Nonexponential decay law of unstable multilevel quantum-systems at long times(2) Equilibrium and nonequilibrium statistical mechanics in systems showing chaos and quantum chaos, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

この論文は国立情報学研究所の電子図書館事業により電子化されました。不安定多準位系における生存確率S(t)の長時間での崩壊様式をN準位Friedrichsモデルに基づき解析する.不安定多準位上にまたがった任意の初期状態に対し,S(t)の長時間での漸近形を求め,それが初期状態の不安定準位の占有の仕方にどのように依存するかを明らかにする.このとき特にS(t)の漸近形を最大化する初期状態が存在することを指摘する.一方その漸近展開の第一項目を消してしまう特別な初期状態も存在する.この場合,従来知られている崩壊則よりも速い崩壊則が得られることが期待される.そこで実際に水素原子からの光子の自熱放出過程を例に,この速い崩壊則を含む崩壊様式の初期状態依存性を数値的に確認する

Zero energy resonance and the logarithmically slow decay of unstable multilevel systems

The long time behavior of the reduced time evolution operator for unstable multilevel systems is studied based on the N-level Friedrichs model in the presence of a zero energy resonance.The latter means the divergence of the resolvent at zero energy. Resorting to the technique developed by Jensen and Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is characterized by the zero energy eigenstate that does not belong to the Hilbert space. It is then shown that for some kinds of the rational form factors the logarithmically slow decay of the reduced time evolution operator can be realized.Comment: 31 pages, no figure

Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems

The long-time behavior of the survival probability for unstable multilevel systems that follows the power-decay law is studied based on the N-level Friedrichs model, and is shown to depend on the initial population in unstable states. A special initial state maximizing the asymptote of the survival probability at long times is found and examined by considering the spontaneous emission process for the hydrogen atom interacting with the electromagnetic field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.

Dynamic cerebral autoregulation during cognitive task:Effect of hypoxia

Changes in cerebral blood flow (CBF) subsequent to alterations in the partial pressures of oxygen and carbon dioxide can modify dynamic cerebral autoregulation (CA). While cognitive activity increases CBF, the extent to which it impacts CA remains to be established. In the present study we determined whether dynamic CA would decrease during a cognitive task and whether hypoxia would further compound impairment. Fourteen young healthy subjects performed a simple Go/No-go task during normoxia and hypoxia (inspired O2 fraction = 12%), and the corresponding relationship between mean arterial pressure (MAP) and mean middle cerebral artery blood velocity (MCA Vmean) was examined. Dynamic CA and steady-state changes in MCA V in relation to changes in arterial pressure were evaluated with transfer function analysis. While MCA Vmean increased during the cognitive activity ( P &lt; 0.001), hypoxia did not cause any additional changes ( P = 0.804 vs. normoxia). Cognitive performance was also unaffected by hypoxia (reaction time, P = 0.712; error, P = 0.653). A decrease in the very low- and low-frequency phase shift (VLF and LF; P = 0.021 and P = 0.01) and an increase in LF gain were observed ( P = 0.037) during cognitive activity, implying impaired dynamic CA. While hypoxia also increased VLF gain ( P &lt; 0.001), it failed to cause any additional modifications in dynamic CA. Collectively, our findings suggest that dynamic CA is impaired during cognitive activity independent of altered systemic O2 availability, although we acknowledge the interpretive complications associated with additional competing, albeit undefined, inputs that could potentially distort the MAP-MCA Vmean relationship. NEW &amp; NOTEWORTHY During normoxia, cognitive activity while increasing cerebral perfusion was shown to attenuate dynamic cerebral autoregulation (CA) yet failed to alter reaction time, thereby questioning its functional significance. No further changes were observed during hypoxia, suggesting that impaired dynamic CA occurs independently of altered systemic O2 availability. However, impaired dynamic CA may reflect a technical artifact, given the confounding influence of additional inputs that could potentially distort the mean arterial pressure-mean middle cerebral artery blood velocity relationship. </jats:p

Quasienergy anholonomy and its application to adiabatic quantum state manipulation

The parametric dependence of a quantum map under the influence of a rank-1 perturbation is investigated. While the Floquet operator of the map and its spectrum have a common period with respect to the perturbation strength $\lambda$, we show an example in which none of the quasienergies nor the eigenvectors obey the same period: After a periodic increment of $\lambda$, the quasienergy arrives at the nearest higher one, instead of the initial one, exhibiting an anholonomy, which governs another anholonomy of the eigenvectors. An application to quantum state manipulations is outlined.Comment: 10pages, 1figure. To be published in Phys. Rev. Lett

Cheon's anholonomies in Floquet operators

Anholonomies in the parametric dependences of the eigenvalues and the eigenvectors of Floquet operators that describe unit time evolutions of periodically driven systems, e.g., kicked rotors, are studied. First, an example of the anholonomies induced by a periodically pulsed rank-1 perturbation is given. As a function of the strength of the perturbation, the perturbed Floquet operator of the quantum map and its spectrum are shown to have a period. However, we show examples where each eigenvalue does not obey the periodicity of the perturbed Floquet operator and exhibits an anholonomy. Furthermore, this induces another anholonomy in the eigenspaces, i.e., the directions of the eigenvectors, of the Floquet operator. These two anholonomies are previously observed in a family of Hamiltonians [T. Cheon, Phys. Lett. A 248, 285 (1998)] and are different from the phase anholonomy known as geometric phases. Second, the stability of Cheon's anholonomies in periodically driven systems is established by a geometrical analysis of the family of Floquet operators. Accordingly, Cheon's anholonomies are expected to be abundant in systems whose time evolutions are described by Floquet operators. As an application, a design principle for quantum state manipulations along adiabatic passages is explained