pinecone/core-2020-05-10-deduplication huggingface dataset:
Adiabatic Berry Phase and Hannay Angle for Open Paths

We obtain the adiabatic Berry phase by defining a generalised gauge potential
whose line integral gives the phase holonomy for arbitrary evolutions of
parameters. Keeping in mind that for classical integrable systems it is hardly
clear how to obtain open-path Hannay angle, we establish a connection between
the open-path Berry phase and Hannay angle by using the parametrised coherent
state approach. Using the semiclassical wavefunction we analyse the open-path
Berry phase and obtain the open-path Hannay angle. Further, by expressing the
adiabatic Berry phase in terms of the commutator of instantaneous projectors
with its differential and using Wigner representation of operators we obtain
the Poisson bracket between distribution function and its differential. This
enables us to talk about the classical limit of the phase holonomy which yields
the angle holonomy for open-paths. An operational definition of Hannay angle is
provided based on the idea of classical limit of quantum mechanical inner
product. A probable application of the open-path Berry phase and Hannay angle
to wave-packet revival phenomena is also pointed out.Comment: Latex, no figures, 24 pages, submitted to Ann. Phy
Condensate Fluctuations in Trapped Bose Gases: Canonical vs.
  Microcanonical Ensemble

We study the fluctuation of the number of particles in ideal Bose-Einstein
condensates, both within the canonical and the microcanonical ensemble.
Employing the Mellin-Barnes transformation, we derive simple expressions that
link the canonical number of condensate particles, its fluctuation, and the
difference between canonical and microcanonical fluctuations to the poles of a
Zeta function that is determined by the excited single-particle levels of the
trapping potential. For the particular examples of one- and three-dimensional
harmonic traps we explore the microcanonical statistics in detail, with the
help of the saddle-point method. Emphasizing the close connection between the
partition theory of integer numbers and the statistical mechanics of ideal
Bosons in one-dimensional harmonic traps, and utilizing thermodynamical
arguments, we also derive an accurate formula for the fluctuation of the number
of summands that occur when a large integer is partitioned.Comment: RevTeX; 32 pages + 1 ps-figur
Between Poisson and GUE statistics: Role of the Breit-Wigner width

We consider the spectral statistics of the superposition of a random diagonal
matrix and a GUE matrix. By means of two alternative superanalytic approaches,
the coset method and the graded eigenvalue method, we derive the two-level
correlation function $X_2(r)$ and the number variance $\Sigma^2(r)$. The graded
eigenvalue approach leads to an expression for $X_2(r)$ which is valid for all
values of the parameter $\lambda$ governing the strength of the GUE admixture
on the unfolded scale. A new twofold integration representation is found which
can be easily evaluated numerically. For $\lambda \gg 1$ the Breit-Wigner width
$\Gamma_1$ measured in units of the mean level spacing $D$ is much larger than
unity. In this limit, closed analytical expression for $X_2(r)$ and
$\Sigma^2(r)$ can be derived by (i) evaluating the double integral
perturbatively or (ii) an ab initio perturbative calculation employing the
coset method. The instructive comparison between both approaches reveals that
random fluctuations of $\Gamma_1$ manifest themselves in modifications of the
spectral statistics. The energy scale which determines the deviation of the
statistical properties from GUE behavior is given by $\sqrt{\Gamma_1}$. This is
rigorously shown and discussed in great detail. The Breit-Wigner $\Gamma_1$
width itself governs the approach to the Poisson limit for $r\to\infty$. Our
analytical findings are confirmed by numerical simulations of an ensemble of
$500\times 500$ matrices, which demonstrate the universal validity of our
results after proper unfolding.Comment: 25 pages, revtex, 5 figures, Postscript file also available at
  http://germania.ups-tlse.fr/frah
Is "the theory of everything'' merely the ultimate ensemble theory?

We discuss some physical consequences of what might be called ``the ultimate
ensemble theory'', where not only worlds corresponding to say different sets of
initial data or different physical constants are considered equally real, but
also worlds ruled by altogether different equations. The only postulate in this
theory is that all structures that exist mathematically exist also physically,
by which we mean that in those complex enough to contain self-aware
substructures (SASs), these SASs will subjectively perceive themselves as
existing in a physically ``real'' world. We find that it is far from clear that
this simple theory, which has no free parameters whatsoever, is observationally
ruled out. The predictions of the theory take the form of probability
distributions for the outcome of experiments, which makes it testable. In
addition, it may be possible to rule it out by comparing its a priori
predictions for the observable attributes of nature (the particle masses, the
dimensionality of spacetime, etc) with what is observed.Comment: 29 pages, revised to match version published in Annals of Physics.
  The New Scientist article and color figures are available at
  http://www.sns.ias.edu/~max/toe_frames.html or from max@ias.ed
Conditionally exactly solvable potentials: A supersymmetric construction
  method

We present in this paper a rather general method for the construction of
so-called conditionally exactly solvable potentials. This method is based on
algebraic tools known from supersymmetric quantum mechanics. Various families
of one-dimensional potentials are constructed whose corresponding Schr\"odinger
eigenvalue problem can be solved exactly under certain conditions of the
potential parameters. Examples of quantum systems on the real line, the half
line as well as on some finite interval are studied in detail.Comment: 24 pages, 11 figures, LaTeX209, amsfont
Algebraic nonlinear collective motion

Finite-dimensional Lie algebras of vector fields determine geometrical
collective models in quantum and classical physics. Every set of vector fields
on Euclidean space that generates the Lie algebra sl(3, R) and contains the
angular momentum algebra so(3) is determined. The subset of divergence-free
sl(3, R) vector fields is proven to be indexed by a real number $\Lambda$. The
$\Lambda=0$ solution is the linear representation that corresponds to the
Riemann ellipsoidal model. The nonlinear group action on Euclidean space
transforms a certain family of deformed droplets among themselves. For positive
$\Lambda$, the droplets have a neck that becomes more pronounced as $\Lambda$
increases; for negative $\Lambda$, the droplets contain a spherical bubble of
radius $|\Lambda|^{{1/3}}$. The nonlinear vector field algebra is extended to
the nonlinear general collective motion algebra gcm(3) which includes the
inertia tensor. The quantum algebraic models of nonlinear nuclear collective
motion are given by irreducible unitary representations of the nonlinear gcm(3)
Lie algebra. These representations model fissioning isotopes ($\Lambda>0$) and
bubble and two-fluid nuclei ($\Lambda<0$).Comment: 32pages, 4 figures not include
Scattering on Dislocations and Cosmic Strings in the Geometric Theory of
  Defects

We consider scattering of elastic waves on parallel wedge dislocations in the
geometric theory of defects or, equivalently, scattering of point particles and
light rays on cosmic strings. Dislocations are described as torsion
singularities located on parallel lines, and trajectories of phonons are
assumed to be the corresponding extremals. Extremals are found for arbitrary
distribution of the dislocations in the monopole, dipole, and quadrupole
approximation and the scattering angle is obtained. Examples of continuous
distribution of wedge and edge dislocations are considered. We have found that
for deficit angles close to -2\pi a star located behind a cosmic string may
have any even number of images, 2,4,6,... The close relationship between
dislocations and conformal maps is elucidated in detail.Comment: 30 pages, 14 figures, minor change
Particle creation in the effective action method

The effect of particle creation by nonstationary external fields is
considered as a radiation effect in the expectation-value spacetime. The energy
of created massless particles is calculated as the vacuum contribution in the
energy-momentum tensor of the expectation value of the metric. The calculation
is carried out for an arbitrary quantum field coupled to all external fields
entering the general second-order equation. The result is obtained as a
functional of the external fields. The paper gives a systematic derivation of
this result on the basis of the nonlocal effective action. Although the
derivation is quite involved and touches on many aspects of the theory, the
result itself is remarkably simple. It brings the quantum problem of particle
creation to the level of complexity of the classical radiation problem. For
external fields like the electromagnetic or gravitational field there appears a
quantity, the radiation moment, that governs both the classical radiation of
waves and the quantum particle production. The vacuum radiation of an
electrically charged source is considered as an example. The research is aimed
at the problem of backreaction of the vacuum radiation.Comment: 129 pages including 7 figures. Latex 2.09. Figures by METAFONT, 300
  DPI. Execute the file "arttotal.tex
Non-Abelian Holonomy of BCS and SDW Quasi-particles

In this work we investigate properties of fermions in the SO(5) theory of
high Tc superconductivity. We show that the adiabatic time evolution of a SO(5)
superspin vector leads to a non-Abelian SU(2) holonomy of the SO(5) spinor
states. Physically, this non-trivial holonomy arises from the non-zero overlap
between the SDW and BCS quasi-particle states. While the usual Berry's phase of
a SO(3) spinor is described by a Dirac magnetic monopole at the degeneracy
point, the non-Abelian holonomy of a SO(5) spinor is described by a Yang
monopole at the degeneracy point, and is deeply related to the existence of the
second Hopf map from $S^7$ to $S^4$. We conclude this work by extending the
bosonic SO(5) nonlinear sigma model to include the fermionic states around the
gap nodes as 4 component Dirac fermions coupled to SU(2) gauge fields in 2+1
dimensions.Comment: 45 pages, 5 figures, typos corrected, references adde
Modular invariance, lattice field theories and finite size corrections

We give a lattice theory treatment of certain one and two dimensional quantum
field theories. In one dimension we construct a combinatorial version of a
non-trivial field theory on the circle which is of some independent interest in
itself while in two dimensions we consider a field theory on a toroidal
triangular lattice. We take a continuous spin Gaussian model on a toroidal
triangular lattice with periods $L_0$ and $L_1$ where the spins carry a
representation of the fundamental group of the torus labeled by phases $u_0$
and $u_1$. We compute the {\it exact finite size and lattice corrections}, to
the partition function $Z$, for arbitrary mass $m$ and phases $u_i$. Summing
$Z^{-1/2}$ over a specified set of phases gives the corresponding result for
the Ising model on a torus. An interesting property of the model is that the
limits $m\rightarrow0$ and $u_i\rightarrow0$ do not commute. Also when $m=0$
the model exhibits a {\it vortex critical phase} when at least one of the $u_i$
is non-zero. In the continuum or scaling limit, for arbitrary $m$, the finite
size corrections to $-\ln Z$ are {\it modular invariant} and for the critical
phase are given by elliptic theta functions. In the cylinder limit
$L_1\rightarrow\infty$ the ``cylinder charge'' $c(u_0,m^2L_0^2)$ is a
non-monotonic function of $m$ that ranges from $2(1+6u_0(u_0-1))$ for $m=0$ to
zero for $m\rightarrow\infty$ but from which one can determine the central
charge $c$. The study of the continuum limit of these field theories provides a
kind of quantum theoretic analog of the link between certain combinatorial and
analytic topological quantities.Comment: 25 pages Plain Te
On Accelerated Inertial Frames in Gravity and Electromagnetism

When a charged insulating spherical shell is uniformly accelerated, an
oppositely directed electric field is produced inside. Outside the field is the
Born field of a uniformly accelerated charge, modified by a dipole. Radiation
is produced. When the acceleration is annulled by the nearly uniform gravity
field of an external shell with a 1 + beta cos theta surface distribution of
mass, the differently viewed Born field is static and joins a static field
outside the external shell; no radiation is produced. We discuss gravitational
analogues of these phenomena. When a massive spherical shell is accelerated, an
untouched test mass inside experiences a uniform gravity field and accelerates
parallelly to the surrounding shell. In the strong gravity regime we illustrate
these effects using exact conformastatic solutions of the Einstein-Maxwell
equations with charged dust. We consider a massive charged shell on which the
forces due to nearly uniform electrical and gravitational fields balance. Both
fields are reduced inside by the ratio of the g_00 inside the shell to that
away from it. The acceleration of a free test particle, relative to a static
observer, is reduced correspondingly. We give physical explanations of these
effects.Comment: 25 pages, LaTeX with 6 encapsulated postscript figures included. To
  appear in Annals of Physic
Loop Corrections and Bosonization Formulae

We study the functional integrals that appear in a path integral bosonization
procedure for more than two spacetime dimensions. Since they are not in general
exactly solvable, their evaluation by a suitable loop expansion would be a
natural procedure, even if the exact fermionic determinant were known. The
outcome of our study is that we can consistently ignore loop corrections in the
functional integral defining the bosonized action, if the same is done for the
functional integral corresponding to the bosonic representation of the
generating functional. If contributions up to some order $l$ in the number of
loops are included in both integrals, all but the lowest terms cancel out in
the final result for the generating functional.Comment: 16 pages, Latex, no figure
Eigenstates of the Atom-Field Interaction and the Binding of Light in
  Photonic Crystals

We solve for the exact atom-field eigenstates of a single atom in a three
dimensional spherical cavity, by mapping the problem onto the anisotropic Kondo
model. The spectrum has a rich bound state structure in comparison with models
where the rotating wave approximation is made. It is shown how to obtain the
Jaynes-Cummings model states in the limit of weak coupling. Non-perturbative
Lamb shifts and decay rates are computed. The massive Kondo model is introduced
to model light localization in the form of photon-atom bound states in photonic
crystals.Comment: 22 pages, one figur
A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities

It is shown that tunnelling splittings in ergodic double wells and resonant
widths in ergodic metastable wells can be approximated as easily-calculated
matrix elements involving the wavefunction in the neighbourhood of a certain
real orbit. This orbit is a continuation of the complex orbit which crosses the
barrier with minimum imaginary action. The matrix element is computed by
integrating across the orbit in a surface of section representation, and uses
only the wavefunction in the allowed region and the stability properties of the
orbit. When the real orbit is periodic, the matrix element is a natural measure
of the degree of scarring of the wavefunction. This scarring measure is
canonically invariant and independent of the choice of surface of section,
within semiclassical error. The result can alternatively be interpretated as
the autocorrelation function of the state with respect to a transfer operator
which quantises a certain complex surface of section mapping. The formula
provides an efficient numerical method to compute tunnelling rates while
avoiding the need for the exceedingly precise diagonalisation endemic to
numerical tunnelling calculations.Comment: Submitted to Annals of Physics. This work has been submitted to
  Academic Press for possible publicatio
Theory of spin excitations in undoped and underdoped cuprates

We consider the magnetic properties of high Tc cuprates from a gauge theory
point of view, with emphasis on the underdoped regime. Underdoped cuprates
possess certain antiferromagnetic correlations, as evidenced, for example, by
different temperature dependence of the Cu and O site NMR relaxation rates,
that are not captured well by slave boson mean field theories of the t-J model.
We show that the inclusion of gauge fluctuations will remedy the deficiencies
of the mean field theories. As a concrete illustration of the gauge-fluctuation
restoration of the antiferromangetic correlation and the feasibility of the 1/N
perturbation theory, the Heisenberg spin chain is analyzed in terms of a 1+1D
U(1) gauge theory with massless Dirac fermions. The 1/N-perturbative treatment
of the same gauge theory in 2+1D (which can be motivated from the mean field
pi-flux phase of the Heisenberg model) leads to a dynamical mass generation
corresponding to an antiferromagnetic ordering. On the other hand, it is argued
that in a similar gauge theory with an additional coupling to a Bose (holon)
field, symmetry breaking does not occur, but antiferromagnetic correlations are
enhanced, which is the situation in the underdoped cuprates.Comment: Typos corrected; minor changes made to match the published version.
  Related (background) materials can be found at
  "http://www.stanford.edu/~donhkim/physics.html
Asymptotic Expansion for the Magnetoconductance Autocorrelation Function

We complement a recent calculation (P.B. Gossiaux and the present authors,
Ann. Phys. (N.Y.) in press) of the autocorrelation function of the conductance
versus magnetic field strength for ballistic electron transport through
microstructures with the shape of a classically chaotic billiard coupled to
ideal leads. The function depends on the total number M of channels and the
parameter t which measures the difference in magnetic field strengths. We
determine the leading terms in an asymptotic expansion for large t at fixed M,
and for large M at fixed t/M. We compare our results and the ones obtained in
the previous paper with the squared Lorentzian suggested by semiclassical
theory.Comment: submitted to Annals of Physics (N.Y.
Quantum Mechanics without Waves: a Generalization of Classical
  Statistical Mechanics

We generalize classical statistical mechanics to describe the kinematics and
the dynamics of systems whose variables are constrained by a single quantum
postulate (discreteness of the spectrum of values of at least one variable of
the theory). This is possible provided we adopt Feynman's suggestion of
dropping the assumption that the probability for an event must always be a
positive number. This approach has the advantage of allowing a reformulation of
quantum theory in phase space without introducing the unphysical concept of
probability amplitudes, together with all the problems concerning their
ambiguous properties.Comment: 25 pages, Late
N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory

The implications of N=1 superconformal symmetry for four dimensional quantum
field theories are studied. Superconformal covariant expressions for two and
three point functions of quasi-primary superfields of arbitrary spin are found
and connected with the operator product expansion. The general formulae are
specialised to cases involving a scalar superfield L, which contains global
symmetry currents, and the supercurrent, which contains the energy momentum
tensor, and the consequences of superconformal Ward identities analysed. The
three point function of L is shown to have unique completely antisymmetric or
symmetric forms. In the latter case the superspace version of the axial anomaly
equation is obtained. The three point function for the supercurrent is shown to
have two linearly independent forms. A linear combination of the associated
coefficients for the general expression is shown to be related to the scale of
the supercurrent two point function through Ward identities. The coefficients
are given for the two free field superconformal theories and are also connected
with the parameters present in the supercurrent anomaly for supergravity
backgrounds. Superconformal invariants, which are possible even in three point
functions, are discussed.Comment: 53 pages, uses harvmac, revised version includes further corrections
  and minor additions, version to be publishe
Aspects of Quasi-Phasestructure of the Schwinger Model on a Cylinder
  with Broken Chiral Symmetry

We consider the N_f-flavour Schwinger Model on a thermal cylinder of
circumference $\beta=1/T$ and of finite spatial length $L$. On the boundaries
$x^1=0$ and $x^1=L$ the fields are subject to an element of a one-dimensional
class of bag-inspired boundary conditions which depend on a real parameter
$\theta$ and break the axial flavour symmetry. For the cases $N_f=1$ and
$N_f=2$ all integrals can be performed analytically. While general theorems do
not allow for a nonzero critical temperature, the model is found to exhibit a
quasi-phase-structure: For finite $L$ the condensate - seen as a function of
$\log(T)$ - stays almost constant up to a certain temperature (which depends on
$L$), where it shows a sharp crossover to a value which is exponentially close
to zero. In the limit $L \to \infty$ the known behaviour for the one-flavour
Schwinger model is reproduced. In case of two flavours direct pictorial
evidence is given that the theory undergoes a phase-transition at $T_c=0$. The
latter is confirmed - as predicted by Smilga and Verbaarschot - to be of second
order but for the critical exponent $\delta$ the numerical value is found to be
2 which is at variance with their bosonization-rule based prediction
$\delta=3$.Comment: Latex, 29 pages, uses epsfig, error in discussion correcte
Non-Standard neutral kaons dynamics from D-brane statistics

The neutral kaon system can be effectively described by non-unitary,
dissipative, completely positive dynamics that extend the usual treatment. In
the framework of open quantum systems, we show how the origin of these
non-standard time evolutions can be traced to the interaction of the kaon
system with a large environment. We find that D-branes, effectively described
by a heat-bath of quanta obeying infinite statistics, could constitute a
realistic example of such an environment.Comment: 14 pages, plain-TeX, no figure