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| Description
| - Uvažujeme kvanotvý hamiltonián ve tvaru H(t)=H+V(t) takový, že spektrum H je poloomezené a diskrétní a vlastní hodnototy se chovají jako E_n~n^a, kde 0<a<1. Speciálně to znamená, že mezery mezi následnými vlastními hodnotami klesají jako n^{a-1}. O V(t) se předpokládá, že je periodický, omezený a spojitě diferencovatlný v silném smyslu a že jeho maticové prvky vzhledem k spektrálnímu rozkladu H splňují odhad ||V (t)_{m,n}|| <= eps |m - n|^{-p} max{m, n}^{-2 g} pro m != n, kde eps > 0, p >= 1 a g = (1 - a)/2. Ukazujeme, že exponent difuze energie může být libovolně malý, pokud p je dostatečně velké a eps je dostatečně malé. Přesněji, pro každou počáteční podmínou Psi z Dom(H^{1/2}) difuze energie splňuje horní odhad <H>_Psi(t) = O(t^s ), kde s = a/(2[p -1] g - 1/2). Jako aplikaci uvažujeme hamiltonián H (t) = |p|^a + eps v(q,t) na L^2(S^1, dq), kerý byl v literatuře dřive diskutován Howlandem. (cs)
- We consider quantum Hamiltonians of the form H (t) = H + V (t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n ~ n^a , with 0 < a < 1. In particular, the gaps between successive eigenvalues decay as n^{a-1}. V (t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate ||V (t)_{m,n}|| <= eps |m - n|^{-p} max{m, n}^{-2 g} for m != n, where eps > 0, p >= 1 and g = (1 - a)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and eps is small enough. More precisely, for any initial condition Psi in Dom(H^{1/2}), the diffusion of energy is bounded from above as <H>_Psi(t) = O(t^s ), where s = a/(2[p -1] g - 1/2). As an application we consider the Hamiltonian H (t) = |p|^a + eps v(q,t) on L^2(S^1, dq) which was discussed earlier in the literature by Howland.
- We consider quantum Hamiltonians of the form H (t) = H + V (t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n ~ n^a , with 0 < a < 1. In particular, the gaps between successive eigenvalues decay as n^{a-1}. V (t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate ||V (t)_{m,n}|| <= eps |m - n|^{-p} max{m, n}^{-2 g} for m != n, where eps > 0, p >= 1 and g = (1 - a)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and eps is small enough. More precisely, for any initial condition Psi in Dom(H^{1/2}), the diffusion of energy is bounded from above as <H>_Psi(t) = O(t^s ), where s = a/(2[p -1] g - 1/2). As an application we consider the Hamiltonian H (t) = |p|^a + eps v(q,t) on L^2(S^1, dq) which was discussed earlier in the literature by Howland. (en)
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| Title
| - On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum
- O růstu energie některých kvantových systémů s periodickou vnější silou a zmenšujícími se mezerami ve spektru (cs)
- On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum (en)
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| skos:prefLabel
| - On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum
- O růstu energie některých kvantových systémů s periodickou vnější silou a zmenšujícími se mezerami ve spektru (cs)
- On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum (en)
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| skos:notation
| - RIV/68407700:21340/08:04136016!RIV09-MSM-21340___
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(GA201/05/0857), Z(MSM6840770039)
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| http://linked.open...iv/cisloPeriodika
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/68407700:21340/08:04136016
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - discrete spectrum; energy growth (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...odStatuVydavatele
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/nazevZdroje
| - Journal of Statistical Physics
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...v/svazekPeriodika
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| http://linked.open...iv/tvurceVysledku
| - Šťovíček, Pavel
- Duclos, P.
- Lev, O.
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| http://linked.open...ain/vavai/riv/wos
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| http://linked.open...n/vavai/riv/zamer
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| issn
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| number of pages
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| http://localhost/t...ganizacniJednotka
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