Resonance theory of decoherence and thermalization

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

doi:10.1016/j.aop.2007.04.013

Cited by 43 publications

(134 citation statements)

References 37 publications

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“…Any real measurement requires finite time and involves interactions with measuring devices and observers [6,[36][37][38][39]. Even the so-called nondemolition and nondestructive measurements may essentially influence the measured system [40][41][42][43]. In what follows, the environment, including measuring apparatuses and observers, acting on the system in the process of measurement, will be called for short a measurer.…”

Section: Quantum State Reductionmentioning

confidence: 99%

Quantum probabilities of composite events in quantum measurements with multimode states

Yukalov

Sornette

2013

Laser Phys.

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The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that the Lüders probability of consecutive measurements is a transition probability between two quantum states and that this probability cannot be treated as a quantum extension of the classical conditional probability. The Wigner distribution is shown to be a weighted transition probability that cannot be accepted as a quantum extension of the classical joint probability. We suggest the definition of quantum joint probabilities by introducing composite events in multichannel measurements. The notion of measurements under uncertainty is defined. We demonstrate that the necessary condition for the mode interference is the entanglement of the composite prospect together with the entanglement of the composite statistical state. As an illustration, we consider an example of a quantum game. A special attention is payed to the application of the approach to systems with multi-mode states, such as atoms, molecules, quantum dots, or trapped Bose-condensed atoms with several coherent modes.

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Section: Quantum State Reductionmentioning

confidence: 99%

Quantum probabilities of composite events in quantum measurements with multimode states

Yukalov

Sornette

2013

Laser Phys.

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“…In the dynamical theory of quantum resonances, the resonances (complex energy eigenvalues) associated to the Liouville operator are determined using spectral deformation-or Mourre theory [13,12,4,16,15]. In order not to muddle the core ideas of the current work, we follow here the technically least complicated situation, where the Hamiltonian is "translation deformation analytic" [13,4].…”

Section: Resultsmentioning

confidence: 99%

“…For instance, the invariant state of the latter is typically the uncoupled system Gibbs equilibrium state, while the true asymptotic state is the restriction of the coupled system-environment equilibrium to the system alone. A more recent dynamical resonance theory [12,16] improves the weak coupling result to…”

Section: The Issuementioning

confidence: 99%

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Completely positive dynamical semigroups and quantum resonance theory

Könenberg

Merkli

2017

Lett Math Phys

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Abstract. Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the following two properties: It is (linearly) small in the system-environment coupling constant for all times, and it vanishes exponentially quickly in the large time limit. Our approach is based on the quantum dynamical resonance theory. The issueDue to the entanglement of an open system with its surroundings, its dynamics V (t) : ρ 0 → ρ t , mapping an initial system density matrix ρ 0 to its value at time t, is not a semigroup in time. For each fixed t, the mapping V (t), called a dynamical map, is a linear, completely positive, trace preserving transformation. 1 Under certain assumptions, one can approximate the dynamics of an open system by a continuous one-parameter semigroup of dynamical maps, called a quantum dynamical semigroup [5,11]. The dynamics given by such a semigroup has two important features: (i) is it markovian due to the semigroup property and (ii) it maps density matrices into density matrices due to its trace and positivity preserving quality. Complete positivity of the dynamical semigroup implies its positivity preservation, but not vice-versa. It is a crucial physical property which ensures that the dynamics of initially entangled systems interacting with an environment is well defined [1,3]. The semigroup property is particularly convenient since the spectral analysis of the generator L of the semigroup yields dynamical properties of the system, such as the final state(s) and convergence speeds. Controlling the remainder in the approximation V (t)ρ 0 ≈ e tL ρ 0 rigorously is difficult. Microscopic derivations, passing from a full (hamiltonian) model of system plus environment and tracing out the environment degrees of freedom, involve approximations (Born, Markov, rotating wave) that are hard to deal with mathematically. In some situations where the system-environment interaction is weak, measured by a small coupling constant λ, one can implement a (time-dependent) perturbation theory, λ = 0 giving the unperturbed (uncoupled) case. For certain systems it has been shown [7] that for all a > 0, lim

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“…In contrast, we work in the context of open quantum systems, and therefore the effective small system does not even have a Hamiltonian. While there has been work on resonances and decoherence in open quantum systems, such as [2] and [14,15], all authors seem to rely on the spectral structure of the full Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Effective Density of States for a Quantum Oscillator Coupled to a Photon Field

Betz

Castrigiano

2010

Commun. Math. Phys.

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Abstract. We give an explicit formula for the effective partition function of a harmonically bound particle minimally coupled to a photon field in the dipole approximation. The effective partition function is shown to be the Laplace transform of a positive Borel measure, the effective measure of states. The absolutely continuous part of the latter allows for an analytic continuation, the singularities of which give rise to resonances. We give the precise location of these singularities, and show that they are well approximated by of first order poles with residues equal the multiplicities of the corresponding eigenspaces of the uncoupled quantum oscillator. Thus we obtain a complete analytic description of the natural line spectrum of the charged oscillator.

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Resonance theory of decoherence and thermalization

Cited by 43 publications

References 37 publications

Quantum probabilities of composite events in quantum measurements with multimode states

Quantum probabilities of composite events in quantum measurements with multimode states

Completely positive dynamical semigroups and quantum resonance theory

Effective Density of States for a Quantum Oscillator Coupled to a Photon Field

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