20,950 research outputs found
Ground-state properties of fermionic mixtures with mass imbalance in optical lattices
Ground-state properties of fermionic mixtures confined in a one-dimensional
optical lattice are studied numerically within the spinless Falicov-Kimball
model with a harmonic trap. A number of remarkable results are found. (i) At
low particle filling the system exhibits the phase separation with heavy atoms
in the center of the trap and light atoms in the surrounding regions. (ii)
Mott-insulating phases always coexist with metallic phases. (iii)
Atomic-density waves are observed in the insulating regions for all particle
fillings near half-filled lattice case. (iv) The variance of the local density
exhibits the universal behavior (independent of the particle filling, the
Coulomb interaction and the strength of a confining potential) over the whole
region of the local density values.Comment: 10 pages, 5 figure
Evading the sign problem in random matrix simulations
We show how the sign problem occurring in dynamical simulations of random
matrices at nonzero chemical potential can be avoided by judiciously combining
matrices into subsets. For each subset the sum of fermionic determinants is
real and positive such that importance sampling can be used in Monte Carlo
simulations. The number of matrices per subset is proportional to the matrix
dimension. We measure the chiral condensate and observe that the statistical
error is independent of the chemical potential and grows linearly with the
matrix dimension, which contrasts strongly with its exponential growth in
reweighting methods.Comment: 4 pages, 3 figures, minor corrections, as published in Phys. Rev.
Let
A Feynman integral via higher normal functions
We study the Feynman integral for the three-banana graph defined as the
scalar two-point self-energy at three-loop order. The Feynman integral is
evaluated for all identical internal masses in two space-time dimensions. Two
calculations are given for the Feynman integral; one based on an interpretation
of the integral as an inhomogeneous solution of a classical Picard-Fuchs
differential equation, and the other using arithmetic algebraic geometry,
motivic cohomology, and Eisenstein series. Both methods use the rather special
fact that the Feynman integral is a family of regulator periods associated to a
family of K3 surfaces. We show that the integral is given by a sum of elliptic
trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm
value is related to the regulator of a class in the motivic cohomology of the
K3 family. We prove a conjecture by David Broadhurst that at a special
kinematical point the Feynman integral is given by a critical value of the
Hasse-Weil L-function of the K3 surface. This result is shown to be a
particular case of Deligne's conjectures relating values of L-functions inside
the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications.
Version to appear in Compositio Mathematic
A Non-Perturbative Treatment of the Pion in the Linear Sigma-Model
Using a non-perturbative method based on the selfconsistent Quasi-particle
Random-Phase Approximation (QRPA) we describe the properties of the pion in the
linear -model. It is found that the pion is massless in the chiral
limit, both at zero- and finite temperature, in accordance with Goldstone's
theorem.Comment: To appear in Nucl.Phys. A, 16 pages, 2 Postscript figure
A subset solution to the sign problem in random matrix simulations
We present a solution to the sign problem in dynamical random matrix
simulations of a two-matrix model at nonzero chemical potential. The sign
problem, caused by the complex fermion determinants, is solved by gathering the
matrices into subsets, whose sums of determinants are real and positive even
though their cardinality only grows linearly with the matrix size. A detailed
proof of this positivity theorem is given for an arbitrary number of fermion
flavors. We performed importance sampling Monte Carlo simulations to compute
the chiral condensate and the quark number density for varying chemical
potential and volume. The statistical errors on the results only show a mild
dependence on the matrix size and chemical potential, which confirms the
absence of sign problem in the subset method. This strongly contrasts with the
exponential growth of the statistical error in standard reweighting methods,
which was also analyzed quantitatively using the subset method. Finally, we
show how the method elegantly resolves the Silver Blaze puzzle in the
microscopic limit of the matrix model, where it is equivalent to QCD.Comment: 18 pages, 11 figures, as published in Phys. Rev. D; added references;
in Sec. VB: added discussion of model satisfying the Silver Blaze for all N
(proof in Appendix E
Effective Operators for Double-Beta Decay
We use a solvable model to examine double-beta decay, focusing on the
neutrinoless mode. After examining the ways in which the neutrino propagator
affects the corresponding matrix element, we address the problem of finite
model-space size in shell-model calculations by projecting our exact wave
functions onto a smaller subspace. We then test both traditional and more
recent prescriptions for constructing effective operators in small model
spaces, concluding that the usual treatment of double-beta-decay operators in
realistic calculations is unable to fully account for the neglected parts of
the model space. We also test the quality of the Quasiparticle Random Phase
Approximation and examine a recent proposal within that framework to use
two-neutrino decay to fix parameters in the Hamiltonian. The procedure
eliminates the dependence of neutrinoless decay on some unfixed parameters and
reduces the dependence on model-space size, though it doesn't eliminate the
latter completely.Comment: 10 pages, 8 figure
Why Snails? How Gastropods Improve Our Understanding of Ecological Disturbance
The concept of equilibrium - the idea that a perturbed system will tend to return to its original state - is the basis for many foundational theories in ecology. Yet, the spatial and temporal dynamics of ecosystems are strongly influenced by disturbance. If a particular disturbance greatly alters local climatic conditions, gastropods should be among the first organisms to show a measurable response. The effects of human alteration of habitats (for example, conversion of forest to agriculture) have much longer-lasting effects than those of natural disturbances
The Kohn-Luttinger Effect in Gauge Theories
Kohn and Luttinger showed that a many body system of fermions interacting via
short range forces becomes superfluid even if the interaction is repulsive in
all partial waves. In gauge theories such as QCD the interaction between
fermions is long range and the assumptions of Kohn and Luttinger are not
satisfied. We show that in a U(1) gauge theory the Kohn-Luttinger phenomenon
does not take place. In QCD attractive channels always exist, but there are
cases in which the primary pairing channel leaves some fermions ungapped. As an
example we consider the unpaired fermion in the 2SC phase of QCD with two
flavors. We show that it acquires a very small gap via a mechanism analogous to
the Kohn-Luttinger effect. The gap is too small to be phenomenologically
relevant.Comment: 5 pages, 2 figure, minor revisions, to appear in PR
Asymptotic Stability, Instability and Stabilization of Relative Equilibria
In this paper we analyze asymptotic stability, instability and stabilization for the relative equilibria, i.e. equilibria modulo a group action, of natural mechanical systems. The practical applications of these results are to rotating mechanical systems where the group is the rotation group. We use a modification of the Energy-Casimir and Energy-Momentum methods for Hamiltonian systems to analyze systems with dissipation. Our work couples the modern theory of block diagonalization to the classical work of Chetaev
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