Decoherence and Thermalization

Merkli, Marco; Sigal, Israel Michael; Berman, G. P.

doi:10.1103/physrevlett.98.130401

Cited by 53 publications

(93 citation statements)

References 30 publications

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“…We show in Theorem 2.1 that this limit exists, and that for all t ≥ 0, e } ≤ ω ′ < τ , with τ > 0 a constant depending on the regularity of g 1 , g 2 (see Condition (A2) in Section 2, and also [16]). The * in the sum (1.17) means that we sum only over configurations σ ′ , τ ′ such that e( σ ′ , τ ′ ) = −e.…”

Section: Introductionmentioning

confidence: 89%

“…Note that if λ 2 = 0 then matrix elements associated to energy differences e such that e 0 = 0 will not decay on the time scale given by the second order in the perturbation (λ 2 1 ). We point out that generically, S + R will reach a joint equilibrium as t → ∞, which means that the final reduced density matrix of S is its Gibbs state modulo a peturbation of the order of the interaction between S and R, see [16]. Hence generically, the density matrix of S does not become diagonal in the energy basis as t → ∞.…”

Section: Introductionmentioning

confidence: 96%

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Dynamics of collective decoherence and thermalization

2008

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We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N 2 , while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N . For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born-or weak coupling (van Hove) approximations.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 96%

Dynamics of collective decoherence and thermalization

2008

Self Cite

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“…Especially H.Primas noted the necessity to regard already large molecules as open systems in interaction with and entangled with the environment, [P75]. Modern rigorous works, relevant in the context of opensystem dynamics are [BO03], the chapter in [AJP06] vol.III by the same authors, [MSB07,O08] and the above mentioned [CSU11].…”

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confidence: 99%

The Structures of State Space Concerning Quantum Dynamical Semigroups

Baumgartner

Narnhofer

2012

Rev. Math. Phys.

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Each semigroup describing time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into orthogonal subspaces: One part is related to decay, some subspaces of the other subspace are ranges of the stationary states. Specialities are highlighted where the complete positivity of evolutions is actually needed for analysis, mainly for evolution of coherence. Decompositions are done the same way for discrete as for continuous time evolutions, but they may show differences: Only for discrete semigroups there may appear cases of sudden decay and of perpetual oscillation. Concluding the analysis we identify the relation of the state space structure to the processes of Decay, Decoherence, Dissipation and Dephasing.

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“…Recently, much attention has been paid to quantum thermalization (e.g., Refs. [4][5][6][7][8][9][10][11][12]). Specifically, a new kind of thermalization, called canonical thermalization (e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Quantum thermalization of two coupled two-level systems in eigenstate and bare-state representations

2011

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We study analytically the quantum thermalization of two coupled two-level systems (TLSs), which are connected with either two independent heat baths (IHBs) or a common heat bath (CHB). We understand the quantum thermalization in eigenstate and bare-state representations when the coupling between the two TLSs is stronger and weaker than the TLS-bath couplings, respectively. In the IHB case, we find that when the two IHBs have the same temperatures, the two coupled TLSs in eigenstate representation can be thermalized with the same temperature as those of the IHBs. However, in the case of two IHBs at different temperatures, just when the energy detuning between the two TLSs satisfies a special condition, the two coupled TLSs in eigenstate representation can be thermalized with an immediate temperature between those of the two IHBs. In bare-state representation, we find a counterintuitive phenomenon that, under some conditions, the temperature of the TLS connected with the high-temperature bath is lower than that of the other TLS, which is connected with the low-temperature bath. In the CHB case, the coupled TLSs in eigenstate representation can be thermalized with the same temperature as that of the CHB in nonresonant cases. In bare-state representation, the TLS with a larger energy separation can be thermalized to a thermal equilibrium with a lower temperature. In the resonant case, we find a phenomenon of anti-thermalization. We also study the steady-state entanglement between the two TLSs in both the IHB and CHB cases.

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Decoherence and Thermalization

Cited by 53 publications

References 30 publications

Dynamics of collective decoherence and thermalization

Dynamics of collective decoherence and thermalization

The Structures of State Space Concerning Quantum Dynamical Semigroups

Quantum thermalization of two coupled two-level systems in eigenstate and bare-state representations

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