pinecone/core-2020-05-10-deduplication huggingface dataset:
The Poincare'-Lyapounov-Nekhoroshev theorem

We give a detailed and mainly geometric proof of a theorem by N.N.
Nekhoroshev for hamiltonian systems in $n$ degrees of freedom with $k$
constants of motion in involution, where $1 \le k \le n$. This states
persistence of $k$-dimensional invariant tori, and local existence of partial
action-angle coordinates, under suitable nondegeneracy conditions. Thus it
admits as special cases the Poincar\'e-Lyapounov theorem (corresponding to
$k=1$) and the Liouville-Arnold one (corresponding to $k = n$), and
interpolates between them. The crucial tool for the proof is a generalization
of the Poincar\'e map, also introduced by Nekhoroshev.Comment: 21 pages, no figure
Superfield Noether Procedure

We develop a superspace Noether procedure for supersymmetric field theories
in 4-dimensions for which an off-shell formulation in ordinary superspace
exists. In this way we obtain an elegant and compact derivation of the various
supercurrents in these theories. We then apply this formalism to compute the
central charges for a variety of effective actions. As a by-product we also
obtain a simple derivation of the anomalous superconformal Ward-identity in N=2
Yang-Mills theory. The connection with linearized supergravity is also
discussed.Comment: 47 pages, Latex, improved pedagogical presentation and references
  adde
Semiclassical theory of quasiparticles in the superconducting state

We have developed a semiclassical approach to solving the Bogoliubov - de
Gennes equations for superconductors. It is based on the study of classical
orbits governed by an effective Hamiltonian corresponding to the quasiparticles
in the superconducting state and includes an account of the Bohr-Sommerfeld
quantisation rule, the Maslov index, torus quantisation, topological phases
arising from lines of phase singularities (vortices), and semiclassical wave
functions for multi-dimensional systems. The method is illustrated by studying
the problem of an SNS junction and a single vortex.Comment: 74 pages, 19 figures, 3 tables. Submitted to Academic Press for
  possible publicatio
Electric multipole plasmons in deformed sodium clusters

The random-phase-approximation (RPA) method with separable residual forces
(SRPA) is proposed for the description of multipole electric oscillations of
valence electrons in deformed alkali metal clusters. Both the deformed mean
field and residual interaction are derived self-consistently from the Kohn-Sham
functional. SRPA drastically simplifies the computational effort which is
urgent if not decisive for deformed systems. The method is applied to the
description of dipole, quadrupole and octupole plasmons in deformed sodium
clusters of a moderate size. We demonstrate that, in clusters with the size
N>50, Landau damping successfully competes with deformation splitting and even
becomes decisive in forming the width and gross structure of the dipole
plasmon. Besides, the plasmon is generated by excitations from both ground
state and shape isomers. In such clusters familiar experimental estimates for
deformation splitting of dipole plasmon are useless.Comment: 27 pages, 10 figure
Thermodynamics of small Fermi systems: quantum statistical fluctuations

We investigate the probability distribution of the quantum fluctuations of
thermodynamic functions of finite, ballistic, phase-coherent Fermi gases.
Depending on the chaotic or integrable nature of the underlying classical
dynamics, on the thermodynamic function considered, and on temperature, we find
that the probability distributions are dominated either (i) by the local
fluctuations of the single-particle spectrum on the scale of the mean level
spacing, or (ii) by the long-range modulations of that spectrum produced by the
short periodic orbits. In case (i) the probability distributions are computed
using the appropriate local universality class, uncorrelated levels for
integrable systems and random matrix theory for chaotic ones. In case (ii) all
the moments of the distributions can be explicitly computed in terms of
periodic orbit theory, and are system-dependent, non-universal, functions. The
dependence on temperature and number of particles of the fluctuations is
explicitly computed in all cases, and the different relevant energy scales are
displayed.Comment: 24 pages, 7 figures, 5 table
The Cangemi-Jackiw manifold in high dimensions and symplectic structure

The notion of Poincare gauge manifold ($G$), proposed in the context of an
(1+1) gravitational theory by Cangemi and Jackiw (D. Cangemi and R. Jackiw,
Ann. Phys. (N.Y.) 225 (1993) 229), is explored from a geometrical point of
view. First $G$ is defined for arbitrary dimensions, and in the sequence a
symplectic structure is attached to $T*G$. Treating the case of five
dimensions, a (4,1)-de Sitter space, aplications are presented studing
representations of the Poincare group in association with kinetic theory and
the Weyl operators in phase space. The central extension in the
Aghassi-Roman-Santilli group (J. J. Aghassi, P. Roman and R. M. Santilli, Phys.
Rev. D 1(1970) 2573) is derived as a subgroup of linear transformations in $G$
with six dimensions.Comment: 19 page
Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random
  Matrices for Bosons

We consider $m$ spinless Bosons distributed over $l$ degenerate
single-particle states and interacting through a $k$-body random interaction
with Gaussian probability distribution (the Bosonic embedded $k$-body
ensembles). We address the cases of orthogonal and unitary symmetry in the
limit of infinite matrix dimension, attained either as $l \to \infty$ or as $m
\to \infty$. We derive an eigenvalue expansion for the second moment of the
many-body matrix elements of these ensembles. Using properties of this
expansion, the supersymmetry technique, and the binary correlation method, we
show that in the limit $l \to \infty$ the ensembles have nearly the same
spectral properties as the corresponding Fermionic embedded ensembles. Novel
features specific for Bosons arise in the dense limit defined as $m \to \infty$
with both $k$ and $l$ fixed. Here we show that the ensemble is not ergodic, and
that the spectral fluctuations are not of Wigner-Dyson type. We present
numerical results for the dense limit using both ensemble unfolding and
spectral unfolding. These differ strongly, demonstrating the lack of ergodicity
of the ensemble. Spectral unfolding shows a strong tendency towards
picket-fence type spectra. Certain eigenfunctions of individual realizations of
the ensemble display Fock-space localization.Comment: Minor corrections; figure 5 slightly modified (30 pages, 6 figs
Fermionic quantum computation

We define a model of quantum computation with local fermionic modes (LFMs) --
sites which can be either empty or occupied by a fermion. With the standard
correspondence between the Foch space of $m$ LFMs and the Hilbert space of $m$
qubits, simulation of one fermionic gate takes $O(m)$ qubit gates and vice
versa. We show that using different encodings, the simulation cost can be
reduced to $O(\log m)$ and a constant, respectively. Nearest-neighbors
fermionic gates on a graph of bounded degree can be simulated at a constant
cost. A universal set of fermionic gates is found. We also study computation
with Majorana fermions which are basically halves of LFMs. Some connection to
qubit quantum codes is made.Comment: 18 pages, Latex; one reference adde
The algebraic cluster model. Three-body clusters

A new method is introduced to study three-body clusters. Triangular
configurations with ${\cal D}_{3h}$ point-group symmetry are analyzed. The
spectrum, transition form factors and $B(E\lambda)$ values of $^{12}$C are
investigated. It is concluded that the low-lying spectrum of $^{12}$C can be
described by three alpha-particles at the vertices of an equilateral triangle,
but not as a rigid structure. Large rotation-vibration interactions, Coriolis
forces and vibration-vibration interactions are needed. Other interpretations,
such as the harmonic oscillator and a soft deformed oscillator with SO(6)
hyperspherical symmetry, appear to be excluded by electron scattering data.Comment: 31 pages, 10 figures, 5 tables. Annals of Physics (N.Y.), in pres
Casimir effect for a perfectly conducting wedge in terms of local zeta
  function

The vacuum energy density of electromagnetic field inside a perfectly
conducting wedge is calculated by making use of the local zeta function
technique. This regularization completely eliminates divergent expressions in
the course of calculations and gives rise to a finite expression for the energy
density in question without any subtractions. Employment of the Hertz
potentials for constructing the general solution to the Maxwell equations
results in a considerable simplification of the calculations. Transition to the
global zeta function is carried out by introducing a cutoff nearby the cusp at
the origin. Proceeding from this the heat kernel coefficients are calculated
and the high temperature asymptotics of the Helmholtz free energy and of the
torque of the Casimir forces are found. The wedge singularity gives rise to a
specific high temperature behaviour $\sim T^2$ of the quantities under
consideration. The obtained results are directly applicable to the free energy
of a scalar massless field and electromagnetic field on the background of a
cosmic string.Comment: 20 pages, REVTeX, no figures, no table
On Hamiltonian formulations of the Schr\"{o}dinger system

We review and compare different variational formulations for the
Schr\"{o}dinger field. Some of them rely on the addition of a conveniently
chosen total time derivative to the hermitic Lagrangian. Alternatively, the
Dirac-Bergmann algorithm yields the Schr\"{o}dinger equation first as a
consistency condition in the full phase space, second as canonical equation in
the reduced phase space. The two methods lead to the same (reduced)
Hamiltonian. As a third possibility, the Faddeev-Jackiw method is shown to be a
shortcut of the Dirac method. By implementing the quantization scheme for
systems with second class constraints, inconsistencies of previous treatments
are eliminated
Magnetic properties of SO(5) superconductivity

The distinction between type I and type II superconductivity is re-examined
in the context of the SO(5) model recently put forth by Zhang. Whereas in
conventional superconductivity only one parameter (the Ginzburg-Landau
parameter $\kappa$) characterizes the model, in the SO(5) model there are two
essential parameters. These can be chosen to be $\kappa$ and another parameter,
$\beta$, related to the doping. There is a more complicated relation between
$\kappa$ and the behavior of a superconductor in a magnetic field. In
particular, one can find type I superconductivity, even when $\kappa$ is large,
for appropriate values of $\beta$.Comment: 17 pages, 7 figure
Condensed vortex ground states of rotating Bose-Einstein condensate in
  harmonic atomic trap

We study a system of $N$ Bose atoms trapped by a symmetric harmonic
potential, interacting via weak central forces. Considering the ground state of
the rotating system as a function of the two conserved quantities, the total
angular momentum and its collective component, we develop an algebraic approach
to derive exact wave functions and energies of these ground states. We describe
a broad class of the interactions for which these results are valid. This
universality class is defined by simple integral condition on the potential.
Most of the potentials of practical interest which have pronounced repulsive
component belong to this universality class.Comment: 34 pages, 10 ps figures, minor revisions, to be publ. in Ann. Phy
Quantum Tunneling and Caustics under Inverse Square Potential

Quantization of a harmonic oscillator with inverse square potential
$V(x)=(m{\omega^2}/2){x^2}+g/{x^2}$ on the line $-\infty<x<\infty$ is
re-examined. It is shown that, for $0<g<3{\hbar^2}/(8m)$, the system admits a
U(2) family of inequivalent quantizations allowing for quantum tunneling
through the potenatial barrier at $x=0$. In the family is a distinguished
quantization which reduces smoothly to the harmonic oscillator as $g\to 0$, in
contrast to the conventional quantization applied to the Calogero model which
prohibits the tunneling and has no such limit. The tunneling renders the
classical caustics anomalous at the quantum level, leading to the possibility
of copying an arbitrary state from one side $x>0$, say, to the other $x<0$.Comment: 13 pages, 1 figure, written by PlainTeX, Ver.4.0. Title changed,
  typos corrected, a new reference and a comment on quantum cloning adde
Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in
relation to entanglement in composite quantum systems consisting of well
separated subsystems. Our studies are motivated by recent experiments and
theoretical investigations on quantum dots and neutral atoms in microtraps as
tools for quantum information processing. We present analogies between
distinguishable particles, bosons and fermions in low-dimensional Hilbert
spaces. We introduce the notion of Slater rank for pure states of pairs of
fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable
particles. This concept is generalized to mixed states and provides a
correlation measure for indistinguishable particles. Then we generalize these
notions to pure fermionic and bosonic states in higher-dimensional Hilbert
spaces and also to the multi-particle case. We review the results on quantum
correlations in mixed fermionic states and discuss the concept of fermionic
Slater witnesses. Then the theory of quantum correlations in mixed bosonic
states and of bosonic Slater witnesses is formulated. In both cases we provide
methods of constructing optimal Slater witnesses that detect the degree of
quantum correlations in mixed fermionic and bosonic states.Comment: 46 pages, 4 eps figure
The non-commutative Landau problem

The Landau problem is discussed in two similar but still different
non-commutative frameworks. The ``standard'' one, where the coupling to the
gauge field is achieved using Poisson brackets, yields all Landau levels. The
``exotic'' approach, where the coupling to the gauge field is achieved using
the symplectic structure, only yields lowest-Landau level states, as advocated
by Peierls and used in the description of the ground states of the Fractional
Quantum Hall Effect. The same reduced model also describes vortex dynamics in a
superfluid ${}^4$He film. Remarkably, the spectrum depends crucially on the
quantization scheme. The system is symmetric w. r. t. area-preserving
diffeomorphisms.Comment: Published with shortened title as Ann. Phys. (N. Y.) 299, pp. 128-140
  (2002) 14 pages, LaTex, no figure
Nonequilibrium relaxation of Bose-Einstein condensates: Real-time
  equations of motion and Ward identities

We present a field-theoretical method to obtain consistently the equations of
motion for small amplitude condensate perturbations in a homogeneous
Bose-condensed gas directly in real time. It is based on linear response, and
combines the Schwinger-Keldysh formulation of nonequilibrium quantum field
theory with the Nambu-Gorkov formalism of quasiparticle excitations in the
condensed phase and the tadpole method in quantum field theory. This method
leads to causal equations of motion that allow to study the nonequilibrium
evolution as an initial value problem. It also allows to extract directly the
Ward identities, which are a consequence of the underlying gauge symmetry and
which in equilibrium lead to the Hugenholtz-Pines theorem. An explicit one-loop
calculation of the equations of motion beyond the Hartree-Fock- Bogoliubov
approximation reveals that the nonlocal, absorptive contributions to the
self-energies corresponding to the Beliaev and Landau damping processes are
necessary to fulfill the Ward identities \emph{in} or \emph{out} of
equilibrium. It is argued that a consistent implementation at low temperatures
must be based on the loop expansion, which is shown to fulfill the Ward
identities order by order in perturbation theory.Comment: Latex (elsart.cls), 41 pages, 4 eps figs, to appear in Ann. Phy
Quantum mechanical analysis of the equilateral triangle billiard:
  periodic orbit theory and wave packet revivals

Using the fact that the energy eigenstates of the equilateral triangle
infinite well (or billiard) are available in closed form, we examine the
connections between the energy eigenvalue spectrum and the classical closed
paths in this geometry, using both periodic orbit theory and the short-term
semi-classical behavior of wave packets. We also discuss wave packet revivals
and show that there are exact revivals, for all wave packets, at times given by
$T_{rev} = 9 \mu a^2/4\hbar \pi$ where $a$ and $\mu$ are the length of one side
and the mass of the point particle respectively. We find additional cases of
exact revivals with shorter revival times for zero-momentum wave packets
initially located at special symmetry points inside the billiard. Finally, we
discuss simple variations on the equilateral
($60^{\circ}-60^{\circ}-60^{\circ}$) triangle, such as the half equilateral
($30^{\circ}-60^{\circ}-90^{\circ}$) triangle and other `foldings', which have
related energy spectra and revival structures.Comment: 34 pages, 9 embedded .eps figure
Electrostatic analogy for integrable pairing force Hamiltonians

For the exactly solved reduced BCS model an electrostatic analogy exists; in
particular it served to obtain the exact thermodynamic limit of the model from
the Richardson Bethe ansatz equations. We present an electrostatic analogy for
a wider class of integrable Hamiltonians with pairing force interactions. We
apply it to obtain the exact thermodynamic limit of this class of models. To
verify the analytical results, we compare them with numerical solutions of the
Bethe ansatz equations for finite systems at half-filling for the ground state.Comment: 14 pages, 6 figures, revtex4. Minor change
The Feynman-Schwinger representation in QCD

The proper time path integral representation is derived explicitly for
Green's functions in QCD. After an introductory analysis of perturbative
properties, the total gluonic field is separated in a rigorous way into a
nonperturbative background and valence gluon part. For nonperturbative
contributions the background perturbation theory is used systematically,
yielding two types of expansions,illustrated by direct physical applications.
As an application, we discuss the collinear singularities in the
Feynman-Schwinger representation formalism. Moreover, the generalization to
nonzero temperature is made and expressions for partition functions in
perturbation theory and nonperturbative background are explicitly written down.Comment: Latex, 61 pages and 7 figure
Effective field theory description of the higher dimensional quantum
  Hall liquid

We derive an effective topological field theory model of the four dimensional
quantum Hall liquid state recently constructed by Zhang and Hu. Using a
generalization of the flux attachment transformation, the effective field
theory can be formulated as a U(1) Chern-Simons theory over the total
configuration space $CP_3$, or as a SU(2) Chern-Simons theory over $S^4$. The
new quantum Hall liquid supports various types of topological excitations,
including the 0-brane (particles), the 2-brane (membranes) and the 4-brane.
There is a topological phase interaction among the membranes which generalizes
the concept of fractional statistics
Probing Physics at Extreme Energies with Cosmic Ultra-High Energy
  Radiation

The highest energy cosmic rays observed possess macroscopic energies and
their origin is likely to be associated with the most energetic processes in
the Universe. Their existence triggered a flurry of theoretical explanations
ranging from conventional shock acceleration to particle physics beyond the
Standard Model and processes taking place at the earliest moments of our
Universe. Furthermore, many new experimental activities promise a strong
increase of statistics at the highest energies and a combination with gamma-ray
and neutrino astrophysics will put strong constraints on these theoretical
models. We give an overview over this quickly evolving research field with
focus on testing new particle physics.Comment: 12 latex pages, 2 postscript figures included; based on invited talk
  at the WHEPP-7 Conference, Allahabad, India (January, 2002
Symmetry Breaking for Bosonic Systems on Orbifolds

We discuss a general class of boundary conditions for bosons living in an extra spatial dimension compactified on S^1/Z_2. Discontinuities for both fields and their first derivatives are allowed at the orbifold fixed points. We analyze examples with free scalar fields and interacting gauge vector bosons, deriving the mass spectrum, that depends on a combination of the twist and the jumps. We discuss how the same physical system can be characterized by different boundary conditions, related by local field redefinitions that turn a twist into a jump or vice-versa. When the description is in term of discontinuous fields, appropriate lagrangian terms should be localized at the orbifold fixed points
Two types of electronic states in one dimensional crystals of finite
  length

Exact and general results on the electronic states in one dimensional
crystals bounded at tau and tau+L - where L=Na, N is a positive integer and a
is the potential period - are presented. Corresponding to each energy band of
Bloch wave, there are N-1 states in the finite crystal and their energies are
dependent on the crystal length L but not on the crystal boundary tau and map
the energy band exactly; There is always one and only one electronic state
correponding to each band gap of the Bloch wave, whose energy is dependent on
the crystal boundary tau but not on the crystal length L. This state is either
a constant energy confined state at a band edge or a surface state in the gap.
A slight change of the boundary tau could change the property and energy of
this state dramaticaly.Comment: 17 pages, 3 figure
Two-Photon Processes and Photon Structure

In this article aspects of photon-photon physics related to the structure of
real and virtual photons are reviewed. A re-calculation of the virtual
photon-photon box is performed and some discrepancies in the literature are
clarified. A useful compilation of various relevant limits derived from the
most general expressions is provided. Furthermore, structure functions of
spin-averaged, transverse and longitudinal virtual target photons are defined
and discussed. Finally, the factorization of two-photon processes in the
Bjorken limit is demonstrated to hold also for the case of virtual target
photons.Comment: LaTeX, 38 page
On Correspondence of BRST-BFV, Dirac and Refined Algebraic Quantizations
  of Constrained Systems

Correspondence between BRST-BFV, Dirac and refined algebraic (group
averaging, projection operator) approaches to quantize constrained systems is
analyzed. For the closed-algebra case, it is shown that the component of the
BFV wave function with maximal (minimal) number of ghosts and antighosts in the
Schrodinger representation may be viewed as a wave function in the refined
algebraic (Dirac) quantization approach. The Giulini-Marolf group averaging
formula for the inner product in the refined algebraic quantization approach is
obtained from the Batalin-Marnelius prescription for the BRST-BFV inner product
which should be generally modified due to topological problems. The considered
prescription for the correspondence of states is observed to be applicable to
the open-algebra case. Refined algebraic quantization approach is generalized
then to the case of nontrivial structure functions. A simple example is
discussed. Correspondence of observables in different quantization methods is
also investigated.Comment: RevTeX, 17 pages, detailed version of hep-th/0106250 and
  hep-th/010706