Spin Relaxation in Phase Space

Kalmykov, Yuri P.; Coffey, W. T.; Titov, S. V.

doi:10.1002/9781119290971.ch2

Cited by 4 publications

(3 citation statements)

References 234 publications

(771 reference statements)

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“…where ŵ(Ω), Ω = (φ, θ) is defined in (19). In the limit of large spins, the Hamiltonian dynamics can be treated semi-classically [20][21][22][23]27]. The equation of motion for the Wigner function of the whole system Wρ (Ω 1 , Ω 2 ) takes the form:…”

Section: Spin-spin Interactionmentioning

confidence: 99%

“…As a rough approach, the evolution of average values can then be estimated within the framework of the so-called Truncated Wigner Approximation (TWA), which consists of propagating points of the initial distribution along the classical trajectories. Such an approximation has been successfully applied for studying a short-time evolution of QS with different dynamic symmetry groups [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Expectably, the TWA fails to describe the non-harmonic evolution beyond the Ehrenfest (or semiclassical) time τ sem , [28][29][30][31][32], where intrinsic quantum correlations effects start to emerge.…”

Section: Introductionmentioning

confidence: 99%

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Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

Morales-Hernández

Castellanos

Romero

et al. 2021

Entropy

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We apply the semi-classical limit of the generalized SO(3) map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on T*S2. Using the asymptotic form of the star-product, we manage to “quantize” one of the classical dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.

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Section: Spin-spin Interactionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

Morales-Hernández

Castellanos

Romero

et al. 2021

Entropy

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“…The dissipative phase-space dynamics of these spinlike systems has been investigated by a number of authors [43,65,66]. Interestingly, the Lindblad evolution can also be recast as a continuity equation with current operators given by Ĵ(±1)…”

Section: A Dissipative Currentsmentioning

confidence: 99%

Quasiprobability currents on the sphere

et al. 2020

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We present analytic expressions for the s-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exploring the appearance of the semiclassical limit in stable, unstable and tunnelling regimes.

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Truncated Wigner approximation as non-positive Kraus map

Klimov¹,

Sainz²,

Romero³

2020

Phys. Scr.

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We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operatorR(t), which does not describe a physical state. The rate of appearance of negative eigenvalues ofR(t) can be efficiently estimated. The short-time dynamics of the Kerr and second harmonic generation Hamiltonains are discussed.

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Spin Relaxation in Phase Space

Cited by 4 publications

References 234 publications

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

Quasiprobability currents on the sphere

Truncated Wigner approximation as non-positive Kraus map

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