Statistical Theory of Finite Fermi-Systems Based on the Structure of Chaotic Eigenstates

The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by the interaction between particles. New type of ``microcanonical'' partition function is introduced and expressed in terms of the average shape of eigenstates $F(E_k,E)$ where $E$ is the total energy of the system. This partition function plays the same role as the canonical expression $exp(-E^{(i)}/T)$ for open systems in thermal bath. The approach allows to calculate mean values and non-diagonal matrix elements of different operators. In particular, the following problems have been considered: distribution of occupation numbers and its relevance to the canonical and Fermi-Dirac distributions; criteria of equilibrium and thermalization; thermodynamical equation of state and the meaning of temperature, entropy and heat capacity, increase of effective temperature due to the interaction. The problems of spreading widths and shape of the eigenstates are also studied.Comment: 17 pages in RevTex and 5 Postscript figures. Changes are RevTex format (instead of plain LaTeX), minor misprint corrections plus additional references. To appear in Phys. Rev.

Nuclear Anapole Moments in Single Particle Approximation

Nuclear anapole moments of $\;^{133}$Cs, $\;^{203,205}$Tl, $\;^{207}$Pb, $\;^{209}$Bi are treated in the single-particle approximation. Analytical results are obtained for the oscillator potential without spin-orbit interaction. Then the anapole moments are calculated numerically in a Woods-Saxon potential which includes spin-orbit interaction. The results obtained demonstrate a remarkable stability of nuclear anapole moment calculations in the single-particle approximation.Comment: 20 pages, LateX, One figure available upon request, BINP-93-11

Variation of fundamental constants in space and time: theory and observations

Review of recent works devoted to the temporal and spatial variation of the fundamental constants and dependence of the fundamental constants on the gravitational potential (violation of local position invariance) is presented. We discuss the variation of the fine structure constant $\alpha=e^2/\hbar c$, strong interaction and fundamental masses (Higgs vacuum), e.g. the electron-to-proton mass ratio $\mu=m_e/M_p$ or $X_e=m_e/\Lambda_{QCD}$ and $X_q=m_q/\Lambda_{QCD}$. We also present new results from Big Bang nucleosynthesis and Oklo natural nuclear reactor data and propose new measurements of enhanced effects in atoms, nuclei and molecules, both in quasar and laboratory spectra.Comment: Proceeding of ACFC, BadHonnef, 2007: to be published in EP

Comment on "Black hole constraints on varying fundamental constants"

In the Letter [1] (also [2]) there is a claim that the generalised second law of thermodynamics (entropy increase) for black holes provides some limits on the rate of variation of the fundamental constants of nature (electric charge e, speed of light c, etc.). We have come to a different conclusion. The results in [1,2] are based on assumption that mass of a black hole does not change without radiation and accreation. We present arguments showing that this assumption is incorrect and give an estimate of the black hole mass variation due to alpha=e^2/\hbar c variation using entropy (and quantum energy level) conservation in an adiabatic process. No model-independent limits on the variation of the fundamental constants are derived from the second law of thermodynamics.Comment: Comment on arXiv:0706.2188 [PRL 99, 061301] by Jane MacGibbo

Return probability: Exponential versus Gaussian decay

We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the Gaussian decay of the return probability, and another one is the well known regime of the exponential decay. Our analytical estimates are confirmed by the numerical data obtained for two models with random interaction. In view of these results, we also briefly discuss the dynamical model which was recently proposed for the implementation of a quantum computation.Comment: 9 pages, 7 figures; revised version accepted for publicatio

Many-body corrections to the nuclear anapole moment II

The contribution of many-body effects to the nuclear anapole moment were studied earlier in [1]. Here, more accurate calculation of the many-body contributions is presented, which goes beyond the constant density approximation for them used in [1]. The effects of pairing are now included. The accuracy of the short range limit of the parity violating nuclear forces is discussed.Comment: 18 pages, LateX2e, 7 figure

The anapole moment and nucleon weak interactions

From the recent measurement of parity nonconservation (PNC) in the Cs atom we have extracted the constant of the nuclear spin dependent electron-nucleon PNC interaction, $\kappa = 0.442 (63)$; the anapole moment constant, $\kappa_a = 0.364 (62)$; the strength of the PNC proton-nucleus potential, $g_p = 7.3 \pm 1.2 (exp.) \pm 1.5 (theor.)$; the $\pi$-meson-nucleon interaction constant, $f_\pi \equiv h_\pi^{1} = [9.5 \pm 2.1 (exp.) \pm 3.5 (theor.)] \times 10^{-7}$; and the strength of the neutron-nucleus potential, $g_n = -1.7 \pm 0.8 (exp.) \pm 1.3 (theor.)$.Comment: Uses RevTex, 12 pages. We have added an explanation of the effect of finite nuclear siz