Effective Schrodinger equation for one-dimensional systems with rapidly oscillating boundary conditions

Tretyakov, N. P.; Golosov, P. E.; Kochanov, Anton

doi:10.1109/icumt.2018.8631204

Cited by 1 publication

(8 citation statements)

References 21 publications

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“…⟩ (these terms are proportional to μ, but the solutions (19) are inversely proportional to μ, so that the result is a zero-order term in μ). Here we need to use the orthonormality properties of trigonometric functions:…”

Section:  mentioning

confidence: 99%

“…The calculation technique repeats that used in [19] and has as a starting point the equation (40) proposed by Di Martino and Facchi in [20]. Consider a particle confined in a moving and dilating box, subject to the action of a (time-independent) potential V(x), i.e.…”

Section: Particle In a Potential Box With Oscillating Widthmentioning

confidence: 99%

“…In [19] we considered the special case when the width of the box remains constant: ℓ 1 = ℓ 2 = 0. Now let us consider the case when the position of the center of the box remains constant, while its width oscillates:…”

Section: Particle In a Potential Box With Oscillating Widthmentioning

confidence: 99%

“…As mentioned in [19], in studies of nonstationary quantum systems, there is a gap between the consideration of systems with nonstationary Hamiltonians and systems with nonstationary boundary conditions [20] (or, more generally, boundary driven quantum systems [21]) and currently, these two areas are engaged in different groups of researchers.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, a correct approach was developed in [16,20,23] to derive effective static Schrödinger equations for such systems. In [19], we considered the one-dimensional motion of a particle in a potential box with movable walls, which equation of motion is reduced to an effective Schrödinger equation with stationary boundary conditions. Note that, as far as we know, this was the first application of the effective Schrödinger equation method to systems with fast nonstationary boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Fast driven quantum systems: interaction picture and boundary conditions

Tretyakov¹

2021

Phys. Scr.

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The work continues systematic applications of the method developed by Di Martino and Facchi (2015) for obtaining, for systems with variable boundary conditions, an equivalent Schrödinger equation with constant boundary conditions. From the resulting equation with rapidly varying terms, an effective equation is then derived for the averaged (slowly varying) wave functions. In this work, we obtain this effective equation for rapidly driven systems in the interaction picture (in first order in reverse frequency of external driving). This is the most suitable picture for systems with external driving. As an example, an extended two-state fast driven system is considered. As a second example, we consider the one-dimensional motion of a particle in a potential box with high-frequency oscillations of its width. Oscillations of width lead to additional terms in the effective equation proportional not only to the second derivative of the potential, but to the first derivative as well. In the case of width oscillations, compared to the oscillations of the box as a whole, the changes are even more significant. In our examples, phenomena such as slow averaged oscillations, resonance, the appearance of volcano potentials are observed, as is often the case in driven systems.

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Section:  mentioning

confidence: 99%

Section: Particle In a Potential Box With Oscillating Widthmentioning

confidence: 99%

Section: Particle In a Potential Box With Oscillating Widthmentioning

confidence: 99%