Geometry of quantum evolution in a nonequilibrium environment

X, Cai; Meng, Ruixuan; Zhang, Yanhui; Wang, Lifei

doi:10.1209/0295-5075/125/30007

Cited by 18 publications

(13 citation statements)

References 83 publications

(114 reference statements)

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“…in agreement with the expression (115), where the minimum is attained by the amplitudes w(s) fulfilling the parallel transport condition (118). This is the Bures metric.…”

Section: The Bures Metricsupporting

confidence: 81%

Geometry of quantum phase transitions

2020

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In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions, whereas in NESS-QPTs this distinction may fade off. The approach described in this review, among other things, can quantitatively assess the quantum character of such critical phenomena. This framework is applied to a paradigmatic class of lattice Fermion systems with local reservoirs, characterised by Gaussian non-equilibrium steady states. The relations between the behaviour of the geometric phase curvature, the divergence of the correlation length, the character of the criticality and the gap-either Hamiltonian or dissipative-are reviewed.

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“…in agreement with the expression (115), where the minimum is attained by the amplitudes w(s) fulfilling the parallel transport condition (118). This is the Bures metric.…”

Section: The Bures Metricsupporting

confidence: 81%

Geometry of quantum phase transitions

2020

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“…Hence, it is necessary to take into extensive consideration the memory effects of the environment, namely, the non-Markovian statistical properties of the environmental noise, to study the dynamical evolution of the quantum system. Recently, the non-Markovian RTN with an exponentially correlated memory kernel has been discussed [57] and widely used to study the relevant issues of open quantum systems [58][59][60][61][62].…”

Section: Introductionmentioning

confidence: 99%

Quantum dephasing induced by non-Markovian random telegraph noise

2020

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We theoretically study the dynamical dephasing of a quantum two level system interacting with an environment exhibiting non-Markovian random telegraph fluctuations. The time evolution of the conditional probability of the environmental noise is governed by a generalized master equation depending on the environmental memory effect. The expression of the dephasing factor is derived exactly which is closely associated with the memory kernel in the generalized master equation for the conditional probability of the environmental noise. In terms of three important types memory kernels, we discuss the quantum dephasing dynamics of the system and the non-Markovian character exhibiting in the dynamical dephasing induced by non-Markovian random telegraph noise. We show that the dynamical dephasing of the quantum system does not always exhibit non-Markovian character which results from that the non-Markovian character in the dephasing dynamics depends both on the environmental non-Markovian character and the interaction between the system and environment. In addition, the dynamical dephasing of the quantum system can be modulated by the external modulation frequency of the environment. This result is significant to quantum information processing and helpful for further understanding non-Markovian dynamics of open quantum systems.

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“…For instance, in physical systems, the transient and ultra-fast dynamical processes can happen on sufficiently short periods such that the initial non-equilibrium state induced by system-environment coupling may not have the ability to return to equilibrium [30][31][32][33][34][35][36]. Moreover, in the recent years, it was shown that non-equilibrium feature of environment with non-stationary statistical properties gives rise to frequency shift which has a dominant effect on the reducing of decoherence effects, quantum speed limits and geometric phase of the quantum systems [37][38][39][40]. To the best of our knowledge, phenomena of freezing discord and sudden transition from classical to quantum decoherence in the presence of non-equilibrium environments have not been studied yet.…”

Section: Introductionmentioning

confidence: 99%

Controlling sudden transition from classical to quantum decoherence via non-equilibrium environments

et al. 2020

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We investigate the freezing and sudden transition in the dynamical behavior of quantum and classical correlations in a system composed of two identical non-interacting qubits locally subjected to their own non-equilibrium environments. In contrast to the equilibrium case, one can observe striking results when a bipartite quantum system couples with the non-equilibrium dephasing environment with non-stationary and non-Markovian features. Remarkably, the finite time interval in which the quantum correlation remains impervious to decoherence can be further prolonged as the environment deviates from equilibrium. This reveals that the non-equilibrium parameter provides an alternative tool to efficiently control the appearance of a sudden transition in the decay rates of correlations and their immunity towards the decoherence. Furthermore, for certain initial states, the appearance of another time-interval over which quantum correlation remains constant and the revival of classical correlation not only depends on the non-Markovianity but also on the non-equilibrium parameter.

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Geometry of quantum evolution in a nonequilibrium environment

Cited by 18 publications

References 83 publications

Geometry of quantum phase transitions

Geometry of quantum phase transitions

Quantum dephasing induced by non-Markovian random telegraph noise

Controlling sudden transition from classical to quantum decoherence via non-equilibrium environments

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