O růstu energie některých kvantových systémů s periodickou vnější silou a zmenšujícími se mezerami ve spektru

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F08%3A04136016" target="_blank" >RIV/68407700:21340/08:04136016 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum

Popis výsledku v původním jazyce

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, whereeps > 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.

Název v anglickém jazyce

On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum

Popis výsledku anglicky

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, whereeps > 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F05%2F0857" target="_blank" >GA201/05/0857: Aplikace algebraických a funkcionálně analytických metod v matematické fyzice</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2008

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Statistical Physics

ISSN

0022-4715

e-ISSN

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Svazek periodika

130

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

25

Strana od-do

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Kód UT WoS článku

000251308800008

EID výsledku v databázi Scopus

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