2,536 research outputs found

### Exact dynamics in the inhomogeneous central-spin model

We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 by
inhomogeneous Heisenberg couplings including a central magnetic field. This
central-spin model describes decoherence in quantum bit systems. An exact
formula for the dynamics of the central spin is presented, based on the Bethe
ansatz. This formula is evaluated explicitly for initial conditions such that
the bath spins are completely polarized at the beginning. For this case we
find, after an initial decay, a persistent oscillatory behaviour of the central
spin. For a large number of bath spins $N_b$, the oscillation frequency is
proportional to $N_b$, whereas the amplitude behaves like $1/N_b$, to leading
order. No asymptotic decay due to the non-uniform couplings is observed, in
contrast to some recent studies.Comment: 7 pages, 3 figure

### Correlation functions of integrable models: a description of the ABACUS algorithm

Recent developments in the theory of integrable models have provided the
means of calculating dynamical correlation functions of some important
observables in systems such as Heisenberg spin chains and one-dimensional
atomic gases. This article explicitly describes how such calculations are
generally implemented in the ABACUS C++ library, emphasizing the universality
in treatment of different cases coming as a consequence of unifying features
within the Bethe Ansatz.Comment: 30 pages, 8 figures, Proceedings of the CRM (Montreal) workshop on
Integrable Quantum Systems and Solvable Statistical Mechanics Model

### Yang-Baxter equation in spin chains with long range interactions

We consider the $su(n)$ spin chains with long range interactions and the
spin generalization of the Calogero-Sutherland models. We show that their
properties derive from a transfer matrix obeying the Yang-Baxter equation. We
obtain the expression of the conserved quantities and we diagonalize them.Comment: Saclay-t93/00

### 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 $d$-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,$\mathbb{R}$) symmetry and is connected with a QES equation of the first
or second type, respectively. One-dimensional results are also derived from the
$d$-dimensional ones with $d \ge 2$, thereby getting QES extensions of the
Mathews-Lakshmanan nonlinear oscillator.Comment: 30 pages, 8 figures, published versio

### Laughlin's wave functions, Coulomb gases and expansions of the discriminant

In the context of the fractional quantum Hall effect, we investigate
Laughlin's celebrated ansatz for the groud state wave function at fractional
filling of the lowest Landau level. Interpreting its normalization in terms of
a one component plasma, we find the effect of an additional quadrupolar field
on the free energy, and derive estimates for the thermodynamically equivalent
spherical plasma. In a second part, we present various methods for expanding
the wave function in terms of Slater determinants, and obtain sum rules for the
coefficients. We also address the apparently simpler question of counting the
number of such Slater states using the theory of integral polytopes.Comment: 97 pages, using harvmac (with big option recommended) and epsf, 7
figures available upon request, Saclay preprint Spht 93/12

### 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

### 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 "$s$-$d$" 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

### Fermi-Bose transformation for the time-dependent Lieb-Liniger gas

Exact solutions of the Schrodinger equation describing a freely expanding
Lieb-Liniger (LL) gas of delta-interacting bosons in one spatial dimension are
constructed. The many-body wave function is obtained by transforming a fully
antisymmetric (fermionic) time-dependent wave function which obeys the
Schrodinger equation for a free gas. This transformation employs a differential
Fermi-Bose mapping operator which depends on the strength of the interaction
and the number of particles.Comment: 4+ pages, 1 figure; added reference

### Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

We introduce an integrable lattice discretization of the quantum system of n
bosonic particles on a ring interacting pairwise via repulsive delta
potentials. The corresponding (finite-dimensional) spectral problem of the
integrable lattice model is solved by means of the Bethe Ansatz method. The
resulting eigenfunctions turn out to be given by specializations of the
Hall-Littlewood polynomials. In the continuum limit the solution of the
repulsive delta Bose gas due to Lieb and Liniger is recovered, including the
orthogonality of the Bethe wave functions first proved by Dorlas (extending
previous work of C.N. Yang and C.P. Yang).Comment: 25 pages, LaTe

- …