961 research outputs found
Gauging of Geometric Actions and Integrable Hierarchies of KP Type
This work consist of two interrelated parts. First, we derive massive
gauge-invariant generalizations of geometric actions on coadjoint orbits of
arbitrary (infinite-dimensional) groups with central extensions, with gauge
group being certain (infinite-dimensional) subgroup of . We show that
there exist generalized ``zero-curvature'' representation of the pertinent
equations of motion on the coadjoint orbit. Second, in the special case of
being Kac-Moody group the equations of motion of the underlying gauged WZNW
geometric action are identified as additional-symmetry flows of generalized
Drinfeld-Sokolov integrable hierarchies based on the loop algebra {\hat \cG}.
For {\hat \cG} = {\hat {SL}}(M+R) the latter hiearchies are equivalent to a
class of constrained (reduced) KP hierarchies called {\sl cKP}_{R,M}, which
contain as special cases a series of well-known integrable systems (mKdV, AKNS,
Fordy-Kulish, Yajima-Oikawa etc.). We describe in some detail the loop algebras
of additional (non-isospectral) symmetries of {\sl cKP}_{R,M} hierarchies.
Apart from gauged WZNW models, certain higher-dimensional nonlinear systems
such as Davey-Stewartson and -wave resonant systems are also identified as
additional symmetry flows of {\sl cKP}_{R,M} hierarchies. Along the way we
exhibit explicitly the interrelation between the Sato pseudo-differential
operator formulation and the algebraic (generalized) Drinfeld-Sokolov
formulation of {\sl cKP}_{R,M} hierarchies. Also we present the explicit
derivation of the general Darboux-B\"acklund solutions of {\sl cKP}_{R,M}
preserving their additional (non-isospectral) symmetries, which for R=1 contain
among themselves solutions to the gauged WZNW field
equations.Comment: LaTeX209, 47 page
Impurity Quantum Phase Transitions
We review recent work on continuous quantum phase transitions in impurity
models, both with fermionic and bosonic baths - these transitions are
interesting realizations of boundary critical phenomena at zero temperature.
The models with fermion bath are generalizations of the standard Kondo model,
with the common feature that Kondo screening of the localized spin can be
suppressed due to competing processes. The models with boson bath are related
to the spin-boson model of dissipative two-level systems, where the interplay
between tunneling and friction results in multiple phases. The competition
inherent to all models can generate unstable fixed points associated with
quantum phase transitions, where the impurity properties undergo qualitative
changes. Interestingly, certain impurity transitions feature both
lower-critical and upper-critical "dimensions" and allow for epsilon-type
expansions. We present results for a number of observables, obtained by both
analytical and numerical renormalization group techniques, and make connections
to experiments.Comment: 22 pages, 11 figs, review article to be published in Phil. Ma
The Kondo Model with a Bulk Mass Term
We introduce two massive versions of the anisotropic spin 1/2 Kondo model and
discuss their integrability. The two models have the same bulk sine-Gordon
interactions, but differ in their boundary interactions. At the Toulouse free
fermion point each of the models can be understood as two decoupled Ising
models in boundary magnetic fields. Reflection S-matrices away from the free
fermion point are conjectured.Comment: 33 pages, Plain Te
Raman Scattering and Anomalous Current Algebra: Observation of Chiral Bound State in Mott Insulators
Recent experiments on inelastic light scattering in a number of insulating
cuprates [1] revealed a new excitation appearing in the case of crossed
polarizations just below the optical absorption threshold. This observation
suggests that there exists a local exciton-like state with an odd parity with
respect to a spatial reflection. We present the theory of high energy large
shift Raman scattering in Mott insulators and interpret the experiment [1] as
an evidence of a chiral bound state of a hole and a doubly occupied site with a
topological magnetic excitation. A formation of these composites is a crucial
feature of various topological mechanisms of superconductivity. We show that
inelastic light scattering provides an instrument for direct measurements of a
local chirality and anomalous terms in the electronic current algebra.Comment: 18 pages, TeX, C Version 3.
Tunneling and orthogonality catastrophe in the topological mechanism of superconductivity
We compute the angular dependence of the order parameter and tunneling
amplitude in a model exhibiting topological superconductivity and sketch its
derivation as a model of a doped Mott insulator. We show that ground states
differing by an odd number of particles are orthogonal and the order parameter
is in the d-representation, although the gap in the electronic spectrum has no
nodes. We also develop an operator algebra, that allowes one to compute
off-diagonal correlation functions.Comment: 4 pages, Revtex, psfig; some references are correcte
Hofstadter butterfly as Quantum phase diagram
The Hofstadter butterfly is viewed as a quantum phase diagram with infinitely
many phases, labelled by their (integer) Hall conductance, and a fractal
structure. We describe various properties of this phase diagram: We establish
Gibbs phase rules; count the number of components of each phase, and
characterize the set of multiple phase coexistence.Comment: 4 prl pages 1 colored figure typos corrected, reference [26] added,
"Ten Martini" assumption adde
Self-Service or Salesman-Service Meat Retailing?
Farmers get about 60 cents of the consumer\u27s meat dollar. Processing and distribution take the other 40 cents. And about half of the latter goes to retailing- by far the largest single cost item in meat distribution
Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
We study a quantum phase transition which occurs in a system composed of two
impurities (or quantum dots) each coupled to a different interacting
(Luttinger-liquid) lead. While the impurities are coupled electrostatically,
there is no tunneling between them. Using a mapping of this system onto a Kondo
model, we show analytically that the system undergoes a
Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the
Luttinger liquid parameter in the leads and the dot-lead interaction. The phase
with low values of the Luttinger-liquid parameter is characterized by an abrupt
switch of the population between the impurities as function of a common applied
gate voltage. However, this behavior is hard to verify numerically since one
would have to study extremely long systems. Interestingly though, at the
transition the entanglement entropy drops from a finite value of to
zero. The drop becomes sharp for infinite systems. One can employ finite size
scaling to extrapolate the transition point and the behavior in its vicinity
from the behavior of the entanglement entropy in moderate size samples. We
employ the density matrix renormalization group numerical procedure to
calculate the entanglement entropy of systems with lead lengths of up to 480
sites. Using finite size scaling we extract the transition value and show it to
be in good agreement with the analytical prediction.Comment: 12 pages, 9 figure
Comparison of costs of service and self-service methods in retail meat departments
The objectives of this study were to compare the costs of service and self-service methods of selling meat and to show the relationship of cost to volume of sales.
Cost data were obtained from 23 self-service and 26 service stores for the period October 6 to 11, 1952. The cost items compared were labor, equipment, market floor space and paper supplies. These costs constitute about 85 percent of the total costs of operating the meat department. The volume of meat sales of the stores in this study ranged from 7,000 per week. Thus, the following results are applicable only to stores in this range.
Physical hours of labor per dollar of sales averaged lower under. self-service than service methods up to a sales volume of about $2,000 per week. Beyond that point the self-service method required more physical hours of labor
Chiral non-linear sigma-models as models for topological superconductivity
We study the mechanism of topological superconductivity in a hierarchical
chain of chiral non-linear sigma-models (models of current algebra) in one,
two, and three spatial dimensions. The models have roots in the 1D
Peierls-Frohlich model and illustrate how the 1D Frohlich's ideal conductivity
extends to a genuine superconductivity in dimensions higher than one. The
mechanism is based on the fact that a point-like topological soliton carries an
electric charge. We discuss a flux quantization mechanism and show that it is
essentially a generalization of the persistent current phenomenon, known in
quantum wires. We also discuss why the superconducting state is stable in the
presence of a weak disorder.Comment: 5 pages, revtex, no figure
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