Density-Matrix Renormalization Group Study of Trapped Imbalanced Fermi Condensates

The density-matrix renormalization group is employed to investigate a harmonically-trapped imbalanced Fermi condensate based on a one-dimensional attractive Hubbard model. The obtained density profile shows a flattened population difference of spin-up and spin-down components at the center of the trap, and exhibits phase separation between the condensate and unpaired majority atoms for a certain range of the interaction and population imabalance $P$. The two-particle density matrix reveals that the sign of the order parameter changes periodically, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov phase. The minority spin atoms contribute to the quasi-condensate up to at least $P \simeq 0.8$. Possible experimental situations to test our predictions are discussed.Comment: 4 pages, 3 figures; added references; accepted for publication in Phys. Rev. Let

A Comparative Study of Some Pseudorandom Number Generators

We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs, manufacturer installed routines and a random number sequence produced from physical noise. We start by traditional statistical tests, followed by detailed bit level and visual tests. The computational speed of various algorithms is also scrutinized. Our results allow direct comparisons between the properties of different generators, as well as an assessment of the efficiency of the various test methods. This information provides the best available criterion to choose the best possible generator for a given problem. However, in light of recent problems reported with some of these generators, we also discuss the importance of developing more refined physical tests to find possible correlations not revealed by the present test methods.Comment: University of Helsinki preprint HU-TFT-93-22 (minor changes in Tables 2 and 7, and in the text, correspondingly

Bogoliubov-de Gennes study of trapped spin-imbalanced unitary Fermi gases

It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One such example is the strongly-interacting Fermi gas with two imbalanced spin species, which has received a great amount of attention due to the possible presence of exotic superfluid phases. By employing novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov de-Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the validity of the local density approximation (LDA), which is often invoked in the extraction of bulk properties from experimental measurements within trapped systems. We show how the validity of the LDA is affected by the trapping geometry, number of atoms and spin imbalance.Comment: 15 pages, 5 figures, to be published in New J. Phys. (focus issue on "Strongly Correlated Quantum Fluids: From Ultracold Quantum Gases to QCD Plasmas"

Chern classes and extraspecial groups

The mod-p cohomology ring of the extraspecial p-group of exponent p is studied for odd p. We investigate the subquotient ch(G) generated by Chern classes modulo the nilradical. The subring of ch(G) generated by Chern classes of one-dimensional representations was studied by Tezuka and Yagita. The subring generated by the Chern classes of the faithful irreducible representations is a polynomial algebra. We study the interplay between these two families of generators, and obtain some relations between them

An Improved Initialization Procedure for the Density-Matrix Renormalization Group

We propose an initialization procedure for the density-matrix renormalization group (DMRG): {\it the recursive sweep method}. In a conventional DMRG calculation, the infinite-algorithm, where two new sites are added to the system at each step, has been used to reach the target system size. We then need to obtain the ground state for a different system size for every site addition, so 1) it is difficult to supply a good initial vector for the numerical diagonalization for the ground state, and 2) when the system reduced to a 1D system consists of an array of nonequivalent sites as in ladders or Hubbard-Holstein model, special care has to be taken. Our procedure, which we call the {\it recursive sweep method}, provides a solution to these problems and in fact provides a faster algorithm for the Hubbard model as well as more complicated ones such as the Hubbard-Holstein model.Comment: 4 pages, 4 figures, submitted to JPS

Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

Influence of s-d interfacial scattering on the magnetoresistance of magnetic tunnel junctions

We propose the two-band s-d model to describe theoretically a diffuse regime of the spin-dependent electron transport in magnetic tunnel junctions (MTJ's) of the form F/O/F where F's are 3d transition metal ferromagnetic layers and O is the insulating spacer. We aim to explain the strong interface sensitivity of the tunneling properties of MTJ's and investigate the influence of electron scattering at the nonideal interfaces on the degradation of the TMR magnitude. The generalized Kubo formalism and the Green's functions method were used to calculate the conductance of the system. The vertex corrections to the conductivity were found with the use of "ladder" approximation combined with the coherent-potential approximation (CPA) that allowed to consider the case of strong electron scattering. It is shown that the Ward identity is satisfied in the framework of this approximation that provides the necessary condition for a conservation of a tunneling current. Based on the known results of ab-initio calculations of the TMR for ballistic junctions, we assume that exchange split quasi-free s-like electrons with the density of states being greater for the majority spin sub-band give the main contribution to the TMR effect. We show that, due to interfacial inter-band scattering, the TMR can be substantially reduced even down to zero value. This is related to the fact that delocalized quasi-free electrons can scatter into the strongly localized d sub-band with the density of states at the Fermi energy being larger for minority spins compared to majority spins. It is also shown that spin-flip electron scattering on the surface magnons within the interface leads to a further decrease of the TMR at finite temperature.Comment: REVTeX4, 20 pages, 9 figures, 1 table, submitted to Phys.Rev.B; In Version 2 the text is substantially improved, the main results and conclusions left the sam

Ground states and dynamics of population-imbalanced Fermi condensates in one dimension

By using the numerically exact density-matrix renormalization group (DMRG) approach, we investigate the ground states of harmonically trapped one-dimensional (1D) fermions with population imbalance and find that the Larkin-Ovchinnikov (LO) state, which is a condensed state of fermion pairs with nonzero center-of-mass momentum, is realized for a wide range of parameters. The phase diagram comprising the two phases of i) an LO state at the trap center and a balanced condensate at the periphery and ii) an LO state at the trap center and a pure majority component at the periphery, is obtained. The reduced two-body density matrix indicates that most of the minority atoms contribute to the LO-type quasi-condensate. With the time-dependent DMRG, we also investigate the real-time dynamics of a system of 1D fermions in response to a spin-flip excitation.Comment: 20 pages, 15 figures, accepted for publication in New Journal of Physic