610 research outputs found
Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases
We investigate the elementary excitations of charge and spin degrees for the
1D interacting two-component Bose and Fermi gases by means of the discrete
Bethe ansatz equations. Analytic results in the limiting cases of strong and
weak interactions are derived, where the Bosons are treated in the repulsive
and the fermions in the strongly attractive regime. We confirm and complement
results obtained previously from the Bethe ansatz equations in the
thermodynamic limit.Comment: 12 pages, 1 figur
Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
We investigate pairing and quantum phase transitions in the one-dimensional
two-component Fermi atomic gas in an external field. The phase diagram,
critical fields, magnetization and local pairing correlation are obtained
analytically via the exact thermodynamic Bethe ansatz solution. At zero
temperature, bound pairs of fermions with opposite spin states form a singlet
ground state when the external field . A completely ferromagnetic
phase without pairing occurs when the external field . In the
region we observe a mixed phase of matter in which paired
and unpaired atoms coexist. The phase diagram is reminiscent of that of type II
superconductors. For temperatures below the degenerate temperature and in the
absence of an external field, the bound pairs of fermions form hard-core bosons
obeying generalized exclusion statistics.Comment: 9 pages, 5 figures, expanded version with additional text, references
and figure
The one-dimensional Hubbard model with open ends: Universal divergent contributions to the magnetic susceptibility
The magnetic susceptibility of the one-dimensional Hubbard model with open
boundary conditions at arbitrary filling is obtained from field theory at low
temperatures and small magnetic fields, including leading and next-leading
orders. Logarithmic contributions to the bulk part are identified as well as
algebraic-logarithmic divergences in the boundary contribution. As a
manifestation of spin-charge separation, the result for the boundary part at
low energies turns out to be independent of filling and interaction strength
and identical to the result for the Heisenberg model. For the bulk part at zero
temperature, the scale in the logarithms is determined exactly from the Bethe
ansatz. At finite temperature, the susceptibility profile as well as the
Friedel oscillations in the magnetisation are obtained numerically from the
density-matrix renormalisation group applied to transfer matrices. Agreement is
found with an exact asymptotic expansion of the relevant correlation function.Comment: 30 pages, 8 figures, reference adde
The open XXZ-chain: Bosonisation, Bethe ansatz and logarithmic corrections
We calculate the bulk and boundary parts of the free energy for an open
spin-1/2 XXZ-chain in the critical regime by bosonisation. We identify the
cutoff independent contributions and determine their amplitudes by comparing
with Bethe ansatz calculations at zero temperature T. For the bulk part of the
free energy we find agreement with Lukyanov's result [Nucl.Phys.B 522, 533
(1998)]. In the boundary part we obtain a cutoff independent term which is
linear in T and determines the temperature dependence of the boundary
susceptibility in the attractive regime for . We further show that at
particular anisotropies where contributions from irrelevant operators with
different scaling dimensions cross, logarithmic corrections appear. We give
explicit formulas for these terms at those anisotropies where they are most
important. We verify our results by comparing with extensive numerical
calculations based on a numerical solution of the T=0 Bethe ansatz equations,
the finite temperature Bethe ansatz equations in the quantum-transfer matrix
formalism, and the density-matrix renormalisation group applied to transfer
matrices.Comment: 35 pages, 8 figure
Exact results for the 1D interacting mixed Bose-Fermi gas
The exact solution of the 1D interacting mixed Bose-Fermi gas is used to
calculate ground-state properties both for finite systems and in the
thermodynamic limit. The quasimomentum distribution, ground-state energy and
generalized velocities are obtained as functions of the interaction strength
both for polarized and non-polarized fermions. We do not observe any demixing
instability of the system for repulsive interactions.Comment: 12 pages, 4 figures, better comparison with hydrodynamic approach,
typos corrected, references added, improved figure
Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions
We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons
and fermions with delta-interaction and arbitrary internal degrees of freedom
to the case of hard wall boundary conditions. We give an analysis of the ground
state properties of fermionic systems with two internal degrees of freedom,
including expansions of the ground state energy in the weak and strong coupling
limits in the repulsive and attractive regimes.Comment: 27 pages, 6 figures, key reference added, typos correcte
Coarse-Graining Hamiltonian Systems Using WSINDy
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy)
has been demonstrated to offer coarse-graining capabilities in the context of
interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In
this work we extend this capability to the problem of coarse-graining
Hamiltonian dynamics which possess approximate symmetries associated with
timescale separation. Such approximate symmetries often lead to the existence
of a Hamiltonian system of reduced dimension that may be used to efficiently
capture the dynamics of the symmetry-invariant dependent variables. Deriving
such reduced systems, or approximating them numerically, is an ongoing
challenge. We demonstrate that WSINDy can successfully identify this reduced
Hamiltonian system in the presence of large intrinsic perturbations while
remaining robust to extrinsic noise. This is significant in part due to the
nontrivial means by which such systems are derived analytically. WSINDy also
naturally preserves the Hamiltonian structure by restricting to a trial basis
of Hamiltonian vector fields. The methodology is computational efficient, often
requiring only a single trajectory to learn the global reduced Hamiltonian, and
avoiding forward solves in the learning process. Using nearly-periodic
Hamiltonian systems as a prototypical class of systems with approximate
symmetries, we show that WSINDy robustly identifies the correct leading-order
system, with dimension reduced by at least two, upon observation of the
relevant degrees of freedom. We also provide a contribution to averaging theory
by proving that first-order averaging at the level of vector fields preserves
Hamiltonian structure in nearly-periodic Hamiltonian systems. We provide
physically relevant examples, namely coupled oscillator dynamics, the
H\'enon-Heiles system for stellar motion within a galaxy, and the dynamics of
charged particles
Pressure-induced structural transitions in MgH
The stability of MgH has been studied up to 20~GPa using
density-functional total-energy calculations. At ambient pressure
-MgH takes a TiO-rutile-type structure. -MgH is
predicted to transform into -MgH at 0.39~GPa. The calculated
structural data for - and -MgH are in very good agreement
with experimental values. At equilibrium the energy difference between these
modifications is very small, and as a result both phases coexist in a certain
volume and pressure field. Above 3.84~GPa -MgH transforms into
-MgH; consistent with experimental findings. Two further
transformations have been identified at still higher pressure: i) - to
-MgH at 6.73 GPa and (ii) - to -MgH at
10.26~GPa.Comment: 4 pages, 4 figure
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
- …