Van Hove Limit for Infinite Systems

Tománek, David

doi:10.1007/s00023-010-0059-y

Cited by 6 publications

(12 citation statements)

References 24 publications

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“…by applying the time-averaging procedure mentioned in [84]. The NTME (3) carries a sum over two sets of Bohr frequencies as master equations in absence of the secular approximation such as the Bloch-Redfield master equation [11].…”

Section: Nonlinear Extensionmentioning

confidence: 99%

Biexponential decay and ultralong coherence of a qubit

Flakowski

Osmanov

Tománek

et al. 2016

EPL

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A quantum two-state system, weakly coupled to a heat bath, is traditionally studied in the Born-Markov regime under the secular approximation with completely positive linear master equations. Despite its success, this microscopic approach exclusively predicts exponential decays and Lorentzian susceptibility profiles, in disagreement with a number of experimental findings. To leave this limited paradigm, we use a phenomenological positive nonlinear master equation being both thermodynamically and statistically consistent. We find that, beyond a temperature-dependent threshold, a bifurcation in the decoherence time T 2 takes place; it gives rise to a biexponential decay and a susceptibility profile being neither Gaussian nor Lorentzian. This implies that, for suitable initial states, a major prolongation of the coherence can be obtained in agreement with recent experiments. Moreover, T 2 is no longer limited by the energy relaxation time T 1 offering novel perspectives to elaborate devices for quantum information processing.

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Section: Nonlinear Extensionmentioning

confidence: 99%

Biexponential decay and ultralong coherence of a qubit

Flakowski

Osmanov

Tománek

et al. 2016

EPL

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“…We shall report here only the essential physical steps of our approach, while referring the reader to 11–13 for a rigorous and complete derivation.…”

Section: General Frameworkmentioning

confidence: 99%

“…We now proceed according to the following: for reasons explained for example in Ref. 13, dictated by symmetry requirements, we chose to insert such a cut‐off collision time $\overline {t} $ not as an integration boundary but instead as a Gaussian weight, so that, after deriving with respect to current time, we obtain: …”

Section: General Frameworkmentioning

confidence: 99%

“…Also, an alternative symmetrized version of the Markov adiabatic procedure (referred to SM in the following) has been recently proposed, which provides a physically 12 and mathematically 13 robust generalization of Davies work to systems with no spectral restriction, and possibly selected by completely positive conditional expectations other than the partial trace projection.…”

Section: Introductionmentioning

confidence: 99%

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Microscopic theory of energy dissipation and decoherence in solid‐state systems: A reformulation of the conventional Markov limit

Tománek

Iotti

Rossi

2012

Physica Status Solidi (b)

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16 pages, 5 figuresInternational audienceWe present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the proposed alternative adiabatic scheme does not threaten positivity at any time. The key idea of our approach rests in the temporal symmetrization and coarse graining of the scattering term in the Liouville-von Neumann equation, before applying the reduction procedure over the environment degrees of freedom. The resulting dynamics is genuinely Lindblad-like and recovers the Fermi's golden rule features in the semiclassical limit. Applications to the prototypical case of a semiconductor quantum dot exposed to incoherent phonon excitation peaked around a central mode are discussed, highlighting the success of our formalism with respect to the critical issues of the conventional Markov limit

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“…The weak coupling, singular coupling, and low-density limits have been applied and defined primarily for confined systems (typically atoms) coupled to free fermion or free boson baths. There is a compelling reason for this in the case of the weak coupling limit: the Hamiltonian of a confined system has discrete spectrum, and therefore a well-defined time scale t S (given by the maximum of the inverse level spacings); in contrast, extended systems may have continuous spectra, corresponding to arbitrarily slow processes in the uncoupled system dynamics, thus invalidating (1) (see, however, [13] for a different approach). A physical example of this is diffusion, where the relevant time scale is set by a spatial scale.…”

Section: Introductionmentioning

confidence: 99%

Derivation of Some Translation-Invariant Lindblad Equations for a Quantum Brownian Particle

Roeck

Spehner

2012

J Stat Phys

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We study the dynamics of a Brownian quantum particle hopping on an infinite lattice with a spin degree of freedom. This particle is coupled to free boson gases via a translation-invariant Hamiltonian which is linear in the creation and annihilation operators of the bosons. We derive the time evolution of the reduced density matrix of the particle in the van Hove limit in which we also rescale the hopping rate. This corresponds to a situation in which both the system-bath interactions and the hopping between neighboring sites are small and they are effective on the same time scale. The reduced evolution is given by a translation-invariant Lindblad master equation which is derived explicitly.KEY WORDS: out-of-equilibrium quantum statistical physics, open quantum systems, weak coupling limit, singular coupling limit, quantum Brownian motion.

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Van Hove Limit for Infinite Systems

Cited by 6 publications

References 24 publications

Biexponential decay and ultralong coherence of a qubit

Biexponential decay and ultralong coherence of a qubit

Microscopic theory of energy dissipation and decoherence in solid‐state systems: A reformulation of the conventional Markov limit

Derivation of Some Translation-Invariant Lindblad Equations for a Quantum Brownian Particle

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