Time evolution of the classical and quantum mechanical versions of diffusive anharmonic oscillator: an example of Lie algebraic techniques

Faria, J. G. Peixoto de

doi:10.1140/epjd/e2006-00278-8

Cited by 19 publications

(19 citation statements)

References 30 publications

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“…Their response to this question was that in a coarse grain approach, the quantum state may behave classically if we consider an ensemble of trajectories. Those results were later confirmed by others [12,19,[21][22][23][24][25]. Ballentine and collaborators also argue that the decoherence is not necessary if we take into account the experimental limitations.…”

Section: Introductionsupporting

confidence: 66%

“…The idea of studying such mixture state is that a Fock state |M is always a pure state, but it can be as quantum as we want, as we have shown in eq. (19). Alternatively, ρ β is a pure state only in the limit T → 0 + , namely the coherent state.…”

Section: Roughness × Negativity: a Comparative Studymentioning

confidence: 99%

“…In order to investigate the dynamical aspects, we use the quartic oscillator model (Kerr oscillator), which was the object of many investigations [12,19,21,22,25,33,[94][95][96][97][98][99][100] with expressive experimental results [101]. The Hamiltonian is given bŷ…”

Section: Dynamic Distance Measure: the Quartic Modelmentioning

confidence: 99%

“…Zurek and Paz [17,18] argue that the quantum system is never isolated, and thus the dynamics of a macroscopic object is modified by the surrounding objects that interact with it. This is the Decoherence Approach to Classical Limit of Quantum Mechanics [17][18][19][20][21][22][23][24][25]. Up to our knowledge, Ballentine and collaborators [26][27][28][29][30] where the first to address the question of which classical dynamics would be reproduced by Quantum Mechanics, a trajectory or an ensemble of them.…”

Section: Introductionmentioning

confidence: 99%

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Roughness as classicality indicator of a quantum state

et al. 2018

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We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the L 2 (R 2 ) distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [0,1], being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number of photons is arbitrarily large, and also for squeezed states at the maximum compression limit. On the other hand, the Roughness reaches its minimum value for thermal states at infinite temperature and, more generally, for infinite entropy states. The Roughness of a coherent state is slightly below one half, so we may say that it is more a classical state than a quantum one. Another important result is that the Roughness performs well for discriminating both pure and mixed states. Since the Roughness measures the inherent quantumness of a state, we propose another function, the Dynamic Distance Measure (DDM), which is suitable for measure how much quantum is a dynamics. Using DDM, we studied the quartic oscillator, and we observed that there is a certain complementarity between dynamics and state, i.e. when dynamics becomes more quantum, the Roughness of the state decreases, while the Roughness grows as the dynamics becomes less quantum.

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Section: Introductionsupporting

confidence: 66%

Section: Roughness × Negativity: a Comparative Studymentioning

confidence: 99%

Section: Dynamic Distance Measure: the Quartic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Roughness as classicality indicator of a quantum state

et al. 2018

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“…Next we apply the rotating frame transformation (2). The key property making this problem analytically tractable and free of the aforementioned positivity issues is that the 7 superoperators {H i , D i } form a closed algebra [55] (see also [56]). In particular, the sets {H i } and {D i }, when taken separately, satisfy independent algebras:…”

Section: Application To a Harmonic Oscillatormentioning

confidence: 99%

Lindblad-Floquet description of finite-time quantum heat engines

2018

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The operation of autonomous finite-time quantum heat engines rely on the existence of a stable limit cycle in which the dynamics becomes periodic. The two main questions that naturally arise are therefore whether such a limit cycle will eventually be reached and, once it has, what is the state of the system within the limit cycle. In this paper we show that the application of Floquet's theory to Lindblad dynamics offers clear answers to both questions. By moving to a generalized rotating frame, we show that it is possible to identify a single object, the Floquet Liouvillian, which encompasses all operating properties of the engine. First, its spectrum dictates the convergence to a limit cycle. And second, the state within the limit cycle is precisely its zero eigenstate, therefore reducing the problem to that of determining the steady-state of a time-independent master equation.To illustrate the usefulness of this theory, we apply it to a harmonic oscillator subject to a time-periodic work protocol and time-periodic dissipation, an open-system generalization of the Ermakov-Lewis theory. The use of this theory to implement a finite-time Carnot engine subject to continuous frequency modulations is also discussed.

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Nonclassicality via the Superpositions of Photon Addition and Subtraction and Quantum Decoherence for Thermal Noise

et al. 2020

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Two new photon-modulated states are introduced by operating a more general coherent superposition (a + ra †) m on two classical states (coherent and thermal) and their nonclassicality caused by the operation (a + ra †) m is investigated via examining the squeezing, sub-Poissonian statistics, nonclassical depth, and negativity of Wigner distribution. Their density-operator and Wigner-distribution evolutions in the thermal channel are also explored. It is found that the high-order operation (a + ra †) m has better performance in creating nonclassicality for certain ratios r and more robustness against decoherence of the two photon-modulated states for thermal noise. For convenience, a new three-variable special polynomial and its generating function are introduced via the normal ordering of operators.

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Time evolution of the classical and quantum mechanical versions of diffusive anharmonic oscillator: an example of Lie algebraic techniques

Cited by 19 publications

References 30 publications

Roughness as classicality indicator of a quantum state

Roughness as classicality indicator of a quantum state

Lindblad-Floquet description of finite-time quantum heat engines

Nonclassicality via the Superpositions of Photon Addition and Subtraction and Quantum Decoherence for Thermal Noise

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