Semilinear response for the heating rate of cold atoms in vibrating traps

Stotland, Alexander; Cohen, Doron; Davidson, Nir

doi:10.1209/0295-5075/86/10004

Cited by 10 publications

(28 citation statements)

References 20 publications

(41 reference statements)

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“…The current manuscript is based and reflects a line of study that has been carried out (in chronological order) in collaboration with [33][34][35][36][37][38][39]…”

Section: Acknowledgmentsmentioning

confidence: 99%

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Energy absorption by ‘sparse’ systems: beyond linear response theory

Cohen¹

2012

Phys. Scr.

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The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".

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“…The current manuscript is based and reflects a line of study that has been carried out (in chronological order) in collaboration with [33][34][35][36][37][38][39]…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…The former unlike the latter is not sensitive to the degree of deformation. For details see [38]. the latter is controlled by the degree of deformation or by the disorder in the system.…”

Section: Introductionmentioning

confidence: 99%

Energy absorption by ‘sparse’ systems: beyond linear response theory

Cohen¹

2012

Phys. Scr.

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“…In the WQC regime the matrix F nm is formed of elements that have a log-wide distribution. The implied sparsity is important for the analysis of the EAR [14,24], as expected from semi-linear response theory (SLRT) [29][30][31]. The main idea behind the theory is demonstrated in Fig.2: one observes that the energy absorption process requires connected sequences of transitions between the energy levels of the system.…”

Section: Introductionmentioning

confidence: 99%

“Weak quantum chaos” and its resistor network modeling

2011

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Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with a displaceable wall (piston). The motion is completely chaotic but with a small Lyapunov exponent. The Hamiltonian matrix does not look like one taken from a Gaussian ensemble, but rather it is very sparse and textured. This can be characterized by parameters s and g which reflect the percentage of large elements and their connectivity, respectively. For g we use a resistor network calculation that has a direct relation to the semilinear response characteristics of the system, hence leading to a prediction regarding the energy absorption rate of cold atoms in optical billiards with vibrating walls.

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“…to go beyond the "Wall formula" prediction, taking into account the implications of having t R ≫ t L , which is the case for small deformation (u ≪ 1). The calculation of the actual absorption coefficient G will be done below either within the framework of LRT using the Kubo formula (getting G LRT ), or within the framework of semi-linear response theory (SLRT) [10][11][12] using a resistor-network calculation (getting G SLRT ). The correlations between collisions lead to an LRT result that we would like to write as G LRT = g c G 0 .…”

mentioning

confidence: 99%

“…as seen in Fig.3. The sparsity and the texture of X are important for the analysis of the energy absorption rate [12] as implied by SLRT [10,11]. Accordingly, we suggest to characterize the sparsity by a resistor network measure…”

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confidence: 99%

Quantum response of weakly chaotic systems

Stotland

Pecora

Cohen

2010

EPL

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Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical billiards with vibrating walls. The Hamiltonian matrix of the driven system does not look like one from a Gaussian ensemble, but rather it is very sparse. This sparsity can be characterized by parameters s and gs that reflect the percentage of large elements, and their connectivity respectively. For gs we use a resistor network calculation that has direct relation to the semi-linear response characteristics of the system.

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Semilinear response for the heating rate of cold atoms in vibrating traps

Cited by 10 publications

References 20 publications

Energy absorption by ‘sparse’ systems: beyond linear response theory

Energy absorption by ‘sparse’ systems: beyond linear response theory

“Weak quantum chaos” and its resistor network modeling

Quantum response of weakly chaotic systems

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