pinecone/core-2020-05-10-deduplication huggingface dataset:
The 2-Channel Kondo Model II: CFT Calculation of Non-Equilibrium
  Conductance through a Nanoconstriction containing 2-Channel Kondo Impurities

Recent experiments by Ralph and Buhrman on zero-bias anomalies in quenched Cu
nanoconstrictions (reviewed in the preceding paper, I), are in accord with the
assumption that the interaction between electrons and nearly degenerate
two-level systems in the constriction can be described, for sufficiently small
voltages and temperatures ($V,T < \Tk$), by the 2-channel Kondo (2CK) model.
Motivated by these experiments, we introduce a generalization of the 2CK model,
which we call the nanoconstriction 2-channel Kondo model (NTKM), that takes
into account the complications arising from the non-equilibrium electron
distribution in the nanoconstriction. We calculate the conductance $G(V,T)$ of
the constriction in the weakly non-equilibrium regime of $V,T \ll \Tk$ by
combining concepts from Hershfield's $Y$-operator formulation of
non-equilibrium problems and Affleck and Ludwig's exact conformal field theory
(CFT) solution of the 2CK problem (CFT technicalities are discussed in a
subsequent paper, III). Finally, we extract from the conductance a universal
scaling curve $\Gamma(v)$ and compare it with experiment. Combining our results
with those of Hettler, Kroha and Hershfield, we conclude that the NTKM achieves
quantitative agreement with the experimental scaling data.Comment: Final published version (minor revisions only), 41 pages RevTeX, 9
  encapsulated postscript figure
Semiclassical Series at Finite Temperature

We derive the semiclassical series for the partition function of a
one-dimensional quantum-mechanical system consisting of a particle in a
single-well potential. We do this by applying the method of steepest descent to
the path-integral representation of the partition function, and we present a
systematic procedure to generate the terms of the series using the minima of
the Euclidean action as the only input. For the particular case of a quartic
anharmonic oscillator, we compute the first two terms of the series, and
investigate their high and low temperature limits. We also exhibit the
nonperturbative character of the terms, as each corresponds to sums over
infinite subsets of perturbative graphs. We illustrate the power of such
resummations by extracting from the first term an accurate nonperturbative
estimate of the ground-state energy of the system and a curve for the specific
heat. We conclude by pointing out possible extensions of our results which
include field theories with spherically symmetric classical solutions.Comment: 25 pages + 5 figure
Universal simple current vertex operators

We construct a vertex operator realization for the simple current primary
fields of WZW theories which are based on simply laced affine Lie algebras g.
This is achieved by employing an embedding of the integrable highest weight
modules of g into the Fock space for a bosonic string compactified on the
weight lattice of g. Our vertex operators are universal in the sense that a
single expression for the vertex operator holds simultaneously for all positive
integral values of the level of g.Comment: 17 pages, LaTeX2
Periodic Orbit Theory and Spectral Statistics for Quantum Graphs

We quantize graphs (networks) which consist of a finite number of bonds and
vertices. We show that the spectral statistics of fully connected graphs is
well reproduced by random matrix theory. We also define a classical phase space
for the graphs, where the dynamics is mixing and the periodic orbits
proliferate exponentially. An exact trace formula for the quantum spectrum is
developed in terms of the same periodic orbits, and it is used to investigate
the origin of the connection between random matrix theory and the underlying
chaotic classical dynamics. Being an exact theory, and due to its relative
simplicity, it offers new insights into this problem which is at the fore-front
of the research in Quantum Chaos and related fields.Comment: 37 pages, 20 figures, other comments, accepted for publication in the
  Annals of Physic
Quantum Caustics for Systems with Quadratic Lagrangians

We study caustics in classical and quantum mechanics for systems with
quadratic Lagrangians. We derive a closed form of the transition amplitude on
caustics and discuss their physical implications in the Gaussian slit
(gedanken-)experiment. Application to the quantum mechanical rotor casts doubt
on the validilty of Jevicki's correspondence hypothesis which states that in
quantum mechanics, stationary points(instantons) arise as simple poles.Comment: TeX, 37 pages, 3 figures, Corrected typos and eq.(3.21
A semiclassical approach to the Dirac equation

We derive a semiclassical time evolution kernel and a trace formula for the
Dirac equation. The classical trajectories that enter the expressions are
determined by the dynamics of relativistic point particles. We carefully
investigate the transport of the spin degrees of freedom along the trajectories
which can be understood geometrically as parallel transport in a vector bundle
with SU(2) holonomy. Furthermore, we give an interpretation in terms of a
classical spin vector that is transported along the trajectories and whose
dynamics, dictated by the equation of Thomas precession, gives rise to
dynamical and geometric phases every orbit is weighted by. We also present an
analogous approach to the Pauli equation which we analyse in two different
limits
Normal forms and complex periodic orbits in semiclassical expansions of
  Hamiltonian systems

Bifurcations of periodic orbits as an external parameter is varied are a
characteristic feature of generic Hamiltonian systems. Meyer's classification
of normal forms provides a powerful tool to understand the structure of phase
space dynamics in their neighborhood. We provide a pedestrian presentation of
this classical theory and extend it by including systematically the periodic
orbits lying in the complex plane on each side of the bifurcation. This allows
for a more coherent and unified treatment of contributions of periodic orbits
in semiclassical expansions. The contribution of complex fixed points is find
to be exponentially small only for a particular type of bifurcation (the
extremal one). In all other cases complex orbits give rise to corrections in
powers of $\hbar$ and, unlike the former one, their contribution is hidden in
the ``shadow'' of a real periodic orbit.Comment: better ps figures available at http://www.phys.univ-tours.fr/~mouchet
  or on request to mouchet@celfi.phys.univ-tours.f
Solving Gauge Invariant Systems without Gauge Fixing: the Physical
  Projector in 0+1 Dimensional Theories

The projector onto gauge invariant physical states was recently constructed
for arbitrary constrained systems. This approach, which does not require gauge
fixing nor any additional degrees of freedom beyond the original ones---two
characteristic features of all other available methods for quantising
constrained dynamics---is put to work in the context of a general class of
quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge
groups are considered specifically, and a comprehensive understanding of the
corresponding physical spectra is achieved in a straightforward manner, using
only standard methods of coherent states and group theory which are directly
amenable to generalisation to other Lie algebras. Results extend by far the few
examples available in the literature from much more subtle and delicate
analyses implying gauge fixing and the characterization of modular space.Comment: 32 pages, LaTeX fil
Modular Wedge Localization and the d=1+1 Formfactor Program

In this paper I continue the study of the new framework of modular
localization and its constructive use in the nonperturbative d=1+1
Karowski-Weisz-Smirnov formfactor program. Particular attention is focussed on
the existence of semilocal generators of the wedge-localized algebra without
vauum polarization (FWG-operators) which are closely related to objects
fulfilling the Zamolodchikov-Faddeev algebraic structure. They generate a
``thermal Hilbert space'' and allow to understand the equivalence of the KMS
conditions with the so-called cyclicity equation for formfactors which was
known to be closely related to crossing symmetry properties. The modular
setting gives rise to interesting new ideas on ``free'' d=2+1 anyons and
plektons.Comment: the fourth section has been rewritten in order to remove an error and
  to gain additional clarity. 32 pages, tcilate
(In-)Consistencies in the relativistic description of excited states in
  the Bethe-Salpeter equation

The Bethe-Salpeter equation provides the most widely used technique to
extract bound states and resonances in a relativistic Quantum Field Theory.
Nevertheless a thorough discussion how to identify its solutions with physical
states is still missing. The occurrence of complex eigenvalues of the
homogeneous Bethe-Salpeter equation complicates this issue further. Using a
perturbative expansion in the mass difference of the constituents we
demonstrate for scalar fields bound by a scalar exchange that the underlying
mechanism which results in complex eigenvalues is the crossing of a normal (or
abnormal) with an abnormal state. Based on an investigation of the
renormalization of one-particle properties we argue that these crossings happen
beyond the applicability region of the ladder Bethe-Salpeter equation. The
implications for a fermion-antifermion bound state in QED are discussed, and a
consistent interpretation of the bound state spectrum of QED is proposed.Comment: 39 pages, 14 figures, LaTeX2e, uses amssymb, minor changes,
  references added, to appear in Annals Phy
Global properties of warped solutions in General Relativity

Assuming the four-dimensional space-time to be a general warped product of
two surfaces we reduce the four-dimensional Einstein equations to a
two-dimensional problem which can be solved. All global vacuum solutions are
explicitly constructed and analysed. The classification of the solutions
includes the Schwarzschild, the (anti-)de Sitter, and other well-known
solutions but also many exact ones whose detailed global properties to our
knowledge have not been discussed before. They have a natural physical
interpretation describing single or several wormholes, domain walls of
curvature singularities, cosmic strings, cosmic strings surrounded by domain
walls, solutions with closed timelike curves, etc.Comment: 35 pages, 5 eps figures, minor change
Multiphonon and ``hot''-phonon Isovector Electric-Dipole Excitations

We argue that a substantial increase in the cross section for Coulomb
excitation in the region of the Double Giant Dipole Resonance should be
expected from Coulomb excitation of excited states involved in the spreading of
the one-phonon resonance, in a manifestation of the Brink-Axel phenomenon. This
generates an additional fluctuating amplitude and a corresponding new term to
be added incoherently to the usual cross-section. The appropriate extension of
an applicable reaction calculation is considered in order to estimate this
effect.Comment: 6 pages, Latex, 1 figure available on reques
First-Order Lagrangians and Path-Integral Quantization in the t-J Model

By using the supersymmetric version of the Faddeev-Jackiw symplectic
formalism, a family of first-order constrained Lagrangians for the t-J model is
found. In this approach the Hubbard ${\hat X}$-operators are used as field
variables. In this framework, we first study the spinless fermion model which
satisfies the graded algebra spl(1,1). Later on, in order to satisfy the
Hubbard ${\hat X}$-operators commutation rules satisfiying the graded algebra
spl(2,1), the number and kind of constraints that must be included in a
classical first-order Lagrangian formalism for the t-J model are found. This
model is also analyzed in the context of the path- integral formalism, and so
the correlation generating functional and the effective Lagrangian are
constructed.Comment: latex file, to appear in Ann. Phys. (NY
On the Correspondence Between the Strongly Coupled 2-Flavor Lattice
  Schwinger Model and the Heisenberg Antiferromagnetic Chain

We study the strong coupling limit of the 2-flavor massless Schwinger model
on a lattice using staggered fermions and the Hamiltonian approach to lattice
gauge theories. Using the correspondence between the low-lying states of the
2-flavor strongly coupled lattice Schwinger model and the antiferromagnetic
Heisenberg chain established in a previous paper, we explicitly compute the
mass gaps of the other excitations in terms of vacuum expectation values
(v.e.v.'s) of powers of the Heisenberg Hamiltonian and spin-spin correlation
functions. We find a satisfactory agreement with the results of the continuum
theory already at the second order in the strong coupling expansion. We show
that the pattern of symmetry breaking of the continuum theory is well
reproduced by the lattice theory; we see indeed that in the lattice theory the
isoscalar and isovector chiral condensates are zero to every order in the
strong coupling expansion. In addition, we find that the chiral condensate
$<\bar{\psi}_{L}^{(2)}\bar{\psi}_{L}^{(1)}\psi_{R}^{(1)}\psi_{R}^{(2)}>$ is non
zero also on the lattice; this is the only relic in this lattice model of the
axial anomaly in the continuum theory. We compute the v.e.v.'s of the spin-spin
correlators of the Heisenberg model which are pertinent to the calculation of
the mass spectrum and obtain an explicit construction of the lowest lying
states for finite size Heisenberg Hamiltonian chains.Comment: A misprint in the last equation correcte
Dirac Particles in Twisted Tubes

We consider the dynamics of a relativistic Dirac particle constrained to move
in the interior of a twisted tube by confining boundary conditions, in the
approximation that the curvature of the tube is small and slowly varying. In
contrast with the nonrelativistic theory, which predicts that a particle's spin
does not change as the particle propagates along the tube, we find that the
angular momentum eigenstates of a relativistic spin-1/2 particle may behave
nontrivially. For example, a particle with its angular momentum initially
polarized in the direction of propagation may acquire a nonzero component of
angular momentum in the opposite direction on turning through 2 \pi radians.
Also, the usual nonrelativistic effective potential acquires an additional
factor in the relativistic theory.Comment: 16 pages, 3 EPS figures, REVTeX using BoxedEPS package; email to
  jaffe@mit.ed
Triaxial Ellipsoidal Quantum Billiards

The classical mechanics, exact quantum mechanics and semiclassical quantum
mechanics of the billiard in the triaxial ellipsoid is investigated. The system
is separable in ellipsoidal coordinates. A smooth description of the motion is
given in terms of a geodesic flow on a solid torus, which is a fourfold cover
of the interior of the ellipsoid. Two crossing separatrices lead to four
generic types of motion. The action variables of the system are integrals of a
single Abelian differential of second kind on a hyperelliptic curve of genus 2.
The classical separability carries over to quantum mechanics giving two
versions of generalized Lam{\'e} equations according to the two sets of
classical coordinates. The quantum eigenvalues define a lattice when
transformed to classical action space. Away from the separatrix surfaces the
lattice is given by EBK quantization rules for the four types of classical
motion. The transition between the four lattices is described by a uniform
semiclassical quantization scheme based on a WKB ansatz. The tunneling between
tori is given by penetration integrals which again are integrals of the same
Abelian differential that gives the classical action variables. It turns out
that the quantum mechanics of ellipsoidal billiards is semiclassically most
elegantly explained by the investigation of its hyperelliptic curve and the
real and purely imaginary periods of a single Abelian differential.Comment: 37 pages, 17 figures, Latex2e, submitted to Annals of Physic
Superconformal Ward Identities for Green Functions with Multiple
  Supercurrent Insertions

Superconformal Ward identities for N=1 supersymmetric quantum field theories
in four dimensions are convenienty obtained in the superfield formalism by
combining diffeomorphisms and Weyl transformations on curved superspace. Using
this approach we study the superconformal transformation properties of Green
functions with one or more insertions of the supercurrent to all orders in
perturbation theory. For the case of two insertions we pay particular attention
to fixing the additional counterterms present, as well as to the purely
geometrical anomalies which contribute to the transformation behaviour.
Moreover we show in a scheme-independent way how the quasi-local terms in the
Ward identities are related to similar terms which contribute to the
supercurrent two and three point functions.
  Furthermore we relate our superfield approach to similar studies which use
the component formalism by discussing the implications of our approach for the
components of the supercurrent and of the supergravity prepotentials.Comment: 35 pages, AMSLaTeX Problems with older LaTeX versions fixed, no
  change of conten
The Weyl representation on the torus

We construct reflection and translation operators on the Hilbert space
corresponding to the torus by projecting them from the plane. These operators
are shown to have the same group properties as their analogue on the plane. The
decomposition of operators in the basis of reflections corresponds to the Weyl
or center representation, conjugate to the chord representation which is based
on quantized translations. Thus, the symbol of any operator on the torus is
derived as the projection of the symbol on the plane. The group properties
allow us to derive the product law for an arbitrary number of operators in a
simple form. The analogy between the center and the chord representations on
the torus to those on the plane is then exploited to treat Hamiltonian systems
defined on the torus and to formulate a path integral representation of the
evolution operator. We derive its semiclassical approximation.Comment: 26 pages, latex, 4 figures Submitted to Annals of Physic
Isotropic cosmological singularities 1: Polytropic perfect fluid
  spacetimes

We consider the conformal Einstein equations for polytropic perfect fluid
cosmologies which admit an isotropic singularity. For the polytropic index
gamma strictly greater than 1 and less than or equal to 2 it is shown that the
Cauchy problem for these equations is well-posed, that is to say that solutions
exist, are unique and depend smoothly on the data, with data consisting of
simply the 3-metric of the singularity. The analogous result for gamma=1 (dust)
is obtained when Bianchi type symmetry is assumed.Comment: LaTeX, 43 pages, no figures, submitted to Ann. Phy
Anomalies, Unitarity and Quantum Irreversibility

The trace anomaly in external gravity is the sum of three terms at
criticality: the square of the Weyl tensor, the Euler density and Box R, with
coefficients, properly normalized, called c, a and a', the latter being
ambiguously defined by an additive constant. Considerations about unitarity and
positivity properties of the induced actions allow us to show that the total RG
flows of a and a' are equal and therefore the a'-ambiguity can be consistently
removed through the identification a'=a. The picture that emerges clarifies
several long-standing issues. The interplay between unitarity and
renormalization implies that the flux of the renormalization group is
irreversible. A monotonically decreasing a-function interpolating between the
appropriate values is naturally provided by a'. The total a-flow is expressed
non-perturbatively as the invariant (i.e. scheme-independent) area of the graph
of the beta function between the fixed points. We test this prediction to the
fourth loop order in perturbation theory, in QCD with Nf ~< 11/2 Nc and in
supersymmetric QCD. There is agreement also in the absence of an interacting
fixed point (QED and phi^4-theory). Arguments for the positivity of a are also
discussed.Comment: 30 pages, 1 figure; some references adde
The saddle-point method for condensed Bose gases

The application of the conventional saddle-point approximation to condensed
Bose gases is thwarted by the approach of the saddle-point to the ground-state
singularity of the grand canonical partition function. We develop and test a
variant of the saddle-point method which takes proper care of this
complication, and provides accurate, flexible, and computationally efficient
access to both canonical and microcanonical statistics. Remarkably, the error
committed when naively employing the conventional approximation in the
condensate regime turns out to be universal, that is, independent of the
system's single-particle spectrum. The new scheme is able to cover all
temperatures, including the critical temperature interval that marks the onset
of Bose--Einstein condensation, and reveals in analytical detail how this onset
leads to sharp features in gases with a fixed number of particles. In
particular, within the canonical ensemble the crossover from the
high-temperature asymptotics to the condensate regime occurs in an
error-function-like manner; this error function reduces to a step function when
the particle number becomes large. Our saddle-point formulas for occupation
numbers and their fluctuations, verified by numerical calculations, clearly
bring out the special role played by the ground state.Comment: 32 pages, 11 figures. Ann. Phys. (N.Y.), in pres
Duality in Quantum Liouville Theory

The quantisation of the two-dimensional Liouville field theory is
investigated using the path integral, on the sphere, in the large radius limit.
The general form of the $N$-point functions of vertex operators is found and
the three-point function is derived explicitly. In previous work it was
inferred that the three-point function should possess a two-dimensional lattice
of poles in the parameter space (as opposed to a one-dimensional lattice one
would expect from the standard Liouville potential). Here we argue that the
two-dimensionality of the lattice has its origin in the duality of the quantum
mechanical Liouville states and we incorporate this duality into the path
integral by using a two-exponential potential. Contrary to what one might
expect, this does not violate conformal invariance; and has the great advantage
of producing the two-dimensional lattice in a natural way.Comment: Plain TeX File; 36 page
Self-Similar Perturbation Theory

A method is suggested for treating those complicated physical problems for
which exact solutions are not known but a few approximation terms of a
calculational algorithm can be derived. The method permits one to answer the
following rather delicate questions: What can be said about the convergence of
the calculational procedure when only a few its terms are available and how to
decide which of the initial approximations of the perturbative algorithm is
better, when several such initial approximations are possible? Definite answers
to these important questions become possible by employing the self-similar
perturbation theory. The novelty of this paper is in developing the stability
analysis based on the method of multipliers and in illustrating the efficiency
of this analysis by different quantum-mechanical problems.Comment: 1 file, 45 pages, LaTe