2,161 research outputs found
Transition from Tonks-Girardeau gas to super-Tonks-Girardeau gas as an exact many-body dynamics problem
We investigate transition of a one-dimensional interacting Bose gas from a
strongly repulsive regime to a strongly attractive regime, where a stable
highly excited state known as the super Tonks-Girardeau gas was experimentally
realized very recently. By solving exact dynamics of the integrable
Lieb-Liniger Bose gas, we demonstrate that such an excited gas state can be a
very stable dynamic state. Furthermore we calculate the breathing mode of the
super Tonks-Girardeau gas which is found to be in good agreement with
experimental observation. Our results show that the highly excited super
Tonks-Girardeau gas phase can be well understood from the fundamental theory of
the solvable Bose gas.Comment: 4 pages, 4 figures, version to appear in Phys. Rev. A as a Rapid
Communicatio
Realization of effective super Tonks-Girardeau gases via strongly attractive one-dimensional Fermi gases
A significant feature of the one-dimensional super Tonks-Girardeau gas is its
metastable gas-like state with a stronger Fermi-like pressure than for free
fermions which prevents a collapse of atoms. This naturally suggests a way to
search for such strongly correlated behaviour in systems of interacting
fermions in one dimension. We thus show that the strongly attractive Fermi gas
without polarization can be effectively described by a super Tonks-Girardeau
gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A
natural description of such super Tonks-Girardeau gases is provided by Haldane
generalized exclusion statistics. In particular, we find that they are
equivalent to ideal particles obeying more exclusive statistics than
Fermi-Dirac statistics.Comment: 4 pages, 2 figure
A Unified Framework for Causal Inference with Multiple Imputation Using Martingale
Multiple imputation is widely used to handle confounders missing at random in
causal inference. Although Rubin's combining rule is simple, it is not clear
whether or not the standard multiple imputation inference is consistent when
coupled with the commonly-used average causal effect (ACE) estimators. This
article establishes a unified martingale representation for the average causal
effect (ACE) estimators after multiple imputation. This representation invokes
the wild bootstrap inference to provide consistent variance estimation. Our
framework applies to asymptotically normal ACE estimators, including the
regression imputation, weighting, and matching estimators. We extend to the
scenarios when both outcome and confounders are subject to missingness and when
the data are missing not at random
A Family of Controllable Cellular Automata for Pseudorandom Number Generation
In this paper, we present a family of novel Pseudorandom Number Generators (PRNGs) based on Controllable Cellular Automata (CCA) ─ CCA0, CCA1, CCA2 (NCA), CCA3 (BCA), CCA4 (asymmetric NCA), CCA5, CCA6 and CCA7 PRNGs. The ENT and DIEHARD test suites are used to evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1-d CA. Moreover, their randomness can be comparable to that of 2-d CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved compared with any individual CCA PRNG
New properties of the concentric circle space and its applications to cardinal inequalities
summary:It is well-known that the concentric circle space has no -diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of -diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities
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