit via a scaling argument.…”

Section: Introductionmentioning

confidence: 99%

Axiomatic construction of quantum Langevin equations

Araújo¹,

Wald²,

Henkel³

2019

J. Stat. Mech.

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A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem is presented. The case of a single harmonic oscillator coupled to a large external bath is analysed in detail. This allows to distinguish a markovian semi-classical approach, due to Bedeaux and Mazur, from a non-markovian full quantum approach, due to to Ford, Kac and Mazur. The quantum-fluctuation-dissipation theorem is seen to be incompatible with a markovian dynamics. Possible applications to the quantum spherical model are discussed.

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“…The impact of constraints on the dynamics of quantum mechanical systems has received a resurgence of interest in recent years [1][2][3][4][5][6][7][8][9][10] . Much of this interest has focused on whether, and when, constraints facilitate or even necessitate violations of the entanglement thermalization hypothesis (ETH) 11,12 .…”

Section: Introductionmentioning

confidence: 99%

Many-body constraints and non-thermal behavior in 1D open systems with Haldane exclusion statistics

Xiong,

Burnell

2021

Preprint

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We study the impact of the inter-level energy constraints imposed by Haldane Exclusion Statistics on relaxation processes in 1-dimensional systems coupled to a bosonic bath. By formulating a second-quantized description of the relevant Fock space, we identify certain universal features of this relaxation dynamics, and show that it is generically slower than that of spinless fermions. Our study focuses on the Calogero-Sutherland model, which realizes Haldane Exclusion statistics exactly in one dimension; however our results apply to any system that has the associated pattern of inter-level occupancy constraints in Fock space.

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Dynamical chaotic phases and constrained quantum dynamics

Cited by 9 publications

References 56 publications

In and out of equilibrium quantum metrology with mean-field quantum criticality

In and out of equilibrium quantum metrology with mean-field quantum criticality

Axiomatic construction of quantum Langevin equations

Many-body constraints and non-thermal behavior in 1D open systems with Haldane exclusion statistics

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