1,928 research outputs found
Families of quasi-exactly solvable extensions of the quantum oscillator in curved spaces
We introduce two new families of quasi-exactly solvable (QES) extensions of
the oscillator in a -dimensional constant-curvature space. For the first
three members of each family, we obtain closed-form expressions of the energies
and wavefunctions for some allowed values of the potential parameters using the
Bethe ansatz method. We prove that the first member of each family has a hidden
sl(2,) symmetry and is connected with a QES equation of the first
or second type, respectively. One-dimensional results are also derived from the
-dimensional ones with , thereby getting QES extensions of the
Mathews-Lakshmanan nonlinear oscillator.Comment: 30 pages, 8 figures, published versio
The spin 1/2 Calogero-Gaudin System and its q-Deformation
The spin 1/2 Calogero-Gaudin system and its q-deformation are exactly solved:
a complete set of commuting observables is diagonalized, and the corresponding
eigenvectors and eigenvalues are explicitly calculated. The method of solution
is purely algebraic and relies on the co-algebra simmetry of the model.Comment: 15 page
Phenomenology of chiral damping in noncentrosymmetric magnets
A phenomenology of magnetic chiral damping is proposed in the context of
magnetic materials lacking inversion symmetry breaking. We show that the
magnetic damping tensor adopts a general form that accounts for a component
linear in magnetization gradient in the form of Lifshitz invariants. We propose
different microscopic mechanisms that can produce such a damping in
ferromagnetic metals, among which spin pumping in the presence of anomalous
Hall effect and an effective "-" Dzyaloshinskii-Moriya antisymmetric
exchange. The implication of this chiral damping in terms of domain wall motion
is investigated in the flow and creep regimes. These predictions have major
importance in the context of field- and current-driven texture motion in
noncentrosymmetric (ferro-, ferri-, antiferro-)magnets, not limited to metals.Comment: 5 pages, 2 figure
Attractive Fermi gases with unequal spin populations in highly elongated traps
We investigate two-component attractive Fermi gases with imbalanced spin
populations in trapped one dimensional configurations. The ground state
properties are determined within local density approximation, starting from the
exact Bethe-ansatz equations for the homogeneous case. We predict that the
atoms are distributed according to a two-shell structure: a partially polarized
phase in the center of the trap and either a fully paired or a fully polarized
phase in the wings. The partially polarized core is expected to be a superfluid
of the FFLO type. The size of the cloud as well as the critical spin
polarization needed to suppress the fully paired shell, are calculated as a
function of the coupling strength.Comment: Final accepted versio
Spectra and Symmetry in Nuclear Pairing
We apply the algebraic Bethe ansatz technique to the nuclear pairing problem
with orbit dependent coupling constants and degenerate single particle energy
levels. We find the exact energies and eigenstates. We show that for a given
shell, there are degeneracies between the states corresponding to less and more
than half full shell. We also provide a technique to solve the equations of
Bethe ansatz.Comment: 15 pages of REVTEX with 2 eps figure
On the exactly solvable pairing models for bosons
We propose the new exactly solvable model for bosons corresponding to the
attractive pairing interaction. Using the electrostatic analogy, the solution
of this model in thermodynamic limit is found. The transition from the
superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of
excitations in the weak coupling regime to the incompressible phase with the
gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page
Pairing states of a polarized Fermi gas trapped in a one-dimensional optical lattice
We study the properties of a one-dimensional (1D) gas of fermions trapped in
a lattice by means of the density matrix renormalization group method, focusing
on the case of unequal spin populations, and strong attractive interaction. In
the low density regime, the system phase-separates into a well defined
superconducting core and a fully polarized metallic cloud surrounding it. We
argue that the superconducting phase corresponds to a 1D analogue of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasi-condensate of
tightly bound bosonic pairs with a finite center-of-mass momentum that scales
linearly with the magnetization. In the large density limit, the system allows
for four phases: in the core, we either find a Fock state of localized pairs or
a metallic shell with free spin-down fermions moving in a fully filled
background of spin-up fermions. As the magnetization increases, the Fock state
disappears to give room for a metallic phase, with a partially polarized
superconducting FFLO shell and a fully polarized metallic cloud surrounding the
core.Comment: 4 pages, 5 fig
Geometry of quantum observables and thermodynamics of small systems
The concept of ergodicity---the convergence of the temporal averages of
observables to their ensemble averages---is the cornerstone of thermodynamics.
The transition from a predictable, integrable behavior to ergodicity is one of
the most difficult physical phenomena to treat; the celebrated KAM theorem is
the prime example. This Letter is founded on the observation that for many
classical and quantum observables, the sum of the ensemble variance of the
temporal average and the ensemble average of temporal variance remains constant
across the integrability-ergodicity transition.
We show that this property induces a particular geometry of quantum
observables---Frobenius (also known as Hilbert-Schmidt) one---that naturally
encodes all the phenomena associated with the emergence of ergodicity: the
Eigenstate Thermalization effect, the decrease in the inverse participation
ratio, and the disappearance of the integrals of motion. As an application, we
use this geometry to solve a known problem of optimization of the set of
conserved quantities---regardless of whether it comes from symmetries or from
finite-size effects---to be incorporated in an extended thermodynamical theory
of integrable, near-integrable, or mesoscopic systems
A simple construction of elliptic -matrices
We show that Belavin's solutions of the quantum Yang--Baxter equation can be
obtained by restricting an infinite -matrix to suitable finite dimensional
subspaces. This infinite -matrix is a modified version of the
Shibukawa--Ueno -matrix acting on functions of two variables.Comment: 6 page
Dynamical correlation functions of the mesoscopic pairing model
We study the dynamical correlation functions of the Richardson pairing model
(also known as the reduced or discrete-state BCS model) in the canonical
ensemble. We use the Algebraic Bethe Ansatz formalism, which gives exact
expressions for the form factors of the most important observables. By summing
these form factors over a relevant set of states, we obtain very precise
estimates of the correlation functions, as confirmed by global sum-rules
(saturation above 99% in all cases considered). Unlike the case of many other
Bethe Ansatz solvable theories, simple two-particle states are sufficient to
achieve such saturations, even in the thermodynamic limit. We provide explicit
results at half-filling, and discuss their finite-size scaling behavior
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