16,220 research outputs found
Exactly solvable models and ultracold Fermi gases
Exactly solvable models of ultracold Fermi gases are reviewed via their
thermodynamic Bethe Ansatz solution. Analytical and numerical results are
obtained for the thermodynamics and ground state properties of two- and
three-component one-dimensional attractive fermions with population imbalance.
New results for the universal finite temperature corrections are given for the
two-component model. For the three-component model, numerical solution of the
dressed energy equations confirm that the analytical expressions for the
critical fields and the resulting phase diagrams at zero temperature are highly
accurate in the strong coupling regime. The results provide a precise
description of the quantum phases and universal thermodynamics which are
applicable to experiments with cold fermionic atoms confined to one-dimensional
tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16
pages, 6 figure
Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms
A simple set of algebraic equations is derived for the exact low-temperature
thermodynamics of one-dimensional multi-component strongly attractive fermionic
atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal
multi-component Tomonaga-Luttinger liquid (TLL) phases are thus determined. For
linear Zeeman splitting, the physics of the gapless phase at low temperatures
belongs to the universality class of a two-component asymmetric TLL
corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms.
The equation of states is also obtained to open up the study of multi-component
TLL phases in 1D systems of N-component Fermi gases with population imbalance.Comment: 12 pages, 3 figure
Universality class of quantum criticality for strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction
Using the thermodynamic Bethe ansatz equations we study the quantum phase
diagram, thermodynamics and criticality of one-dimensional spin-1 bosons with
strongly repulsive density-density and antiferromagnetic spin-exchange
interactions. We analytically derive a high precision equation of state from
which the Tomonaga-Luttinger liquid physics and quantum critical behavior of
the system are computed. We obtain explicit forms for the scaling functions
near the critical points yielding the dynamical exponent and correlation
length exponent for the quantum phase transitions driven by either
the chemical potential or the magnetic field. Consequently, we further
demonstrate that quantum criticality of the system can be mapped out from the
finite temperature density and magnetization profiles of the 1D trapped gas.
Our results provide the physical origin of quantum criticality in a 1D
many-body system beyond the Tomonaga-Luttinger liquid description.Comment: 12 pages, 11 figure
Specific heat and thermal conductivity of ferromagnetic magnons in Yttrium Iron Garnet
The specific heat and thermal conductivity of the insulating ferrimagnet
YFeO (Yttrium Iron Garnet, YIG) single crystal were measured
down to 50 mK. The ferromagnetic magnon specific heat shows a
characteristic dependence down to 0.77 K. Below 0.77 K, a downward
deviation is observed, which is attributed to the magnetic dipole-dipole
interaction with typical magnitude of 10 eV. The ferromagnetic magnon
thermal conductivity does not show the characteristic
dependence below 0.8 K. To fit the data, both magnetic defect
scattering effect and dipole-dipole interaction are taken into account. These
results complete our understanding of the thermodynamic and thermal transport
properties of the low-lying ferromagnetic magnons.Comment: 5 pages, 5 figure
Universal local pair correlations of Lieb-Liniger bosons at quantum criticality
The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system
featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion
quantum criticality. We analytically calculate finite temperature local pair
correlations for the strong coupling Bose gas at quantum criticality using the
polylog function in the framework of the Yang-Yang thermodynamic equations. We
show that the local pair correlation has the universal value in the quantum critical regime, the TLL phase and the
quasi-classical region, where is the pressure per unit length rescaled by
the interaction energy with interaction
strength and linear density . This suggests the possibility to test
finite temperature local pair correlations for the TLL in the relativistic
dispersion regime and to probe quantum criticality with the local correlations
beyond the TLL phase. Furthermore, thermodynamic properties at high
temperatures are obtained by both high temperature and virial expansion of the
Yang-Yang thermodynamic equation.Comment: 8 pages, 6 figures, additional text and reference
The Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem
A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of
the standard pairing problem is established based on the Heine-Stieltjes
correspondence. For pairs of valence nucleons on different
single-particle levels, it is found that solutions of the Bethe ansatz
equations can be obtained from one (k+1)x(k+1) and one (n-1)x(k+1) matrices,
which are associated with the extended Heine-Stieltjes and Van Vleck
polynomials, respectively. Since the coefficients in these polynomials are free
from divergence with variations in contrast to the original Bethe ansatz
equations, the approach thus provides with a new efficient and systematic way
to solve the problem, which, by extension, can also be used to solve a large
class of Gaudin-type quantum many-body problems and to establish a new
efficient angular momentum projection method for multi-particle systems.Comment: ReVTeX, 4 pages, no figur
Evidence for the super Tonks-Girardeau gas
We provide evidence in support of a recent proposal by Astrakharchik at al.
for the existence of a super Tonks-Girardeau gas-like state in the attractive
interaction regime of quasi-one-dimensional Bose gases. We show that the super
Tonks-Giradeau gas-like state corresponds to a highly-excited Bethe state in
the integrable interacting Bose gas for which the bosons acquire hard-core
behaviour. The gas-like state properties vary smoothly throughout a wide range
from strong repulsion to strong attraction. There is an additional stable
gas-like phase in this regime in which the bosons form two-body bound states
behaving like hard-core bosons.Comment: 10 pages, 1 figure, 2 tables, additional text on the stability of the
super T-G gas-like stat
Quantum Criticality of 1D Attractive Fermi Gas
We obtain an analytical equation of state for one-dimensional strongly
attractive Fermi gas for all parameter regime in current experiments. From the
equation of state we derive universal scaling functions that control whole
thermodynamical properties in quantum critical regimes and illustrate physical
origin of quantum criticality. It turns out that the critical properties of the
system are described by these of free fermions and those of mixtures of
fermions with mass and . We also show how these critical properties of
bulk systems can be revealed from the density profile of trapped Fermi gas at
finite temperatures and can be used to determine the T=0 phase boundaries
without any arbitrariness.Comment: extended version, 9 pages, 7 eps figures, corrections of few typo
Uniqueness and examples of compact toric Sasaki-Einstein metrics
In [11] it was proved that, given a compact toric Sasaki manifold of positive
basic first Chern class and trivial first Chern class of the contact bundle,
one can find a deformed Sasaki structure on which a Sasaki-Einstein metric
exists. In the present paper we first prove the uniqueness of such Einstein
metrics on compact toric Sasaki manifolds modulo the action of the identity
component of the automorphism group for the transverse holomorphic structure,
and secondly remark that the result of [11] implies the existence of compatible
Einstein metrics on all compact Sasaki manifolds obtained from the toric
diagrams with any height, or equivalently on all compact toric Sasaki manifolds
whose cones have flat canonical bundle. We further show that there exists an
infinite family of inequivalent toric Sasaki-Einstein metrics on for each positive integer .Comment: Statements of the results are modifie
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