7,740 research outputs found
Hyperfine splitting of the dressed hydrogen atom ground state in non-relativistic QED
We consider a spin-1/2 electron and a spin-1/2 nucleus interacting with the
quantized electromagnetic field in the standard model of non-relativistic QED.
For a fixed total momentum sufficiently small, we study the multiplicity of the
ground state of the reduced Hamiltonian. We prove that the coupling between the
spins of the charged particles and the electromagnetic field splits the
degeneracy of the ground state.Comment: 22 page
Higher spins on AdS from the worldsheet
It was recently shown that the CFT dual of string theory on , the symmetric orbifold of , contains a
closed higher spin subsector. Via holography, this makes precise the sense in
which tensionless string theory on this background contains a Vasiliev higher
spin theory. In this paper we study this phenomenon directly from the
worldsheet. Using the WZW description of the background with pure NS-NS flux,
we identify the states that make up the leading Regge trajectory and show that
they fit into the even spin Vasiliev higher spin theory. We also
show that these higher spin states do not become massless, except for the
somewhat singular case of level where the theory contains a stringy tower
of massless higher spin fields coming from the long string sector.Comment: 29+8 pages, 3 figure
Spectral properties of zero temperature dynamics in a model of a compacting granular column
The compacting of a column of grains has been studied using a one-dimensional
Ising model with long range directed interactions in which down and up spins
represent orientations of the grain having or not having an associated void.
When the column is not shaken (zero 'temperature') the motion becomes highly
constrained and under most circumstances we find that the generator of the
stochastic dynamics assumes an unusual form: many eigenvalues become
degenerate, but the associated multi-dimensional invariant spaces have but a
single eigenvector. There is no spectral expansion and a Jordan form must be
used. Many properties of the dynamics are established here analytically; some
are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table
Hierarchies of Spin Models related to Calogero-Moser Models
The universal formulation of spin exchange models related to Calogero-Moser
models implies the existence of integrable hierarchies, which have not been
explored. We show the general structures and features of the spin exchange
model hierarchies by taking as examples the well-known Heisenberg spin chain
with the nearest neighbour interactions. The energy spectra of the second
member of the hierarchy belonging to the models based on the root systems
are explicitly and {\em exactly} evaluated. They show many many
interesting features and in particular, much higher degree of degeneracy than
the original Heisenberg model, as expected from the integrability.Comment: 12pages, LaTeX2e, packages used: pstricks, pst-node, pstcol, if these
are not available, an eps file will be sent upon reques
Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature
We determine the spectra of a class of quantum spin chains of Temperley-Lieb
type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ
chain as a reference system. We consider open boundary conditions and in
particular periodic boundary conditions. For both types of boundaries the
identification with XXZ spectra is performed within isomorphic representations
of the underlying Temperley-Lieb algebra. For open boundaries the spectra of
these models differ from the spectrum of the associated XXZ chain only in the
multiplicities of the eigenvalues. The periodic case is rather different. Here
we show how the spectrum is obtained sector-wise from the spectra of globally
twisted XXZ chains. As a spin-off, we obtain a compact formula for the
degeneracy of the momentum operator eigenvalues. Our representation theoretical
results allow for the study of the thermodynamics by establishing a
TL-equivalence at finite temperature and finite field.Comment: 29 pages, LaTeX, two references added, redundant figures remove
Ground states for a class of deterministic spin models with glassy behaviour
We consider the deterministic model with glassy behaviour, recently
introduced by Marinari, Parisi and Ritort, with \ha\ , where is the discrete sine Fourier transform. The
ground state found by these authors for odd and prime is shown to
become asymptotically dege\-ne\-ra\-te when is a product of odd primes,
and to disappear for even. This last result is based on the explicit
construction of a set of eigenvectors for , obtained through its formal
identity with the imaginary part of the propagator of the quantized unit
symplectic matrix over the -torus.Comment: 15 pages, plain LaTe
Quantum lump dynamics on the two-sphere
It is well known that the low-energy classical dynamics of solitons of
Bogomol'nyi type is well approximated by geodesic motion in M_n, the moduli
space of static n-solitons. There is an obvious quantization of this dynamics
wherein the wavefunction evolves according to the Hamiltonian H_0 equal to
(half) the Laplacian on M_n. Born-Oppenheimer reduction of analogous mechanical
systems suggests, however, that this simple Hamiltonian should receive
corrections including k, the scalar curvature of M_n, and C, the n-soliton
Casimir energy, which are usually difficult to compute, and whose effect on the
energy spectrum is unknown. This paper analyzes the spectra of H_0 and two
corrections to it suggested by work of Moss and Shiiki, namely H_1=H_0+k/4 and
H_2=H_1+C, in the simple but nontrivial case of a single CP^1 lump moving on
the two-sphere. Here M_1=TSO(3), a noncompact kaehler 6-manifold invariant
under an SO(3)xSO(3) action, whose geometry is well understood. The symmetry
gives rise to two conserved angular momenta, spin and isospin. A hidden
isometry of M_1 is found which implies that all three energy spectra are
symmetric under spin-isospin interchange. The Casimir energy is found exactly
on the zero section of TSO(3), and approximated numerically on the rest of M_1.
The lowest 19 eigenvalues of H_i are found for i=0,1,2, and their spin-isospin
and parity compared. The curvature corrections in H_1 lead to a qualitatively
unchanged low-level spectrum while the Casimir energy in H_2 leads to
significant changes. The scaling behaviour of the spectra under changes in the
radii of the domain and target spheres is analyzed, and it is found that the
disparity between the spectra of H_1 and H_2 is reduced when the target sphere
is made smaller.Comment: 35 pages, 3 figure
On the stationary points of the TAP free energy
In the context of the p-spin spherical model, we introduce a method for the
computation of the number of stationary points of any nature (minima, saddles,
etc.) of the TAP free energy. In doing this we clarify the ambiguities related
to the approximations usually adopted in the standard calculations of the
number of states in mean field spin glass models.Comment: 11 pages, 1 Postscript figure, plain Te
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