1,944 research outputs found
Distribution of occupation numbers in finite Fermi-systems and role of interaction in chaos and thermalization
New method is developed for calculation of single-particle occupation numbers
in finite Fermi systems of interacting particles. It is more accurate than the
canonical distribution method and gives the Fermi-Dirac distribution in the
limit of large number of particles. It is shown that statistical effects of the
interaction are absorbed by an increase of the effective temperature. Criteria
for quantum chaos and statistical equilibrium are considered. All results are
confirmed by numerical experiments in the two-body random interaction model.Comment: 4 pages, Latex, 4 figures in the form of PS-file
Noninteracting Fermions in infinite dimensions
Usually, we study the statistical behaviours of noninteracting Fermions in
finite (mainly two and three) dimensions. For a fixed number of fermions, the
average energy per fermion is calculated in two and in three dimensions and it
becomes equal to 50 and 60 per cent of the fermi energy respectively. However,
in the higher dimensions this percentage increases as the dimensionality
increases and in infinite dimensions it becomes 100 per cent. This is an
intersting result, at least pedagogically. Which implies all fermions are
moving with Fermi momentum. This result is not yet discussed in standard text
books of quantum statistics. In this paper, this fact is discussed and
explained. I hope, this article will be helpful for graduate students to study
the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010
Radial Spin Helix in Two-Dimensional Electron Systems with Rashba Spin-Orbit Coupling
We suggest a long-lived spin polarization structure, a radial spin helix, and
study its relaxation dynamics. For this purpose, starting with a simple and
physically clear consideration of spin transport, we derive a system of
equations for spin polarization density and find its general solution in the
axially symmetric case. It is demonstrated that the radial spin helix of a
certain period relaxes slower than homogeneous spin polarization and plain spin
helix. Importantly, the spin polarization at the center of the radial spin
helix stays almost unchanged at short times. At longer times, when the initial
non-exponential relaxation region ends, the relaxation of the radial spin helix
occurs with the same time constant as that describing the relaxation of the
plain spin helix.Comment: 9 pages, 7 figure
Sub-milliKelvin spatial thermometry of a single Doppler cooled ion in a Paul trap
We report on observations of thermal motion of a single, Doppler-cooled ion
along the axis of a linear radio-frequency quadrupole trap. We show that for a
harmonic potential the thermal occupation of energy levels leads to Gaussian
distribution of the ion's axial position. The dependence of the spatial thermal
spread on the trap potential is used for precise calibration of our imaging
system's point spread function and sub-milliKelvin thermometry. We employ this
technique to investigate the laser detuning dependence of the Doppler
temperature.Comment: 5 pages, 4 figure
THE AKR THYMIC ANTIGEN AND ITS DISTRIBUTION IN LEUKEMIAS AND NERVOUS TISSUES
A clear-cut serological differentiation between AKR lymphocytes of thymic and non-thymic origin is reported: these two cell types are antigenically distinct. In newborn mice, the AKR thymic antigen was found at a high concentration only in thymus. In adult mice, the antigen was present at a high level in thymus, all nervous tissues tested, and some leukemias. It was present at much lower levels in lymph node lymphocytes, splenic lymphocytes, appendix, lung, and certain other leukemias, which appeared to be of non-thymic origin. The AKR thymic antigen was present at a high level in thymus and nervous tissues of RF mice, but was absent from thymocytes of sixteen other mouse strains. These sixteen strains possessed the C3HeB/Fe thymic antigen. The distribution of this antigen in neonatal and adult tissues of the strains tested was similar to that of the AKR thymic antigen in AKR mice. No exceptions were found. These results were obtained by use of immune cytolysis, and of a new method for the quantitative treatment of data from absorption experiments
Quantum mechanical sum rules for two model systems
Sum rules have played an important role in the development of many branches
of physics since the earliest days of quantum mechanics. We present examples of
one-dimensional quantum mechanical sum rules and apply them in two familiar
systems, the infinite well and the single delta-function potential. These cases
illustrate the different ways in which such sum rules can be realized, and the
varying mathematical techniques by which they can be confirmed. Using the same
methods, we also evaluate the second-order energy shifts arising from the
introduction of a constant external field, namely the Stark effect.Comment: 23 pages, no figures, to appear in Am. J. Phy
The chemical equilibration volume: measuring the degree of thermalization
We address the issue of the degree of equilibrium achieved in a high energy
heavy-ion collision. Specifically, we explore the consequences of incomplete
strangeness chemical equilibrium. This is achieved over a volume V of the order
of the strangeness correlation length and is assumed to be smaller than the
freeze-out volume. Probability distributions of strange hadrons emanating from
the system are computed for varying sizes of V and simple experimental
observables based on these are proposed. Measurements of such observables may
be used to estimate V and as a result the degree of strangeness chemical
equilibration achieved. This sets a lower bound on the degree of kinetic
equilibrium. We also point out that a determination of two-body correlations or
second moments of the distributions are not sufficient for this estimation.Comment: 16 pages, 15 figures, revtex
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 where is the total energy of the system. This
partition function plays the same role as the canonical expression
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.
Quantum Dissipation and Decoherence via Interaction with Low-Dimensional Chaos: a Feynman-Vernon Approach
We study the effects of dissipation and decoherence induced on a harmonic
oscillator by the coupling to a chaotic system with two degrees of freedom.
Using the Feynman-Vernon approach and treating the chaotic system
semiclassically we show that the effects of the low dimensional chaotic
environment are in many ways similar to those produced by thermal baths. The
classical correlation and response functions play important roles in both
classical and quantum formulations. Our results are qualitatively similar to
the high temperature regime of the Caldeira-Leggett model.Comment: 31 pages, 4 figure
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